Hardware-efficient quantum annealing with error mitigation via classical shadow
arXiv:2503.22269 · doi:10.1103/stb4-wms8
Abstract
Quantum annealing (QA) is an efficient method for finding the ground-state energy of the problem Hamiltonian. However, in practical implementation, the system suffers from decoherence. On the other hand, recently, ``Localized virtual purification" (LVP) was proposed to suppress decoherence in the context of noisy intermediate-scale quantum (NISQ) devices. Suppose observables have spatially local support in the lattice. In that case, the requirement for LVP is to calculate the expectation value with a reduced density matrix on a portion of the total system. In this work, we propose a method to mitigate decoherence errors in QA using LVP. The key idea is to use the so-called classical shadow method to construct the reduced density matrix. Thanks to the CS, unlike the previous schemes to mitigate decoherence error for QA, we do not need either two-qubit gates or mid-circuit measurements, which means that our method is hardware-efficient.
8 pages, 2 figures
References in corpus (75)
- Quantum Computing in the NISQ era and beyond
- A variational eigenvalue solver on a quantum processor
- Variational Quantum Algorithms
- The theory of variational hybrid quantum-classical algorithms
- A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem
- Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing
- Simulated Quantum Computation of Molecular Energies
- Error mitigation for short-depth quantum circuits
- Predicting Many Properties of a Quantum System from Very Few Measurements
- An atom-by-atom assembler of defect-free arbitrary 2d atomic arrays
- Extending the computational reach of a noisy superconducting quantum processor
- Hartree-Fock on a superconducting qubit quantum computer
- Quantum Annealing and Analog Quantum Computation
- Quantum computing with atomic qubits and Rydberg interactions: Progress and challenges
- Lieb-Schultz-Mattis in Higher Dimensions
- Efficient variational quantum simulator incorporating active error minimisation
- Quantum Error Mitigation
- Spectral Gap and Exponential Decay of Correlations
- Practical Quantum Error Mitigation for Near-Future Applications
- Hybrid quantum-classical algorithms and quantum error mitigation
- Hybrid Quantum-Classical Hierarchy for Mitigation of Decoherence and Determination of Excited States
- Robustness of adiabatic quantum computation
- Theory of variational quantum simulation
- Lieb-Robinson Bounds and the Exponential Clustering Theorem
- Demonstration of qubit operations below a rigorous fault tolerance threshold with gate set tomography
- Mathematical Foundation of Quantum Annealing
- Bounds for the adiabatic approximation with applications to quantum computation
- Low-cost error mitigation by symmetry verification
- Error-mitigated digital quantum simulation
- Variational quantum simulation of general processes
- Experimental investigations of the dipolar interactions between single Rydberg atoms
- Adiabatic Quantum Computation in Open Systems
- Single-qubit-gate error below 10^-4 in a trapped ion
- Error corrected quantum annealing with hundreds of qubits
- Consistency of the Adiabatic Theorem
- Quantum Speedup by Quantum Annealing
- Decoherence in adiabatic quantum computation
- Robust shadow estimation
- Exponential Error Suppression for Near-Term Quantum Devices
- Quantum error mitigation as a universal error-minimization technique: applications from NISQ to FTQC eras
- Quantum annealing with antiferromagnetic fluctuations
- Noise resistance of adiabatic quantum computation using random matrix theory
- Nonstoquastic Hamiltonians and Quantum Annealing of an Ising Spin Glass
- Mitigating realistic noise in practical noisy intermediate-scale quantum devices
- Decoherence in a scalable adiabatic quantum computer
- Tunneling and speedup in quantum optimization for permutation-symmetric problems
- Generalized quantum subspace expansion
- Exponential Speedup of Quantum Annealing by Inhomogeneous Driving of the Transverse Field
- Mid-circuit measurements on a single species neutral alkali atom quantum processor
- Error mitigation via verified phase estimation
- Optimal resource cost for error mitigation
- Shadow Distillation: Quantum Error Mitigation with Classical Shadows for Near-Term Quantum Processors
- Evaluating energy differences on a quantum computer with robust phase estimation
- Quantum annealing of the -spin model under inhomogeneous transverse field driving
- Self-consistent tomography of the state-measurement Gram matrix
- Error-Mitigated Quantum Metrology via Virtual Purification
- The quantum adiabatic search with decoherence in the instantaneous energy eigenbasis
- Variational optimization of the quantum annealing schedule for the Lechner-Hauke-Zoller scheme
- Optimal quantum annealing: A variational shortcut to adiabaticity approach
- Relationship between costs for quantum error mitigation and non-Markovian measures
- Estimating expectation values using approximate quantum states
- Variationally Scheduled Quantum Simulation
- Mitigating algorithmic errors in quantum optimization through energy extrapolation
- Necessary Adiabatic Run Times in Quantum Optimization
- Ensemble-learning error mitigation for variational quantum shallow-circuit classifiers
- Quantum annealing with capacitive-shunted flux qubits
- Localized Virtual Purification
- Quantum annealing with twisted fields
- Generalized Adiabatic Theorems: Quantum Systems Driven by Modulated Time-Varying Fields
- Enhancing quantum annealing performance by a degenerate two-level system
- Scalable evaluation of quantum-circuit error loss using Clifford sampling
- Pulsed quantum annealing
- Virtual mitigation of coherent non-adiabatic transitions by echo verification
- How to experimentally evaluate the adiabatic condition for quantum annealing
- Hardware-efficient quantum annealing with error mitigation via classical shadow