# Dr Peter Rohde

**Senior Lecturer,**A/DRsch Centre for Quantum Software and Information

**Core Member,**Centre for Quantum Software and Information

BE (UQ), PhD (UQ)

**Phone**

+61 2 9514 5991

## Chapters

Rohde, P., Gard, B.T., Motes, K.R., Olson, J.P. & Dowling, J.P. 2015, 'An introduction to boson-sampling' in Malinovskaya, S.A. & Novikova, I. (eds),

*From Atomic to Mesoscale The Role of Quantum Coherence in Systems of Various Complexities*, World Scientific. Simple, discrete quantum systems, along with methods that make use of
resonance and coherence to manipulate and measure such systems, have been
the bread and butter of atomic physics for a century. In experiments on atomic
beams ...

## Conferences

Motes, K.R., Olson, J.P., Rabeaux, E.J., Dowling, J.P., Olson, S.J. & Rohde, P.P. 2015, 'Linear optical quantum metrology with single photons',

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*Proceedings of Frontiers in Optics 2015, FIO 2015*, Frontiers in Optics 2015, OSA Publishing, San Jose, California United States.View/Download from: Publisher's site

© OSA 2015. We show that a passive, linear-optical interferometer (fed with only single-photon inputs and utilizing single-mode photodetection) is capable of beating the shotnoise limit, providing a potential pathway forward to practical quantum metrology.

Schreiber, A., Gábris, A., Rohde, P.P., Laiho, K., Štefaňak, M., Potoček, V., Hamilton, C., Jex, I. & Silberhorn, C. 2014, 'Simulations of two-particle interactions with 2D quantum walks in time',

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*AIP Conference Proceedings*, pp. 204-209.View/Download from: Publisher's site

© 2014 AIP Publishing LLC.We present the experimental implementation of a quantum walk on a two-dimensional lattice and show how to employ the optical system to simulate the quantum propagation of two interacting particles. Our quantum walk in time transfers the spatial spread of a quantum walk into the time domain, which guarantees a high stability and scalability of the setup. We present with our device quantum walks over 12 steps on a 2D lattice. By changing the properties of the driving quantum coin, we investigate different kinds of two-particle interactions and reveal their impact on the occurring quantum propagation.

Schreiber, A., Katzschmann, F., Gabris, A., Rohde, P.P., Laiho, K., Stefanak, M., Potocek, V., Hamilton, C., Jex, I. & Silberhorn, C. 2013, 'Simulations of two particle dynamics employing dynamic coin control in 2D quantum walks',

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*2013 Conference on Lasers and Electro-Optics Europe and International Quantum Electronics Conference, CLEO/Europe-IQEC 2013*.View/Download from: Publisher's site

There has been constantly rising interest in quantum walks in recent years, as they are a well-snited framework to study quantum algorithms, for example [1, 2] or to use them as a simulator for other quantum systems, which are not as readily accessible [3]. A key element for a versatile simulator is the ability to dynamically control the quantum-coin, which is the main entity responsible for the evolution of the quantum walk. © 2013 IEEE.

Schreiber, A., Katzschmann, F., Gábris, A., Rohde, P.P., Laiho, K., Štefaňák, M., Potoček, V., Hamilton, C., Jex, I. & Silberhorn, C. 2013, 'Simulations of two particle dynamics employing dynamic coin control in 2D quantum walks',

*Optics InfoBase Conference Papers*. Schreiber, A., Gábris, A., Rohde, P.P., Laiho, K., Stefanak, M., Potoček, V., Hamilton, C., Jex, I. & Silberhorn, C. 2012, 'Quantum simulations with a two-dimensional quantum walk',

*Optics InfoBase Conference Papers*. We present an experimental implementation of a quantum walk in two dimensions, employing an optical fiber network. We simulated entangling operations and nonlinear multi-particle interactions revealing phenomena such as bound states. © 2011 Optical Society of America.

Schreiber, A., Gábris, A., Rohde, P.P., Laiho, K., Stefanak, M., Potoček, V., Hamilton, C., Jex, I. & Silberhorn, C. 2012, 'Quantum simulations with a two-dimensional quantumwalk',

*CLEO: Science and Innovations, CLEO_SI 2012*. We present an experimental implementation of a quantum walk in two dimensions, employing an optical fiber network. We simulated entangling operations and nonlinear multi-particle interactions revealing phenomena such as bound states. © 2011 Optical Society of America.

Schreiber, A., Gábris, A., Rohde, P.P., Laiho, K., Stefanak, M., Potoček, V., Hamilton, C., Jex, I. & Silberhorn, C. 2012, 'Quantum simulations with a two-dimensional quantumwalk',

*CLEO: Applications and Technology, CLEO_AT 2012*. We present an experimental implementation of a quantum walk in two dimensions, employing an optical fiber network. We simulated entangling operations and nonlinear multi-particle interactions revealing phenomena such as bound states. © 2011 Optical Society of America.

Schreiber, A., Gábris, A., Rohde, P.P., Laiho, K., Stefanak, M., Potoček, V., Hamilton, C., Jex, I. & Silberhorn, C. 2012, 'Quantum simulations with a two-dimensional quantum walk',

*2012 Conference on Lasers and Electro-Optics, CLEO 2012*. We present an experimental implementation of a quantum walk in two dimensions, employing an optical fiber network. We simulated entangling operations and nonlinear multi-particle interactions revealing phenomena such as bound states. © 2012 OSA.

Rohde, P.P., Pryde, G.J., O'Brien, J.L. & Ralph, T.C. 2005, 'Quantum gate characterization in an extended Hilbert space',

*Quantum Electronics and Laser Science Conference (QELS)*, pp. 7-9. We describe an approach for characterizing optical quantum gates, by constructing models which incorporate mode-matching effects. Quantum process tomography is then performed on the model. The techniques can be generalized to other quantum computing architectures. © 2005 Optical Society of America.

