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 (46)

• 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
• Surface codes: Towards practical large-scale quantum computation
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• The theory of variational hybrid quantum-classical algorithms
• Improved Simulation of Stabilizer Circuits
• Error mitigation for short-depth quantum circuits
• Extending the computational reach of a noisy superconducting quantum processor
• Robust randomized benchmarking of quantum processes
• Hartree-Fock on a superconducting qubit quantum computer
• Determining eigenstates and thermal states on a quantum computer using quantum imaginary time evolution
• Exact and Approximate Unitary 2-Designs: Constructions and Applications
• Hybrid quantum-classical algorithms and quantum error mitigation
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Robust determination of molecular spectra on a quantum processor
• Cloud Quantum Computing of an Atomic Nucleus
• Single ion-qubit exceeding one hour coherence time
• Quantum walks on a programmable two-dimensional 62-qubit superconducting processor
• Error-mitigated digital quantum simulation
• Low-cost error mitigation by symmetry verification
• Learning-based quantum error mitigation
• Virtual Distillation for Quantum Error Mitigation
• Unbiasing Fermionic Quantum Monte Carlo with a Quantum Computer
• Scalable error mitigation for noisy quantum circuits produces competitive expectation values
• Digital zero noise extrapolation for quantum error mitigation
• Asymmetric quantum error correcting codes
• 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
• Resource Efficient Zero Noise Extrapolation with Identity Insertions
• Quantum computation with realistic magic state factories
• Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
• Correcting coherent errors with surface codes
• Quantum computation with universal error mitigation on superconducting quantum processor
• Error-Mitigated Quantum Gates Exceeding Physical Fidelities in a Trapped-Ion System
• Simple Mitigation of Global Depolarizing Errors in Quantum Simulations
• Error mitigation for universal gates on encoded qubits
• Error mitigation via verified phase estimation
• Dual-state purification for practical quantum error mitigation
• A hybrid quantum-classical approach to mitigating measurement errors
• QuESTlink -- Mathematica embiggened by a hardware-optimised quantum emulator
• Error mitigation and quantum-assisted simulation in the error corrected regime
• Accelerated quantum Monte Carlo with mitigated error on noisy quantum computer
• Efficient Two-Electron Ansatz for Benchmarking Quantum Chemistry on a Quantum Computer
• Scalable evaluation of quantum-circuit error loss using Clifford sampling

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