Error mitigation and quantum-assisted simulation in the error corrected regime

Abstract

A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations to a universal set by the addition of `magic' quantum states. In this context, we develop a general framework to discuss the value of the available, non-ideal magic resources, relative to those ideally required. We single out a quantity, the Quantum-assisted Robustness of Magic (QRoM), which measures the overhead of simulating the ideal resource with the non-ideal ones through quasiprobability-based methods. This extends error mitigation techniques, originally developed for Noisy Intermediate Scale Quantum (NISQ) devices, to the case where qubits are logically encoded. The QRoM shows how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit and enables the construction of explicit protocols, interpolating between classical simulation and an ideal quantum computer.

References in corpus (6)

• Hybrid quantum-classical algorithms and quantum error mitigation
• Restrictions on Transversal Encoded Quantum Gate Sets
• Application of a resource theory for magic states to fault-tolerant quantum computing
• Magic state distillation with low overhead
• Error mitigation for universal gates on encoded qubits
• Comparative Study of Sampling-Based Simulation Costs of Noisy Quantum Circuits

Cited by in corpus (12)

• Quantum Error Mitigation
• Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors
• Fundamental limits of quantum error mitigation
• Error mitigation for universal gates on encoded qubits
• Generalized quantum subspace expansion
• Error statistics and scalability of quantum error mitigation formulas
• Error Suppression for Arbitrary-Size Black Box Quantum Operations
• Information recoverability of noisy quantum states
• Quantum Error Mitigation via Quantum-Noise-Effect Circuit Groups
• Mitigating Quantum Errors via Truncated Neumann Series
• Quantum error mitigation for rotation symmetric bosonic codes with symmetry expansion
• Automated quantum error mitigation based on probabilistic error reduction