## Journal articles

Alexander, R.N., Gabay, N.C., Rohde, P.P. & Menicucci, N.C. 2017, 'Measurement-Based Linear Optics',

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*Physical Review Letters*, vol. 118, no. 11.View/Download from: Publisher's site

© 2017 American Physical Society.A major challenge in optical quantum processing is implementing large, stable interferometers. We offer a novel approach: virtual, measurement-based interferometers that are programed on the fly solely by the choice of homodyne measurement angles. The effects of finite squeezing are captured as uniform amplitude damping. We compare our proposal to existing (physical) interferometers and consider its performance for BosonSampling, which could demonstrate postclassical computational power in the near future. We prove its efficiency in time and squeezing (energy) in this setting.

Motes, K.R., Gilchrist, A. & Rohde, P.P. 2016, 'Quantum random walks on congested lattices and the effect of dephasing',

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*Scientific Reports*, vol. 6.View/Download from: Publisher's site

We consider quantum random walks on congested lattices and contrast them to classical random walks. Congestion is modelled on lattices that contain static defects which reverse the walkerâ € s direction. We implement a dephasing process after each step which allows us to smoothly interpolate between classical and quantum random walks as well as study the effect of dephasing on the quantum walk. Our key results show that a quantum walker escapes a finite boundary dramatically faster than a classical walker and that this advantage remains in the presence of heavily congested lattices.

Motes, K.R., Mann, R.L., Olson, J.P., Studer, N.M., Bergeron, E.A., Gilchrist, A., Dowling, J.P., Berry, D.W. & Rohde, P.P. 2016, 'Efficient recycling strategies for preparing large Fock states from single-photon sources: Applications to quantum metrology',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 94, no. 1.View/Download from: Publisher's site

© 2016 American Physical Society.Fock states are a fundamental resource for many quantum technologies such as quantum metrology. While much progress has been made in single-photon source technologies, preparing Fock states with a large photon number remains challenging. We present and analyze a bootstrapped approach for nondeterministically preparing large photon-number Fock states by iteratively fusing smaller Fock states on a beamsplitter. We show that by employing state recycling we are able to exponentially improve the preparation rate over conventional schemes, allowing the efficient preparation of large Fock states. The scheme requires single-photon sources, beamsplitters, number-resolved photodetectors, fast-feedforward, and an optical quantum memory.

Rohde, P.P. 2015, 'Simple scheme for universal linear-optics quantum computing with constant experimental complexity using fiber loops',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 91, no. 1.View/Download from: Publisher's site

© 2015 American Physical Society.Recently, Motes, Gilchrist, Dowling, and Rohde [Phys. Rev. Lett. 113, 120501 (2014).PRLTAO0031-900710.1103/PhysRevLett.113.120501] presented a scheme for photonic boson sampling using a fiber-loop architecture. Here we show that the same architecture can be modified to implement full, universal linear-optics quantum computing, in various incarnations. The scheme employs two embedded fiber loops, a single push-button photon source, three dynamically controlled beamsplitters, and a single time-resolved photodetector. The architecture has only a single point of interference, and thus may be significantly easier to align than other schemes. The experimental complexity of the scheme is constant, irrespective of the size of the computation, limited only by fiber lengths and their respective loss rates.

Rohde, P.P. 2015, 'Boson sampling with photons of arbitrary spectral structure',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 91, no. 1.View/Download from: Publisher's site

© 2015 American Physical Society.Boson sampling has attracted much interest as a simplified approach to implementing a subset of optical quantum computing. Boson sampling requires indistinguishable photons, but far fewer of them than universal optical quantum computing architectures. In reality, photons are never indistinguishable, and exhibit a rich spectral structure. Here we consider the operation of boson sampling with photons of arbitrary spectral structure and relate the sampling statistics of the device to matrix permanents. This sheds light on the computational complexity of different regimes of the photons' spectral characteristics, and provides very general results for the operation of linear optics interferometers in the presence of partially distinguishable photons. Our results apply to both the cases of spectrally resolving and nonspectrally resolving detectors.

Olson, J.P., Seshadreesan, K.P., Motes, K.R., Rohde, P.P. & Dowling, J.P. 2015, 'Sampling arbitrary photon-added or photon-subtracted squeezed states is in the same complexity class as boson sampling',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 91, no. 2.View/Download from: Publisher's site

© 2015 American Physical Society.Boson sampling is a simple model for nonuniversal linear optics quantum computing using far fewer physical resources than universal schemes. An input state comprising vacuum and single-photon states is fed through a Haar-random linear optics network and sampled at the output by using coincidence photodetection. This problem is strongly believed to be classically hard to simulate. We show that an analogous procedure implements the same problem, using photon-added or -subtracted squeezed vacuum states (with arbitrary squeezing), where sampling at the output is performed via parity measurements. The equivalence is exact and independent of the squeezing parameter, and hence provides an entire class of quantum states of light in the same complexity class as boson sampling.

Rohde, P.P., Motes, K.R., Knott, P.A., Fitzsimons, J., Munro, W.J. & Dowling, J.P. 2015, 'Evidence for the conjecture that sampling generalized cat states with linear optics is hard',

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*Physical Review A*, vol. 91, no. 1.View/Download from: Publisher's site

Rohde, P.P., Helt, L.G., Steel, M.J. & Gilchrist, A. 2015, 'Multiplexed single-photon-state preparation using a fiber-loop architecture',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 92, no. 5.View/Download from: Publisher's site

© 2015 American Physical Society. Heralded spontaneous parametric down-conversion (SPDC) has become the mainstay for single-photon-state preparation in present-day photonics experiments. Because they are heralded, in principle one knows when a single photon has been prepared. However, the heralding efficiencies in experimentally realistic SPDC sources are typically very low. To overcome this, multiplexing techniques have been proposed which employ a bank of SPDC sources in parallel and route successfully heralded photons to the output, thereby effectively boosting the heralding efficiency. However, running a large bank of independent SPDC sources is costly and requires complex switching. We analyze a multiplexing technique based on time-bin encoding that allows the heralding efficiency of just a single SPDC source to be increased. The scheme is simple and experimentally viable using present-day technology. We analyze the operation of the scheme in terms of experimentally realistic considerations, such as losses, detector inefficiency, and pump power.

