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)

The resurgence of the linear optics quantum interferometer — recent advances & applications

© 2019 Linear optics has seen a resurgence for applications in quantum information processing owing to its miniaturisation on-chip, and increase in production efficiency and quality of single photons. Time-bin encodings have also become feasible owing to architectural breakthroughs, and new processing capabilities. Theoretical efforts have found new ways to implement universal quantum computations with linear optics requiring less resources, and to demonstrate the capabilities of linear optics without requiring a universal optical quantum computer

Trade-off between the tolerance of located and unlocated errors in nondegenerate quantum error-correcting codes

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

Information capacity of a single photon

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

Quantum walks with memory provided by recycled coins and a memory of the coin-flip history

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

Spontaneous parametric down-conversion photon sources are scalable in the asymptotic limit for boson sampling

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

Quantum walks with tuneable self-avoidance in one dimension

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

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

Photonic quantum error correction of linear optics using W-state encoding

Error-detection and correction are necessary prerequisites for any scalable quantum computing architecture. Given the inevitability of unwanted physical noise in quantum systems and the propensity for errors to spread as computations proceed, computational outcomes can become substantially corrupted. This observation applies regardless of the choice of physical implementation. In the context of photonic quantum information processing, there has recently been much interest in passive linear optics quantum computing, which includes boson-sampling, as this model eliminates the highly-challenging requirements for feed-forward via fast, active control. That is, these systems are passive by definition. In usual scenarios, error detection and correction techniques are inherently active, making them incompatible with this model, arousing suspicion that physical error processes may be an insurmountable obstacle. Here we explore a photonic error-detection technique, based on W-state encoding of photonic qubits, which is entirely passive, based on post-selection, and compatible with these near-term photonic architectures of interest. We show that this W-state redundant encoding techniques enables the suppression of dephasing noise on photonic qubits via simple fan-out style operations, implemented by optical Fourier transform networks, which can be readily realised today. The protocol effectively maps dephasing noise into heralding failures, with zero failure probability in the ideal no-noise limit

Quantum leap: how to complete a quantum walk in a single step

Quantum walks provide simple models of various fundamental processes. It is pivotal to know when the dynamics underlying a walk lead to quantum advantages just by examining its statistics. A walk with many indistinguishable particles and measurements of non-classical multi-particle correlations is likely to reveal the quantum nature. The number of elements $O(n)$ in a setup realizing walks grows with their length or spread $n$. We introduce the concept of a quantum leap, a process which can be achieved with fewer or complementary resources and which in a single step simulates another long process. The process and its leap are described by the same Hamiltonian but, the latter parametrizes the evolution with a tunable parameter of a setup. In the case of walks, a leap immediately gives a probability distribution which results only after many steps. This may be appealing for simulation of processes which are lengthy or require dynamical control. We discuss a leap based on the multi-particle Hong--Ou--Mandel interference, an inherently quantum phenomenon. It reproduces a quantum walk enabling perfect state transfer through spin chains. It requires a beam splitter, two detectors and $n$ particles to mimic a walk on a chain of size $O(n)$, for time fixed by beam-splitter's reflectivity. Our results apply to a broad class of systems where the HOM-like effects can be observed, and may constitute a new approach to simulation of complex Hamiltonians with passive interferometers