Overlapped grouping measurement: A unified framework for measuring quantum states

Abstract

Quantum algorithms designed for realistic quantum many-body systems, such as chemistry and materials, usually require a large number of measurements of the Hamiltonian. Exploiting different ideas, such as {importance sampling,} observable compatibility, or classical shadows of quantum states, different advanced measurement schemes have been proposed to greatly reduce the large measurement cost. Yet, the underline cost reduction mechanisms seem distinct from each other, and how to systematically find the optimal scheme remains a critical challenge. Here, we address this challenge by proposing a unified framework of quantum measurements, incorporating advanced measurement methods as special cases. Our framework allows us to introduce a general scheme~ -- ~overlapped grouping measurement, which simultaneously exploits the advantages of most existing methods. An intuitive understanding of the scheme is to partition the measurements into overlapped groups with each one consisting of compatible measurements. We provide explicit grouping strategies and numerically verify its performance for different molecular Hamiltonians with up to 16 qubits. Our numerical result shows significant improvements over existing schemes. Our work paves the way for efficient quantum measurement and fast quantum processing with current and near-term quantum devices.

arXiv comment6 figures, 5 tables

References in corpus (64)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Barren plateaus in quantum neural network training landscapes
• The theory of variational hybrid quantum-classical algorithms
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• Error mitigation for short-depth quantum circuits
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Many-body quantum state tomography with neural networks
• Scalable Quantum Simulation of Molecular Energies
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Hartree-Fock on a superconducting qubit quantum computer
• Towards Practical Quantum Variational Algorithms
• Quantum Approximate Optimization Algorithm: Performance, Mechanism, and Implementation on Near-Term Devices
• Efficient variational quantum simulator incorporating active error minimisation
• Quantum optimization using variational algorithms on near-term quantum devices
• 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
• Variational Quantum Computation of Excited States
• Robust determination of molecular spectra on a quantum processor
• Theory of variational quantum simulation
• Quantum chemistry calculations on a trapped-ion quantum simulator
• Cloud Quantum Computing of an Atomic Nucleus
• Mitigating measurement errors in multi-qubit experiments
• Reconstructing quantum states with generative models
• Subspace-search variational quantum eigensolver for excited states
• Measurement Optimization in the Variational Quantum Eigensolver Using a Minimum Clique Cover
• Low Depth Quantum Simulation of Electronic Structure
• Efficient and Noise Resilient Measurements for Quantum Chemistry on Near-Term Quantum Computers
• Learning-based quantum error mitigation
• Fermionic neural-network states for ab-initio electronic structure
• Variational quantum simulation of general processes
• Variational Fast Forwarding for Quantum Simulation Beyond the Coherence Time
• Efficient estimation of Pauli observables by derandomization
• Digital zero noise extrapolation for quantum error mitigation
• Variational algorithms for linear algebra
• Efficient quantum measurement of Pauli operators in the presence of finite sampling error
• Quantum simulations of materials on near-term quantum computers
• Fermionic partial tomography via classical shadows
• Optimizing Variational Quantum Algorithms using Pontryagin's Minimum Principle
• Variational Quantum Eigensolver with Fewer Qubits
• Robust shadow estimation
• Quantum Overlapping Tomography
• Application of fermionic marginal constraints to hybrid quantum algorithms
• Decoding quantum errors with subspace expansions
• Measurement reduction in variational quantum algorithms
• Experimental Estimation of Quantum State Properties from Classical Shadows
• Mitigating realistic noise in practical noisy intermediate-scale quantum devices
• Quantum simulation with hybrid tensor networks
• Minimizing State Preparations in Variational Quantum Eigensolver by Partitioning into Commuting Families
• Precise measurement of quantum observables with neural-network estimators
• Experimental quantum state measurement with classical shadows
• Generalized swap networks for near-term quantum computing
• Variational Hamiltonian Diagonalization for Dynamical Quantum Simulation
• Quantum computed moments correction to variational estimates
• Decision Diagrams for Quantum Measurements with Shallow Circuits
• Perturbative quantum simulation
• Adaptive Pauli Shadows for Energy Estimation
• Deterministic improvements of quantum measurements with grouping of compatible operators, non-local transformations, and covariance estimates

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