Rohde, P.P. & Dowling, J.P. 2015, 'The on-ramp to the all-optical quantum information processing highway',

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*Science*, vol. 349, no. 6249, p. 696.View/Download from: Publisher's site

Brennen, G.K., Rohde, P., Sanders, B.C. & Singh, S. 2015, 'Multiscale quantum simulation of quantum field theory using wavelets',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 92, no. 3.View/Download from: Publisher's site

© 2015 American Physical Society. ©2015 American Physical Society. A successful approach to understand field theories is to resolve the physics into different length or energy scales using the renormalization group framework. We propose a quantum simulation of quantum field theory which encodes field degrees of freedom in a wavelet basis - a multiscale description of the theory. Since wavelet families can be constructed to have compact support at all resolutions, this encoding allows for quantum simulations to create particle excitations which are local at some chosen scale and provides a natural way to associate observables in the theory to finite-resolution detectors.

Motes, K.R., Olson, J.P., Rabeaux, E.J., Dowling, J.P., Olson, S.J. & Rohde, P.P. 2015, 'Linear Optical Quantum Metrology with Single Photons: Exploiting Spontaneously Generated Entanglement to Beat the Shot-Noise Limit',

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*Physical Review Letters*, vol. 114, no. 17.View/Download from: Publisher's site

© 2015 American Physical Society.Quantum number-path entanglement is a resource for supersensitive quantum metrology and in particular provides for sub-shot-noise or even Heisenberg-limited sensitivity. However, such number-path entanglement has been thought to be resource intensive to create in the first place - typically requiring either very strong nonlinearities, or nondeterministic preparation schemes with feedforward, which are difficult to implement. Very recently, arising from the study of quantum random walks with multiphoton walkers, as well as the study of the computational complexity of passive linear optical interferometers fed with single-photon inputs, it has been shown that such passive linear optical devices generate a superexponentially large amount of number-path entanglement. A logical question to ask is whether this entanglement may be exploited for quantum metrology. We answer that question here in the affirmative by showing that a simple, passive, linear-optical interferometer - fed with only uncorrelated, single-photon inputs, coupled with simple, single-mode, disjoint photodetection - is capable of significantly beating the shot-noise limit. Our result implies a pathway forward to practical quantum metrology with readily available technology.

Motes, K.R., Dowling, J.P., Gilchrist, A. & Rohde, P.P. 2015, 'Implementing BosonSampling with time-bin encoding: Analysis of loss, mode mismatch, and time jitter',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 92, no. 5.View/Download from: Publisher's site

©2015 American Physical Society. It was recently shown by Motes, Gilchrist, Dowling, and Rohde [Phys. Rev. Lett. 113, 120501 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.120501] that a time-bin encoded fiber-loop architecture can implement an arbitrary passive linear optics transformation. This was shown in the case of an ideal scheme whereby the architecture has no sources of error. In any realistic implementation, however, physical errors are present, which corrupt the output of the transformation. We investigate the dominant sources of error in this architecture - loss and mode mismatch - and consider how it affects the BosonSampling protocol, a key application for passive linear optics. For our loss analysis we consider two major components that contribute to loss - fiber and switches - and calculate how this affects the success probability and fidelity of the device. Interestingly, we find that errors due to loss are not uniform (unique to time-bin encoding), which asymmetrically biases the implemented unitary. Thus loss necessarily limits the class of unitaries that may be implemented, and therefore future implementations must prioritize minimizing loss rates if arbitrary unitaries are to be implemented. Our formalism for mode mismatch is generalized to account for various phenomenon that may cause mode mismatch, but we focus on two - errors in fiber-loop lengths and time jitter of the photon source. These results provide a guideline for how well future experimental implementations might perform in light of these error mechanisms.

Seshadreesan, K.P., Olson, J.P., Motes, K.R., Rohde, P.P. & Dowling, J.P. 2015, 'Boson sampling with displaced single-photon Fock states versus single-photon-added coherent states: The quantum-classical divide and computational-complexity transitions in linear optics',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 91, no. 2.View/Download from: Publisher's site

© 2015 American Physical Society.Boson sampling is a specific quantum computation, which is likely hard to implement efficiently on a classical computer. The task is to sample the output photon-number distribution of a linear-optical interferometric network, which is fed with single-photon Fock-state inputs. A question that has been asked is if the sampling problems associated with any other input quantum states of light (other than the Fock states) to a linear-optical network and suitable output detection strategies are also of similar computational complexity as boson sampling. We consider the states that differ from the Fock states by a displacement operation, namely the displaced Fock states and the photon-added coherent states. It is easy to show that the sampling problem associated with displaced single-photon Fock states and a displaced photon-number detection scheme is in the same complexity class as boson sampling for all values of displacement. On the other hand, we show that the sampling problem associated with single-photon-added coherent states and the same displaced photon-number detection scheme demonstrates a computational-complexity transition. It transitions from being just as hard as boson sampling when the input coherent amplitudes are sufficiently small to a classically simulatable problem in the limit of large coherent amplitudes.

Motes, K.R., Gilchrist, A., Dowling, J.P. & Rohde, P.P. 2014, 'Scalable boson sampling with time-bin encoding using a loop-based architecture',

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*Physical Review Letters*, vol. 113, no. 12.View/Download from: Publisher's site

© 2014 American Physical Society.We present an architecture for arbitrarily scalable boson sampling using two nested fiber loops. The architecture has fixed experimental complexity, irrespective of the size of the desired interferometer, whose scale is limited only by fiber and switch loss rates. The architecture employs time-bin encoding, whereby the incident photons form a pulse train, which enters the loops. Dynamically controlled loop coupling ratios allow the construction of the arbitrary linear optics interferometers required for boson sampling. The architecture employs only a single point of interference and may thus be easier to stabilize than other approaches. The scheme has polynomial complexity and could be realized using demonstrated present-day technologies.

