Resource-efficient Generalized Quantum Subspace Expansion
arXiv:2309.14171 · doi:10.1103/PhysRevApplied.23.054021
Abstract
Realizing practical quantum computing requires overcoming a number of computation errors and the limitation of device size, which have intensively been tackled by quantum error mitigation (QEM) these days. As a unified approach of noise-agnostic QEM, generalized quantum subspace expansion (GSE) has lately been proposed to be remarkably robust against stochastic and coherent errors, integrating quantum subspace expansion and virtual state purification. However, the requirement in GSE to perform entangled measurements between copies of the quantum states remains a significant drawback under the current situation of quantum devices with a restricted number of qubits and their connectivity. In this work, we propose ``Dual-GSE'', a resource-efficient implementation of GSE to circumvent this overhead by constructing an ansatz of error-mitigated quantum states via dual-state purification without state copies. Remarkably, the proposed method can further simulate larger quantum systems beyond the size of available quantum hardware, achieved by a suitable ansatz construction inspired by the divide-and-conquer strategy that classically reintroduces the effect of entanglement. While classically forging the entanglement comes with additional cost, the total sampling overhead can be notably reduced by reusing the same Pauli expectation values among divided-and-conquered subsystems. We comprehensively analyze the advantages and overhead of Dual-GSE and perform numerical simulations of the eight-qubit transverse-field Ising model under various setups. Our results demonstrate that Dual-GSE estimates the ground state energy with high accuracy under gate noise with low mitigation overhead and practical sampling cost.
41 pages, 32 figures
References in corpus (45)
- Supplementary information for "Quantum supremacy using a programmable superconducting processor"
- A variational eigenvalue solver on a quantum processor
- Variational Quantum Algorithms
- Quantum computational advantage using photons
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- Error mitigation for short-depth quantum circuits
- Predicting Many Properties of a Quantum System from Very Few Measurements
- The Variational Quantum Eigensolver: a review of methods and best practices
- Extending the computational reach of a noisy superconducting quantum processor
- Exact and Approximate Unitary 2-Designs: Constructions and Applications
- Efficient variational quantum simulator incorporating active error minimisation
- Quantum Error Mitigation
- Variational ansatz-based quantum simulation of imaginary time evolution
- 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
- Probabilistic error cancellation with sparse Pauli-Lindblad models on noisy quantum processors
- Characterizing large-scale quantum computers via cycle benchmarking
- Fermionic neural-network states for ab-initio electronic structure
- Gate Set Tomography
- Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
- Doubling the size of quantum simulators by entanglement forging
- Fundamental limits of quantum error mitigation
- Variational Quantum Eigensolver with Fewer Qubits
- Exponential Error Suppression for Near-Term Quantum Devices
- Decoding quantum errors with subspace expansions
- Constructing a virtual two-qubit gate by sampling single-qubit operations
- Quantum simulation with hybrid tensor networks
- Generalized quantum subspace expansion
- A theory of quantum subspace diagonalization
- Constructing Smaller Pauli Twirling Sets for Arbitrary Error Channels
- Shadow Distillation: Quantum Error Mitigation with Classical Shadows for Near-Term Quantum Processors
- Universal Sampling Lower Bounds for Quantum Error Mitigation
- Dual-state purification for practical quantum error mitigation
- Universal cost bound of quantum error mitigation based on quantum estimation theory
- Solving Quasiparticle Band Spectra of Real Solids using Neural-Network Quantum States
- Efficient quantum readout-error mitigation for sparse measurement outcomes of near-term quantum devices
- Perturbative quantum simulation
- Doubly optimal parallel wire cutting without ancilla qubits
- Characterization of entanglement on superconducting quantum computers of up to 414 qubits
- Testing Scalable Bell Inequalities for Quantum Graph States on IBM Quantum Devices
- Optimal quantum circuit cuts with application to clustered Hamiltonian simulation
- Localized Virtual Purification
- Divide-and-conquer verification method for noisy intermediate-scale quantum computation
- Quantum Circuit Cutting for Classical Shadows