Decision Diagrams for Quantum Measurements with Shallow Circuits

Abstract

We consider the problem of estimating quantum observables on a collection of qubits, given as a linear combination of Pauli operators, with shallow quantum circuits consisting of single-qubit rotations. We introduce estimators based on randomised measurements, which use decision diagrams to sample from probability distributions on measurement bases. This approach generalises previously known uniform and locally-biased randomised estimators. The decision diagrams are constructed given target quantum operators and can be optimised considering different strategies. We show numerically that the estimators introduced here can produce more precise estimates on some quantum chemistry Hamiltonians, compared to previously known randomised protocols and Pauli grouping methods.

arXiv commentOmitting labels of vertices in the figures due to the differences of outputs by pdflatex from LuaLaTeX. No changes in contents. 19 pages and 7 figures

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Cited by in corpus (16)

• The randomized measurement toolbox
• Emerging quantum computing algorithms for quantum chemistry
• Fermionic partial tomography via classical shadows
• Classical Shadows With Noise
• Exact and efficient Lanczos method on a quantum computer
• Overlapped grouping measurement: A unified framework for measuring quantum states
• Classical shadows with Pauli-invariant unitary ensembles
• Adaptive estimation of quantum observables
• Fluid fermionic fragments for optimizing quantum measurements of electronic Hamiltonians in the variational quantum eigensolver
• Improving quantum measurements by introducing "ghost" Pauli products
• Decision Diagrams for Quantum Measurements with Shallow Circuits
• Gradient-descent quantum process tomography by learning Kraus operators
• Towards a variational Jordan-Lee-Preskill quantum algorithm
• Measurement optimization of variational quantum simulation by classical shadow and derandomization
• Testing Scalable Bell Inequalities for Quantum Graph States on IBM Quantum Devices
• Guaranteed efficient energy estimation of quantum many-body Hamiltonians using ShadowGrouping