Mitigating realistic noise in practical noisy intermediate-scale quantum devices

Abstract

Quantum error mitigation (QEM) is vital for noisy intermediate-scale quantum (NISQ) devices. While most conventional QEM schemes assume discrete gate-based circuits with noise appearing either before or after each gate, the assumptions are inappropriate for describing realistic noise that may have strong gate-dependence and complicated nonlocal effects, and general computing models such as analog quantum simulators. To address these challenges, we first extend the scenario, where each computation process, being either digital or analog, is described by a continuous time evolution. For noise from imperfections of the engineered Hamiltonian or additional noise operators, we show it can be effectively suppressed by a novel stochastic QEM method. Since our method only assumes accurate single qubit controls, it is applicable to all digital quantum computers and various analog simulators. Meanwhile, errors in the mitigation procedure can be suppressed by leveraging the Richardson extrapolation method. As we numerically test our method with various Hamiltonians under energy relaxation and dephasing noise and digital quantum circuits with additional two-qubit crosstalk, we show an improvement of simulation accuracy by two orders. We assess the resource cost of our scheme and conclude the feasibility of accurate quantum computing with NISQ devices.

References in corpus (71)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Simulation
• Probing many-body dynamics on a 51-atom quantum simulator
• A Quantum Engineer's Guide to Superconducting Qubits
• Error mitigation for short-depth quantum circuits
• Microwave photonics with superconducting quantum circuits
• Scalable multi-particle entanglement of trapped ions
• Quantum many-body systems out of equilibrium
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Dynamical decoupling and noise spectroscopy with a superconducting flux qubit
• Extending the computational reach of a noisy superconducting quantum processor
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• Quantum computing with atomic qubits and Rydberg interactions: Progress and challenges
• Quantum simulation of frustrated magnetism in triangular optical lattices
• Efficient variational quantum simulator incorporating active error minimisation
• High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Quantum spin dynamics and entanglement generation with hundreds of trapped ions
• Practical Quantum Error Mitigation for Near-Future Applications
• Direct observation of dynamical quantum phase transitions in an interacting many-body system
• High-Fidelity Universal Gate Set for ${}^9$Be${}^{+}$ Ion Qubits
• Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
• Experimental Comparison of Two Quantum Computing Architectures
• Procedure for systematically tuning up crosstalk in the cross resonance gate
• A blueprint for demonstrating quantum supremacy with superconducting qubits
• Robust determination of molecular spectra on a quantum processor
• Observation of antiferromagnetic correlations in the Hubbard model with ultracold atoms
• Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
• Decoherence of flux qubits due to 1/f flux noise
• Experimental Test of Quantum Jarzynski Equality with a Trapped Ion System
• Cloud Quantum Computing of an Atomic Nucleus
• Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits
• Verified Quantum Information Scrambling
• Practical characterization of quantum devices without tomography
• Dephasing of a superconducting qubit induced by photon noise
• Can One Trust Quantum Simulators?
• Demonstration of Universal Parametric Entangling Gates on a Multi-Qubit Lattice
• Controlling fast transport of cold trapped ions
• Error-mitigated digital quantum simulation
• Low-cost error mitigation by symmetry verification
• Experimental demonstration of fault-tolerant state preparation with superconducting qubits
• Quantum simulation of open-system dynamical maps with trapped ions
• Process verification of two-qubit quantum gates by randomized benchmarking
• Mitigation of readout noise in near-term quantum devices by classical post-processing based on detector tomography
• Demonstration of fidelity improvement using dynamical decoupling with superconducting qubits
• Magnet field sensing beyond the standard quantum limit under the effect of decoherence
• Dephasing of a superconducting flux qubit
• Interacting two-level defects as sources of fluctuating high-frequency noise in superconducting circuits
• Calculating critical temperatures for ferromagnetic order in two-dimensional materials
• Detector Tomography on IBM 5-qubit Quantum Computers and Mitigation of Imperfect Measurement
• Error Mitigation by Symmetry Verification on a Variational Quantum Eigensolver
• Decoding quantum errors with subspace expansions
• Digital-Analog Quantum Computation
• Coherent coupled qubits for quantum annealing
• Digital-Analog Quantum Simulations with Superconducting Circuits
• Fermion-Fermion Scattering in Quantum Field Theory with Superconducting Circuits
• Phase Transitions in the Spin-Half J_1--J_2 Model
• Monte-Carlo study of the reorientation transition in Heisenberg models with dipole interactions
• Recovering noise-free quantum observables
• Fluctuations From Edge Defects in Superconducting Resonators
• Learning the dynamics of open quantum systems from their steady states
• Quantum-classical simulation of two-site dynamical mean-field theory on noisy quantum hardware
• Independent, extensible control of same-frequency superconducting qubits by selective broadcasting
• Digital-analog quantum algorithm for the quantum Fourier transform
• Theory of magnetic order in the three-dimensional spatially anisotropic Heisenberg model
• Prethermalization and dynamical transition in an isolated trapped ion spin chain
• Probing individual tunneling fluctuators with coherently controlled tunneling systems
• Quantum Zeno effect with a superconducting qubit
• Understanding analog quantum simulation dynamics in coupled ion-trap qubits

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• Variational Quantum Algorithms
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• Decoherence predictions in a superconductive quantum device using the steepest-entropy-ascent quantum thermodynamics framework
• Performance Analysis of Multi-Angle QAOA for p > 1
• Experimental Bayesian estimation of quantum state preparation, measurement, and gate errors in multi-qubit devices
• Optimized noise-assisted simulation of the Lindblad equation with time-dependent coefficients on a noisy quantum processor
• Continuous-time dynamics and error scaling of noisy highly-entangling quantum circuits
• Quantum Error Mitigation via Quantum-Noise-Effect Circuit Groups
• Probing spectral features of quantum many-body systems with quantum simulators
• Mitigating Quantum Errors via Truncated Neumann Series
• Random coordinate descent: a simple alternative for optimizing parameterized quantum circuits
• Divide-and-conquer verification method for noisy intermediate-scale quantum computation
• Quantum error cancellation in photonic systems -- undoing photon losses
• Increasing the Measured Effective Quantum Volume with Zero Noise Extrapolation
• Qubit fidelity under stochastic Schrödinger equations driven by colored noise
• Machine learning of quantum channels on NISQ devices
• Quantum error mitigation in the regime of high noise using deep neural network: Trotterized dynamics
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• Quantum error mitigation for rotation symmetric bosonic codes with symmetry expansion
• Noisy Probabilistic Error Cancellation and Generalized Physical Implementability
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• Detecting and Eliminating Quantum Noise of Quantum Measurements
• Error Mitigation Thresholds in Noisy Random Quantum Circuits
• Hardware-efficient quantum annealing with error mitigation via classical shadow
• Noise tolerance via reinforcement: Learning a reinforced quantum dynamics
• Efficient Simulation of Open Quantum Systems on NISQ Trapped-Ion Hardware