Approximation of real error channels by Clifford channels and Pauli measurements

Abstract

The Gottesman-Knill theorem allows for the efficient simulation of stabilizer-based quantum error-correction circuits. Errors in these circuits are commonly modeled as depolarizing channels by using Monte Carlo methods to insert Pauli gates randomly throughout the circuit. Although convenient, these channels are poor approximations of common, realistic channels like amplitude damping. Here we analyze a larger set of efficiently simulable error channels by allowing the random insertion of any one-qubit gate or measurement that can be efficiently simulated within the stabilizer formalism. Our new error channels are shown to be a viable method for accurately approximating real error channels.

arXiv comment6 pages, 4 figures

References in corpus (15)

• Fault-tolerant quantum computation by anyons
• Good Quantum Error-Correcting Codes Exist
• Topological quantum memory
• Improved Simulation of Stabilizer Circuits
• Quantum Computing with Very Noisy Devices
• Topological Quantum Distillation
• Distance measures to compare real and ideal quantum processes
• Operator Quantum Error Correcting Subsystems for Self-Correcting Quantum Memories
• Overhead and noise threshold of fault-tolerant quantum error correction
• Fault-Tolerant Error Correction with Efficient Quantum Codes
• Approximate quantum error correction can lead to better codes
• Bosonic Quantum Codes for Amplitude Damping
• Modeling quantum noise for efficient testing of fault-tolerant circuits
• Environment-invariant measure of distance between evolutions of an open quantum system
• Tight Noise Thresholds for Quantum Computation with Perfect Stabilizer Operations

Cited by in corpus (41)

• Low-distance Surface Codes under Realistic Quantum Noise
• Correcting coherent errors with surface codes
• Modelling and Simulating the Noisy Behaviour of Near-term Quantum Computers
• Efficient error models for fault-tolerant architectures and the Pauli twirling approximation
• Tensor-Network Simulations of the Surface Code under Realistic Noise
• Performance of quantum error correction with coherent errors
• Simulating the performance of a distance-3 surface code in a linear ion trap
• Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions
• Errors and pseudo-thresholds for incoherent and coherent noise
• Unbiased Simulation of Near-Clifford Quantum Circuits
• Transversality and lattice surgery: exploring realistic routes towards coupled logical qubits with trapped-ion quantum processors
• Quantum Computing: An Overview Across the System Stack
• Comparison of a quantum error correction threshold for exact and approximate errors
• Accounting for Classical Hardware in the Control of Quantum Devices
• A taxonomy of small Markovian errors
• Tractable Simulation of Error Correction with Honest Approximations to Realistic Fault Models
• Fault Tolerance with Bare Ancillae for a [[7,1,3]] Code
• Fault-tolerant protection of near-term trapped-ion topological qubits under realistic noise sources
• Quantum computing by color-code lattice surgery
• Prospect of using Grover's search in the noisy-intermediate-scale quantum-computer era
• Quantum error correction failure distributions: comparison of coherent and stochastic error models
• Quantitative Robustness Analysis of Quantum Programs (Extended Version)
• Simulating prethermalization using near-term quantum computers
• Optimizing quantum noise-induced reservoir computing for nonlinear and chaotic time series prediction
• Efficient simulation of quantum error correction under coherent error based on non-unitary free-fermionic formalism
• A Silicon Surface Code Architecture Resilient Against Leakage Errors
• Analytical Error Analysis of Clifford Gates by the Fault-Path Tracer Method
• Randomized Benchmarking of Clifford Operators
• Exponential Families for Bayesian Quantum Process Tomography
• Non-Pauli errors can be efficiently sampled in qudit surface codes
• Dynamical subset sampling of quantum error correcting protocols
• In-situ Adaptive Encoding for Asymmetric Quantum Error Correcting Codes
• Normalizer Circuits and Quantum Computation
• Managing approximation errors in quantum programs
• Characterization of coherent errors in gate layers with robustness to Pauli noise
• Statistical mechanical mapping and maximum-likelihood thresholds for the surface code under generic single-qubit coherent errors
• Wildcard error: Quantifying unmodeled errors in quantum processors
• Gleipnir: Toward Practical Error Analysis for Quantum Programs (Extended Version)
• High-Rate Amplitude-Damping Shor Codes with Immunity to Collective Coherent Errors
• Improved performance of the Bacon-Shor code with Steane's syndrome extraction method
• Comparison of spin-qubit architectures for quantum error-correcting codes