Sampling Overhead Analysis of Quantum Error Mitigation: Uncoded vs. Coded Systems

Abstract

Quantum error mitigation (QEM) is a promising technique of protecting hybrid quantum-classical computation from decoherence, but it suffers from sampling overhead which erodes the computational speed. In this treatise, we provide a comprehensive analysis of the sampling overhead imposed by QEM. In particular, we show that Pauli errors incur the lowest sampling overhead among a large class of realistic quantum channels having the same average fidelity. Furthermore, we show that depolarizing errors incur the lowest sampling overhead among all kinds of Pauli errors. Additionally, we conceive a scheme amalgamating QEM with quantum channel coding, and analyse its sampling overhead reduction compared to pure QEM. Especially, we observe that there exist a critical number of gates contained in quantum circuits, beyond which their amalgamation is preferable to pure QEM.

References in corpus (39)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• A variational eigenvalue solver on a quantum processor
• Quantum algorithm for solving linear systems of equations
• The theory of variational hybrid quantum-classical algorithms
• A Quantum Approximate Optimization Algorithm
• Quantum computational chemistry
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Error mitigation for short-depth quantum circuits
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
• A simple formula for the average gate fidelity of a quantum dynamical operation
• Exact and Approximate Unitary 2-Designs: Constructions and Applications
• Quantum optimization using variational algorithms on near-term quantum devices
• Practical Quantum Error Mitigation for Near-Future Applications
• Variational Quantum Computation of Excited States
• Robust determination of molecular spectra on a quantum processor
• Quantum Process Tomography: Resource Analysis of Different Strategies
• Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits
• Sparse Graph Codes for Quantum Error-Correction
• Quantum Data Hiding
• Resilient Quantum Computation: Error Models and Thresholds
• Variational quantum algorithms for discovering Hamiltonian spectra
• Low-cost error mitigation by symmetry verification
• Fault-tolerant quantum error detection
• Quantum computation with universal error mitigation on superconducting quantum processor
• Entanglement-assisted quantum turbo codes
• Fault-Tolerant Postselected Quantum Computation: Schemes
• Introduction to Quantum Gate Set Tomography
• Concatenated Quantum Codes
• Fault-Tolerant Postselected Quantum Computation: Threshold Analysis
• EXIT-Chart Aided Near-Capacity Quantum Turbo Code Design
• Near-Hashing-Bound Multiple-Rate Quantum Turbo Short-Block Codes
• Noise Threshold of Quantum Supremacy
• A Query-based Quantum Eigensolver
• A polar decomposition for quantum channels (with applications to bounding error propagation in quantum circuits)
• Kerdock Codes Determine Unitary 2-Designs

Cited by in corpus (8)

• Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors
• Fundamental limits of quantum error mitigation
• Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
• Generalized quantum subspace expansion
• Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?
• Operational applications of the diamond norm and related measures in quantifying the non-physicality of quantum maps
• Quantum Error Mitigation via Quantum-Noise-Effect Circuit Groups
• Quantum error mitigation for rotation symmetric bosonic codes with symmetry expansion