Optimizing the information extracted by a single qubit measurement

Abstract

We consider a quantum computation that only extracts one bit of information per $N$-qubit quantum state preparation. This is relevant for error mitigation schemes where the remainder of the system is measured to detect errors. We optimize the estimation of the expectation value of an operator by its linear decomposition into bitwise-measurable terms. We prove that optimal decompositions must be in terms of reflections with eigenvalues $\pm 1$. We find the optimal reflection decomposition of a fast-forwardable operator, and show a numerical improvement over a simple Pauli decomposition by a factor $N^{0.7}$

arXiv comment16 pages, 4 figures

References in corpus (30)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Quantum-enhanced measurements: beating the standard quantum limit
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Quantum metrology
• The theory of variational hybrid quantum-classical algorithms
• On the Power of One Bit of Quantum Information
• Hamiltonian Simulation by Qubitization
• Optimal Hamiltonian Simulation by Quantum Signal Processing
• Towards Practical Quantum Variational Algorithms
• Efficient variational quantum simulator incorporating active error minimisation
• Quantum Algorithms for Fermionic Simulations
• General parameter-shift rules for quantum gradients
• Measurement Optimization in the Variational Quantum Eigensolver Using a Minimum Clique Cover
• Efficient and Noise Resilient Measurements for Quantum Chemistry on Near-Term Quantum Computers
• Error-mitigated digital quantum simulation
• Low-cost error mitigation by symmetry verification
• Optimal Quantum Measurements of Expectation Values of Observables
• Efficient quantum measurement of Pauli operators in the presence of finite sampling error
• Near-optimal ground state preparation
• Application of fermionic marginal constraints to hybrid quantum algorithms
• Methodology for replacing indirect measurements with direct measurements
• Demonstrating Heisenberg-limited unambiguous phase estimation without adaptive measurements
• Low-depth gradient measurements can improve convergence in variational hybrid quantum-classical algorithms
• Hamiltonian tomography in an access-limited setting without state initialization
• Error mitigation via verified phase estimation
• Indirect Quantum Tomography of Quadratic Hamiltonians
• Dual-state purification for practical quantum error mitigation
• Nearly Optimal Quantum Algorithm for Estimating Multiple Expectation Values
• Noise-resilient phase estimation with randomized compiling

Cited by in corpus (12)

• Quantum Error Mitigation
• Purification-based quantum error mitigation of pair-correlated electron simulations
• A hybrid quantum algorithm to detect conical intersections
• In the shadow of the Hadamard test: Using the garbage state for good and further modifications
• Probing the limits of variational quantum algorithms for nonlinear ground states on real quantum hardware: The effects of noise
• Virtual mitigation of coherent non-adiabatic transitions by echo verification
• Hardware-efficient quantum phase estimation via local control
• Learning Density Functionals from Noisy Quantum Data
• Simulating sparse SYK model with a randomized algorithm on a trapped-ion quantum computer
• A quantum eigenvalue solver based on tensor networks
• Qudit-native measurement protocol for dynamical correlations using Hadamard tests
• End-to-End Quantum Algorithms for the Jones Polynomial