Camilleri, E., Rohde, P.P. & Twamley, J. 2014, 'Quantum walks with tuneable self-avoidance in one dimension',

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*Scientific Reports*, vol. 4.View/Download from: Publisher's site

Quantum walks exhibit many unique characteristics compared to classical random walks. In the classical setting, self-avoiding random walks have been studied as a variation on the usual classical random walk. Here the walker has memory of its previous locations and preferentially avoids stepping back to locations where it has previously resided. Classical self-avoiding random walks have found numerous algorithmic applications, most notably in the modelling of protein folding. We consider the analogous problem in the quantum setting - a quantum walk in one dimension with tunable levels of self-avoidance. We complement a quantum walk with a memory register that records where the walker has previously resided. The walker is then able to avoid returning back to previously visited sites or apply more general memory conditioned operations to control the walk. We characterise this walk by examining the variance of the walker's distribution against time, the standard metric for quantifying how quantum or classical a walk is. We parameterise the strength of the memory recording and the strength of the memory back-action on the walker, and investigate their effect on the dynamics of the walk. We find that by manipulating these parameters, which dictate the degree of self-avoidance, the walk can be made to reproduce ideal quantum or classical random walk statistics, or a plethora of more elaborate diffusive phenomena. In some parameter regimes we observe a close correspondence between classical self-avoiding random walks and the quantum self-avoiding walk.

Rohde, P.P., Brennen, G.K. & Gilchrist, A. 2013, 'Quantum walks with memory provided by recycled coins and a memory of the coin-flip history',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 87, no. 5.View/Download from: Publisher's site

Quantum walks have emerged as an interesting approach to quantum information processing, exhibiting many unique properties compared to the analogous classical random walk. Here we introduce a model for a discrete-time quantum walk with memory by endowing the walker with multiple recycled coins and using a physical memory function via a history dependent coin flip. By numerical simulation we observe several phenomena. First in one dimension, walkers with memory have persistent quantum ballistic speed up over classical walks just as found in previous studies of multicoined walks with trivial memory function. However, measurement of the multicoin state can dramatically shift the mean of the spatial distribution. Second, we consider spatial entanglement in a two-dimensional quantum walk with memory and find that memory destroys entanglement between the spatial dimensions, even when entangling coins are employed. Finally, we explore behavior in the presence of spatial randomness and find that in the time regime where single-coined walks localize, multicoined walks do not and in fact a memory function can speed up the walk relative to a multicoin walker with no memory. We explicitly show how to construct linear optics circuits implementing the walks, and discuss prospects for classical simulation. © 2013 American Physical Society.

Rohde, P.P., Fitzsimons, J.F. & Gilchrist, A. 2013, 'Information capacity of a single photon',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 88, no. 2.View/Download from: Publisher's site

Quantum states of light are the obvious choice for communicating quantum information. To date, encoding information into the polarization states of single photons has been widely used as these states form a natural closed two-state qubit. However, photons are able to encode much more - in principle, infinite - information via the continuous spatiotemporal degrees of freedom. Here we consider the information capacity of an optical quantum channel, such as an optical fiber, where a spectrally encoded single photon is the means of communication. We use the Holevo bound to calculate an upper bound on the channel capacity, and relate this to the spectral encoding basis and the spectral properties of the channel. Further, we derive analytic bounds on the capacity of such channels, and, in the case of a symmetric two-state encoding, calculate the exact capacity of the corresponding channel. © 2013 American Physical Society.

Rohde, P.P., Schreiber, A., Štefaňák, M., Jex, I., Gilchrist, A. & Christine, S. 2013, 'Increasing the dimensionality of quantum walks using multiple walkers',

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*Journal of Computational and Theoretical Nanoscience*, vol. 10, no. 7, pp. 1644-1652.View/Download from: Publisher's site

We show that with the addition of multiple walkers, quantum walks on a line can be transformed into lattice graphs of higher dimension. Thus, multi-walker walks can simulate single-walker walks on higher dimensional graphs and vice versa. This exponential complexity opens up new applications for present-day quantum walk experiments. We discuss the applications of such higher-dimensional structures and how they relate to linear optics quantum computing. In particular we show that multi-walker quantum walks are equivalent to the BosonSampling model for linear optics quantum computation proposed by Aaronson and Arkhipov. With the addition of control over phase-defects in the lattice, which can be simulated with entangling gates, asymmetric lattice structures can be constructed which are universal for quantum computation. Copyright © 2013 American Scientific Publishers.

Motes, K.R., Dowling, J.P. & Rohde, P.P. 2013, 'Spontaneous parametric down-conversion photon sources are scalable in the asymptotic limit for boson sampling',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 88, no. 6.View/Download from: Publisher's site

Boson sampling has emerged as a promising avenue towards postclassical optical quantum computation, and numerous elementary demonstrations have recently been performed. Spontaneous parametric down-conversion (SPDC) is the mainstay for single-photon state preparation, the technique employed in most optical quantum information processing implementations to date. Here we present a simple architecture for boson sampling based on multiplexed SPDC sources and demonstrate that the architecture is limited only by the postselection detection efficiency assuming that other errors, such as spectral impurity, dark counts, and interferometric instability, are negligible. For any given number of input photons, there exists a minimum detector efficiency that allows postselection. If this efficiency is achieved, photon-number errors in the SPDC sources are sufficiently low as to guarantee correct boson sampling most of the time. In this scheme, the required detector efficiency must increase exponentially in the photon number. Thus, we show that idealized SPDC sources will not present a bottleneck for future boson-sampling implementations. Rather, photodetection efficiency is the limiting factor, and thus, future implementations may continue to employ SPDC sources. © 2013 American Physical Society.

Rohde, P.P. 2012, 'Optical quantum computing with photons of arbitrarily low fidelity and purity',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 86, no. 5.View/Download from: Publisher's site

Linear optics quantum computing (LOQC) is a leading candidate for the implementation of large scale quantum computers. Here quantum information is encoded into the quantum states of light and computation proceeds via a linear optics network. It is well known that in such schemes there are stringent requirements on the spatiotemporal structure of photons-they must be completely indistinguishable and of very high purity. We show that in the boson-sampling model for LOQC these conditions may be significantly relaxed. We present evidence that by increasing the size of the system we can implement a computationally hard algorithm even if our photons have arbitrarily low fidelity and purity. These relaxed conditions may make boson-sampling LOQC within reach of present-day technology. © 2012 American Physical Society.

