Fault Tolerant Filtering and Fault Detection for Quantum Systems Driven By Fields in Single Photon States

The purpose of this paper is to solve a fault tolerant filtering and fault detection problem for a class of open quantum systems driven by a continuous-mode bosonic input field in single photon states when the systems are subject to stochastic faults. Optimal estimates of both the system observables and the fault process are simultaneously calculated and characterized by a set of coupled recursive quantum stochastic differential equations.Comment: arXiv admin note: text overlap with arXiv:1504.0678

Resilient Quantum Computation: Error Models and Thresholds

Recent research has demonstrated that quantum computers can solve certain types of problems substantially faster than the known classical algorithms. These problems include factoring integers and certain physics simulations. Practical quantum computation requires overcoming the problems of environmental noise and operational errors, problems which appear to be much more severe than in classical computation due to the inherent fragility of quantum superpositions involving many degrees of freedom. Here we show that arbitrarily accurate quantum computations are possible provided that the error per operation is below a threshold value. The result is obtained by combining quantum error-correction, fault tolerant state recovery, fault tolerant encoding of operations and concatenation. It holds under physically realistic assumptions on the errors.Comment: 19 pages in RevTex, many figures, the paper is also avalaible at http://qso.lanl.gov/qc

Resilience to time-correlated noise in quantum computation

Fault-tolerant quantum computation techniques rely on weakly correlated noise. Here I show that it is enough to assume weak spatial correlations: time correlations can take any form. In particular, single-shot error correction techniques exhibit a noise threshold for quantum memories under spatially local stochastic noise.Comment: 16 pages, v3: as accepted in journa

Tractable Simulation of Error Correction with Honest Approximations to Realistic Fault Models

In previous work, we proposed a method for leveraging efficient classical simulation algorithms to aid in the analysis of large-scale fault tolerant circuits implemented on hypothetical quantum information processors. Here, we extend those results by numerically studying the efficacy of this proposal as a tool for understanding the performance of an error-correction gadget implemented with fault models derived from physical simulations. Our approach is to approximate the arbitrary error maps that arise from realistic physical models with errors that are amenable to a particular classical simulation algorithm in an "honest" way; that is, such that we do not underestimate the faults introduced by our physical models. In all cases, our approximations provide an "honest representation" of the performance of the circuit composed of the original errors. This numerical evidence supports the use of our method as a way to understand the feasibility of an implementation of quantum information processing given a characterization of the underlying physical processes in experimentally accessible examples.Comment: 34 pages, 9 tables, 4 figure

A Study on the Noise Threshold of Fault-tolerant Quantum Error Correction

Quantum circuits implementing fault-tolerant quantum error correction (QEC) for the three qubit bit-flip code and five-qubit code are studied. To describe the effect of noise, we apply a model based on a generalized effective Hamiltonian where the system-environment interactions are taken into account by including stochastic fluctuating terms in the system Hamiltonian. This noise model enables us to investigate the effect of noise in quantum circuits under realistic device conditions and avoid strong assumptions such as maximal parallelism and weak storage errors. Noise thresholds of the QEC codes are calculated. In addition, the effects of imprecision in projective measurements, collective bath, fault-tolerant repetition protocols, and level of parallelism in circuit constructions on the threshold values are also studied with emphasis on determining the optimal design for the fault-tolerant QEC circuit. These results provide insights into the fault-tolerant QEC process as well as useful information for designing the optimal fault-tolerant QEC circuit for particular physical implementation of quantum computer.Comment: 9 pages, 9 figures; to be submitted to Phys. Rev.