Error statistics and scalability of quantum error mitigation formulas

Abstract

Quantum computing promises advantages over classical computing in many problems. Nevertheless, noise in quantum devices prevents most quantum algorithms from achieving the quantum advantage. Quantum error mitigation provides a variety of protocols to handle such noise using minimal qubit resources . While some of those protocols have been implemented in experiments for a few qubits, it remains unclear whether error mitigation will be effective in quantum circuits with tens to hundreds of qubits. In this paper, we apply statistics principles to quantum error mitigation and analyse the scaling behaviour of its intrinsic error. We find that the error increases linearly $O(\epsilon N)$ with the gate number $N$ before mitigation and sub-linearly $O({\epsilon }^{\prime }{N}^{\gamma })$ after mitigation, where $\gamma \approx 0.5$, $\epsilon$ is the error rate of a quantum gate, and ${\epsilon }^{\prime }$ is a protocol-dependent factor. The $\sqrt{N}$ scaling is a consequence of the law of large numbers, and it indicates that error mitigation can suppress the error by a larger factor in larger circuits. We propose the importance Clifford sampling as a key technique for error mitigation in large circuits to obtain this result.

References in corpus (12)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Surface codes: Towards practical large-scale quantum computation
• Robust randomized benchmarking of quantum processes
• Hybrid quantum-classical algorithms and quantum error mitigation
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Scalable error mitigation for noisy quantum circuits produces competitive expectation values
• Fast simulation of stabilizer circuits using a graph state representation
• Fundamental limits of quantum error mitigation
• Mitigating depolarizing noise on quantum computers with noise-estimation circuits
• Dual-state purification for practical quantum error mitigation
• Accelerated quantum Monte Carlo with mitigated error on noisy quantum computer
• Efficient Two-Electron Ansatz for Benchmarking Quantum Chemistry on a Quantum Computer

Cited by in corpus (9)

• Universal cost bound of quantum error mitigation based on quantum estimation theory
• Modeling the unphysical pseudomode model with physical ensembles: simulation, mitigation, and restructuring of non-Markovian quantum noise
• Localized Virtual Purification
• Polarization and Orbital Angular Momentum Encoded Quantum Toffoli Gate Enabled by Diffractive Neural Networks
• Density matrix representation of hybrid tensor networks for noisy quantum devices
• Measuring Correlation and Entanglement between Molecular Orbitals on a Trapped-Ion Quantum Computer
• Circuit-Noise-Resilient Virtual Distillation
• Prime Number Identification Demonstrated with Quantum Processors Using a New Rescaling-Based Noise Mitigation Technique
• Physics-Guided Linear Mapper for Quantum Error Mitigation