Rohde, P.P., Fitzsimons, J.F. & Gilchrist, A. 2012, 'Quantum walks with encrypted data',

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*Physical Review Letters*, vol. 109, no. 15.View/Download from: Publisher's site

In the setting of networked computation, data security can be a significant concern. Here we consider the problem of allowing a server to remotely manipulate client supplied data, in such a way that both the information obtained by the client about the server's operation and the information obtained by the server about the client's data are significantly limited. We present a protocol for achieving such functionality in two closely related models of restricted quantum computation-the boson sampling and quantum walk models. Because of the limited technological requirements of the boson scattering model, small scale implementations of this technique are feasible with present-day technology. © 2012 American Physical Society.

Rohde, P.P. & Ralph, T.C. 2012, 'Error tolerance of the boson-sampling model for linear optics quantum computing',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 85, no. 2.View/Download from: Publisher's site

Linear optics quantum computing is a promising approach to implementing scalable quantum computation. However, this approach has very demanding physical resource requirements. Recently, Aaronson and Arkhipov (e-print arXiv:1011.3245) showed that a simplified model, which avoids the requirement for fast feed-forward and postselection, while likely not capable of solving BQP-complete problems efficiently, can solve an interesting sampling problem believed to be classically hard. Loss and mode mismatch are the dominant sources of error in such systems. We provide evidence that even lossy systems or systems with mode mismatch are likely to be classically hard to solve. This is of practical interest to experimentalists wishing to demonstrate such systems since it suggests that, even with errors in their implementation, they are likely implementing an algorithm that is classically hard to solve. Our results also equivalently apply to the multiwalker quantum walk model. © 2012 American Physical Society.

Rohde, P.P., Fedrizzi, A. & Ralph, T.C. 2012, 'Entanglement dynamics and quasi-periodicity in discrete quantum walks',

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*Journal of Modern Optics*, vol. 59, no. 8, pp. 710-720.View/Download from: Publisher's site

We study the entanglement dynamics of discrete time quantum walks acting on bounded finite sized graphs. We demonstrate that, depending on system parameters, the dynamics may be monotonic, oscillatory but highly regular, or quasi-periodic. While the dynamics of the system are not chaotic since the system comprises linear evolution, the dynamics often exhibit some features similar to chaos such as high sensitivity to the system's parameters, irregularity and infinite periodicity. Our observations are of interest for entanglement generation, which is one primary use for the quantum walk formalism. Furthermore, we show that the systems we model can easily be mapped to optical beamsplitter networks, rendering experimental observation of quasi-periodic dynamics within reach. © 2012 Copyright Taylor and Francis Group, LLC.

Schreiber, A., Gábris, A., Rohde, P.P., Laiho, K., Štefaňák, M., Potoček, V., Hamilton, C., Jex, I. & Silberhorn, C. 2012, 'A 2D quantum walk simulation of two-particle dynamics',

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*Science*, vol. 335, no. 6077, pp. 55-58.View/Download from: Publisher's site

Multidimensional quantum walks can exhibit highly nontrivial topological structure, providing a powerful tool for simulating quantum information and transport systems. We present a flexible implementation of a two-dimensional (2D) optical quantum walk on a lattice, demonstrating a scalable quantum walk on a nontrivial graph structure. We realized a coherent quantum walk over 12 steps and 169 positions by using an optical fiber network. With our broad spectrum of quantum coins, we were able to simulate the creation of entanglement in bipartite systems with conditioned interactions. Introducing dynamic control allowed for the investigation of effects such as strong nonlinearities or two-particle scattering. Our results illustrate the potential of quantum walks as a route for simulating and understanding complex quantum systems.

Rohde, P.P. & Ralph, T.C. 2011, 'Time-resolved detection and mode mismatch in a linear optics quantum gate',

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*New Journal of Physics*, vol. 13.View/Download from: Publisher's site

Linear optics (LO) is a promising candidate for the implementation of quantum information processing protocols. In such systems, single photons are used to represent qubits. In practice, single photons from different sources will not be perfectly temporally and frequency matched. Therefore, understanding the effects of temporal and frequency mismatch is important in characterizing the dynamics of the system. In this paper, we discuss the impact of temporal and frequency mismatch, how they differ from each other and what their effect is on a simple LO quantum gate. We show that temporal and frequency mismatch have inherently different effects on the operation of the gate. We also consider the spectral effects of the photodetectors, focusing on time-resolved detection, which we show has a strong impact on the operation of such protocols. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

Rohde, P.P., Schreiber, A., Štefaňák, M., Jex, I. & Silberhorn, C. 2011, 'Multi-walker discrete time quantum walks on arbitrary graphs, their properties and their photonic implementation',

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*New Journal of Physics*, vol. 13.View/Download from: Publisher's site

Quantum walks have emerged as an interesting alternative to the usual circuit model for quantum computing. While still universal for quantum computing, the quantum walk model has very different physical requirements, which lends itself more naturally to some physical implementations, such as linear optics. Numerous authors have considered walks with one or two walkers, on one-dimensional graphs, and several experimental demonstrations have been performed. In this paper, we discuss generalizing the model of discrete time quantum walks to the case of an arbitrary number of walkers acting on arbitrary graph structures. We present a formalism that allows for the analysis of such situations, and several example scenarios for how our techniques can be applied. We consider the most important features of quantum walks-measurement, distinguishability, characterization and the distinction between classical and quantum interference. We also discuss the potential for physical implementation in the context of linear optics, which is of relevance to present-day experiments. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

Barrett, S.D., Rohde, P.P. & Stace, T.M. 2010, 'Scalable quantum computing with atomic ensembles',

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*New Journal of Physics*, vol. 12.View/Download from: Publisher's site

Atomic ensembles, comprising clouds of atoms addressed by laser fields, provide an attractive system for both the storage of quantum information and the coherent conversion of quantum information between atomic and optical degrees of freedom. We describe a scheme for full-scale quantum computing with atomic ensembles, in which qubits are encoded in symmetric collective excitations of many atoms. We consider the most important sources of error-imperfect exciton-photon coupling and photon losses-and demonstrate that the scheme is extremely robust against these processes: the required photon emission and collection efficiency threshold is 86%. Our scheme uses similar methods to those already demonstrated experimentally in the context of quantum repeater schemes and yet has information processing capabilities far beyond those proposals. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

Haselgrove, H.L. & Rohde, P.P. 2008, 'Trade-off between the tolerance of located and unlocated errors in nondegenerate quantum error-correcting codes',

*Quantum Information and Computation*, vol. 8, no. 5, pp. 0399-0410. In a recent study [Rohde et al., quant-ph/0603130 (2006)] of several quantum error correcting protocols designed for tolerance against qubit loss, it was shown that these protocols have the undesirable effect of magnifying the effects of depolarization noise. This raises the question of which general properties of quantum error-correcting codes might explain such an apparent trade-off between tolerance to located and unlocated error types. We extend the counting argument behind the well-known quantum Hamming bound to derive a bound on the weights of combinations of located and unlocated errors which are correctable by nondegenerate quantum codes. Numerical results show that the bound gives an excellent prediction to which combinations of unlocated and located errors can be corrected with high probability by certain large degenerate codes. The numerical results are explained partly by showing that the generalized bound, like the original, is closely connected to the information-theoretic quantity the quantum coherent information. However, we also show that as a measure of the exact performance of quantum codes, our generalized Hamming bound is provably far from tight. © Rinton Press.

Rohde, P.P., Munro, W.J., Ralph, T.C., Van Loock, P. & Nemoto, K. 2008, 'Practical effects in the preparation of cluster states using weak non-linearities',

*Quantum Information and Computation*, vol. 8, no. 1-2, pp. 0053-0067. We discuss experimental effects in the implementation of a recent scheme for performing bus mediated entangling operations between qubits. Here a bus mode, a strong coherent state, successively undergoes weak Kerr-type non-linear interactions with qubits. A quadrature measurement on the bus then projects the qubits into an entangled state. This approach has the benefit that entangling gates are non-destructive, may be performed non-locally, and there is no need for efficient single photon detection. In this paper we examine practical issues affecting its experimental implementation. In particular, we analyze the effects of post-selection errors, qubit loss, bus loss, mismatched coupling rates and mode-mismatch. We derive error models for these effects and relate them to realistic fault-tolerant thresholds, providing insight into realistic experimental requirements. © Rinton Press.

Gauger, E.M., Rohde, P.P., Stoneham, A.M. & Lovett, B.W. 2008, 'Strategies for entangling remote spins with unequal coupling to an optically active mediator',

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*New Journal of Physics*, vol. 10.View/Download from: Publisher's site

We demonstrate that two remote qubits can be entangled through an optically active intermediary even if the coupling strengths between mediator and qubits are different. This is true for a broad class of interactions. We consider two contrasting scenarios. Firstly, we extend the analysis of a previously studied gate operation which relies on pulsed, dynamical control of the optical state and which may be performed quickly. We show that remote spins can be entangled in this case even when the intermediary coupling strengths are unequal. Secondly, we propose an alternative adiabatic control procedure, and find that the system requirements become even less restrictive in this case. The scheme could be tested immediately in a range of systems including molecules, quantum dots, or defects in crystals. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

Rohde, K. & Rohde, P.P. 2008, 'How to measure ecological host specificity',

*Vie et Milieu*, vol. 58, no. 2, pp. 121-124. Rohde's original host specificity index and the modified index correcting for number of host species are discussed, using some arbitrary examples. The indices can be applied to address ecological questions involving parasites, herbivores, symbionts and commensals, where phylogenetic relationships of hosts are irrelevant.

Rohde, P.P., Mauerer, W. & Silberhorn, C. 2007, 'Spectral structure and decompositions of optical states, and their applications',

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*New Journal of Physics*, vol. 9.View/Download from: Publisher's site

We discuss the spectral structure and decomposition of multiphoton states. Ordinarily 'multi-photon states' and 'Fock states' are regarded as synonymous. However, when the spectral degrees of freedom are included this is not the case, and the class of 'multi-photon' states is much broader than the class of 'Fock' states. We discuss the criteria for a state to be considered a Fock state. We then address the decomposition of general multi-photon states into bases of orthogonal eigenmodes, building on existing multi-mode theory, and introduce an occupation number representation that provides an elegant description of such states. This representation allows us to work in bases imposed by experimental constraints, simplifying calculations in many situations. Finally we apply this technique to several example situations, which are highly relevant for state of the art experiments. These include Hong-Ou-Mandel interference, spectral filtering, finite bandwidth photo-detection, homodyne detection and the conditional preparation of Schrödinger kitten and Fock states. Our techniques allow for very simple descriptions of each of these examples. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

Rohde, P.P. & Barrett, S.D. 2007, 'Strategies for the preparation of large cluster states using non-deterministic gates',

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*New Journal of Physics*, vol. 9.View/Download from: Publisher's site

The cluster state model for quantum computation has paved the way for schemes that allow scalable quantum computing, even when using non-deterministic quantum gates. Here the initial step is to prepare a large entangled state using non-deterministic gates. A key question in this context is the relative efficiencies of different 'strategies', i.e. in what order should the non-deterministic gates be applied, in order to maximize the size of the resulting cluster states? In this paper we consider this issue in the context of 'large' cluster states. Specifically, we assume an unlimited resource of qubits and ask what the steady state rate at which 'large' clusters are prepared from this resource is, given an entangling gate with particular characteristics. We measure this rate in terms of the number of entangling gate operations that are applied. Our approach works for a variety of different entangling gate types, with arbitrary failure probability. Our results indicate that strategies whereby one preferentially bonds together clusters of identical length are considerably more efficient than those in which one does not. Additionally, compared to earlier analytic results, our numerical study offers substantially improved resource scaling. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

Rohde, P.P., Ralph, T.C. & Munro, W.J. 2007, 'Error tolerance and tradeoffs in loss- and failure-tolerant quantum computing schemes',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 75, no. 1.View/Download from: Publisher's site

Qubit loss and gate failure are significant problems for the development of scalable quantum computing. Recently, various schemes have been proposed for tolerating qubit loss and gate failure. These include schemes based on cluster and parity states. We show that by designing such schemes specifically to tolerate these error types we cause an exponential blowout in depolarizing noise. We discuss several examples and propose techniques for minimizing this problem. In general, this introduces a tradeoff with other undesirable effects. In some cases this is physical resource requirements, while in others it is noise rates. © 2007 The American Physical Society.

Rohde, P.P., Webb, J.G., Huntington, E.H. & Ralph, T.C. 2007, 'Photon number projection using non-number-resolving detectors',

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*New Journal of Physics*, vol. 9.View/Download from: Publisher's site

Number-resolving photo-detection is necessary for many quantum optics experiments, especially in the application of entangled state preparation. Several schemes have been proposed for approximating number-resolving photodetection using non-number-resolving detectors. Such techniques include multiport detection and time-division multiplexing. We provide a detailed analysis and comparison of different number-resolving detection schemes, with a view to creating a useful reference for experimentalists. We show that the ideal architecture for projective measurements is a function of the detector's dark count and efficiency parameters. We also describe a process for selecting an appropriate topology given actual experimental component parameters.

Rohde, P.P. & Ralph, T.C. 2006, 'Error models for mode mismatch in linear optics quantum computing',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 73, no. 6.View/Download from: Publisher's site

One of the most significant challenges facing the development of linear optics quantum computing (LOQC) is mode mismatch, whereby photon distinguishability is introduced within circuits, undermining quantum interference effects. We examine the effects of mode mismatch on the parity (or fusion) gate, the fundamental building block in several recent LOQC schemes. We derive simple error models for the effects of mode mismatch on its operation, and relate these error models to current fault-tolerant-threshold estimates. © 2006 The American Physical Society.

Rohde, P.P., Ralph, T.C. & Munro, W.J. 2006, 'Practical limitations in optical entanglement purification',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 73, no. 3.View/Download from: Publisher's site

Entanglement purification protocols play an important role in the distribution of entangled systems, which is necessary for various quantum information processing applications. We consider the effects of photodetector efficiency and bandwidth, channel loss and mode mismatch on the operation of an optical entanglement purification protocol. We derive necessary detector and mode-matching requirements to facilitate practical operation of such a scheme, without having to resort to destructive coincidence-type demonstrations. © 2006 The American Physical Society.

Rohde, P.P. & Ralph, T.C. 2006, 'Modelling photo-detectors in quantum optics',

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*Journal of Modern Optics*, vol. 53, no. 11, pp. 1589-1603.View/Download from: Publisher's site

Photo-detection plays a fundamental role in experimental quantum optics and is of particular importance in the emerging field of linear optics quantum computing. Present theoretical treatment of photo-detectors is highly idealized and fails to consider many important physical effects. We present a physically motivated model for photo-detectors which accommodates for the effects of finite resolution, bandwidth and efficiency, as well as dark counts and dead-time. We apply our model to two simple well-known applications, which illustrates the significance of these characteristics.

Rohde, P.P., Pryde, G.J., O'Brien, J.L. & Ralph, T.C. 2005, 'Quantum-gate characterization in an extended Hilbert space',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 72, no. 3.View/Download from: Publisher's site

We describe an approach for characterizing the process performed by a quantum gate using quantum process tomography, by first modeling the gate in an extended Hilbert space, which includes nonqubit degrees of freedom. To prevent unphysical processes from being predicted, present quantum process tomography procedures incorporate mathematical constraints, which make no assumptions as to the actual physical nature of the system being described. By contrast, the procedure presented here assumes a particular class of physical processes, and enforces physicality by fitting the data to this model. This allows quantum process tomography to be performed using a smaller experimental data set, and produces parameters with a direct physical interpretation. The approach is demonstrated by example of mode matching in an all-optical controlled-NOT gate. The techniques described are general and could be applied to other optical circuits or quantum computing architectures. © 2005 The American Physical Society.

Rohde, P.P., Ralph, T.C. & Nielsen, M.A. 2005, 'Optimal photons for quantum-information processing',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 72, no. 5.View/Download from: Publisher's site

Photonic quantum-information processing schemes, such as linear optics quantum computing, and other experiments relying on single-photon interference, inherently require complete photon indistinguishability to enable the desired photonic interactions to take place. Mode-mismatch is the dominant cause of photon distinguishability in optical circuits. Here we study the effects of photon wave-packet shape on tolerance against the effects of mode mismatch in linear optical circuits, and show that Gaussian distributed photons with large bandwidth are optimal. The result is general and holds for arbitrary linear optical circuits, including ones which allow for postselection and classical feed forward. Our findings indicate that some single photon sources, frequently cited for their potential application to quantum-information processing, may in fact be suboptimal for such applications. © 2005 The American Physical Society.

Rohde, P.P. 2005, 'Non-deterministic approximation of photon number discriminating detectors using non-discriminating detectors',

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*Journal of Optics B: Quantum and Semiclassical Optics*, vol. 7, no. 2, pp. 82-86.View/Download from: Publisher's site

We present a scheme for non-deterministically approximating photon number resolving detectors using non-discriminating detectors. The model is simple in construction and employs very few physical resources. Despite its non-determinism, the proposal may nonetheless be suitable for use in some quantum optics experiments in which non-determinism can be tolerated. We analyse the detection scheme in the context of an optical implementation of the controlled-NOT gate, an inherently non-deterministic device. This allows the gate's success probability to be traded away for improved gate fidelity, assuming high efficiency detectors. The scheme is compared to two other proposals, both deterministic, for approximating discriminating detectors using non-discriminating detectors: the cascade and time division multiplexing schemes. © 2005 IOP Publishing Ltd.

Rohde, P.P. & Ralph, T.C. 2005, 'Frequency and temporal effects in linear optical quantum computing',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 71, no. 3.View/Download from: Publisher's site

Typically linear optical quantum computing (LOQC) models assume that all input photons are completely indistinguishable. In practice there will inevitably be nonidealities associated with the photons and the experimental setup which will introduce a degree of distinguishability between photons. We consider a nondeterministic optical controlled-NOT gate, a fundamental LOQC gate, and examine the effect of temporal and spectral distinguishability on its operation. We also consider the effect of utilizing nonideal photon counters, which have finite bandwidth and time response. ©2005 The American Physical Society.

Rohde, P.P., Pryde, G.J., O'Brien, J.L. & Ralph, T.C. 2005, 'Erratum: Quantum-gate characterization in an extended Hilbert space (Physics Review (2005) 72 (032306))',

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*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 72, no. 3.View/Download from: Publisher's site

Rohde, K. & Rohde, P.P. 2001, 'Fuzzy Chaos: Reduced Chaos in the Combined Dynamics of Several Independently Chaotic Populations',

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*The American Naturalist*, vol. 158, no. 5, pp. 553-556.View/Download from: Publisher's site

Rohde, P.P., 'Optimising number resolving photo-detectors using classical post-processing'.

Many present day quantum optics experiments, particularly in optical quantum
information processing, rely on number-resolving photo-detection as a basic
building block. In this paper we demonstrate that a simple classical
optimisation technique can sometimes be employed to post-process the detector
signature and improve the confidence of the measurement outcome in the presence
of photon-number errors such as loss or dark-counts. While the regime in which
this technique is applicable is rather restrictive, and will likely not be very
useful for the large-scale quantum information processing applications of the
future, the ideas presented might be employed in some present-day experiments
where photo-detectors are typically very poor.

Rohde, P.P., 'Are quantum walks the saviour of optical quantum computing?'.

Quantum walks have emerged as an interesting candidate for the implementation
of quantum information processing protocols. Optical implementations of quantum
walks have been demonstrated by various groups and some have received
high-profile coverage. It is often claimed that quantum walks provide an avenue
towards universal quantum computation. In this comment I wish to dispel some
misconceptions surrounding the prospects of quantum walks as a route towards
universal optical quantum computation.

Rohde, P.P., Webb, J.G., Huntington, E.H. & Ralph, T.C., 'Comparison of architectures for approximating number-resolving photo-detection using non-number-resolving detectors',

*New J. Phys.*, vol. 9, p. 233. Number-resolving photo-detection is necessary for many quantum optics
experiments, especially in the application of entangled state preparation.
Several schemes have been proposed for approximating number-resolving
photo-detection using non-number-resolving detectors. Such techniques include
multi-port detection and time-division multiplexing. We provide a detailed
analysis and comparison of different number-resolving detection schemes, with a
view to creating a useful reference for experimentalists. We show that the
ideal architecture for projective measurements is a function of the detector's
dark count and efficiency parameters. We also describe a process for selecting
an appropriate topology given actual experimental component parameters.

Rohde, P.P., 'Improving the fidelity of single photon preparation from conditional down-conversion via asymmetric multiport detection'.

We discuss the conditional preparation of single photons via parametric
down-conversion. This technique is commonly used as a single photon source in
modern quantum optics experiments. A significant problem facing this technique
is the inability of present day photo-detectors to resolve photon number. This
results in mixing with higher photon number terms. To overcome this several
techniques have been proposed, including multi-port detection and time-division
multiplexing. These techniques help approximate number resolving detection even
when using non-number resolving detectors. In this paper we focus on 2-port
detection, the simplest such scheme. We show that by making the 2-port device
asymmetric the fidelity of prepared photons can be improved.

Rohde, P.P., 'Noise thresholds for entanglement purification'.

We consider the effects of gate noise on the operation of an entanglement
purification protocol. We characterize the performance of the protocol by two
measures, the minimum purifiable input state fidelity, and the maximum output
state fidelity. Both these measures are a function of gate error rate. For
sufficiently large gate error rate these two measures converge, defining a
threshold on gate error rates. Numerically, we estimate this threshold to be
$9.2\times 10^{-2}$, which is achievable with many present day experimental
architectures. (This paper is written in an experimental rapid communication
format).

Rohde, P.P. & Lund, A.P., 'Practical effects in cat state breeding'.

A cat state is a superposition of macroscopically distinct states. In quantum
optics one such type of state is a superposition of distinct coherent states.
Recently, a protocol has been proposed for preparing large optical cat states
from a resource of smaller ones. We consider the effects of mode-mismatch and
loss in the preparation of large cat states using this protocol with a view to
understand experimental limitations. (This paper is written in an experimental
rapid communication format).

Rohde, P.P., Ralph, T.C. & Munro, W.J., 'Error propagation in loss- and failure-tolerant quantum computation schemes'.

Qubit loss and gate failure are significant obstacles for the implementation
of scalable quantum computation. Recently there have been several proposals for
overcoming these problems, including schemes based on parity and cluster
states. While effective at dealing with loss and gate failure, these schemes
typically lead to a blow-out in effective depolarizing noise rates. In this
supplementary paper we present a detailed analysis of this problem and
techniques for minimizing it.

Rohde, P.P., 'Quantum state tomography of single photons in the spectral degree of freedom'.

Quantum State Tomography (QST) of optical states is typically performed in
the photon number degree of freedom, a procedure which is well understood and
has been experimentally demonstrated. However, optical states have other
degrees of freedom than just photon number, such as the spatial and
temporal/spectral ones. Full characterization of photonic states requires state
reconstruction in these additional degrees of freedom. In this paper we present
a technique for performing QST of single photon states in the spectral degree
of freedom. This is of importance, for example, in quantum information
processing applications, which typically impose strict requirements on the
purity and distinguishability of independently produced single photons. The
described technique allows for full reconstruction of the spectral density
matrix, allowing the purity and distinguishability of different sources to be
readily calculated.

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