aiqbench analysis
This paper advances the theoretical framework for simulating quantum systems by introducing "readout-aware" error analysis, directly addressing how approximation errors in Heisenberg picture propagation impact expectation values. By establishing exact identities linking discarded operator components to simulation inaccuracies, it provides a rigorous basis for improving the fidelity of classical algorithms used to model quantum dynamics. This work is essential for researchers developing high-precision quantum simulators and validating near-term quantum hardware performance.
A Readout-Aware Theory of Approximate Heisenberg Propagation
arXiv:2610.26222v1 Announce Type: new Abstract: Classical methods for computing quantum expectation values often propagate observables in the Heisenberg picture. To remain tractable, these methods rely on approximations that discard operator components during evolution. Yet the magnitude of these components alone does not determine the resulting expectation-value error, which also depends on their subsequent evolution and the input state. We develop \emph{generalized Pauli propagation}, a common algebraic framework encompassing Pauli propagation, Lie-algebraic simulation, and Krylov subspace methods. Using weighted commutator graphs, we derive exact identities that relate approximation errors to the signed contributions of omitted and discarded operator components. Our central result establishes \emph{delayed observability}, identifying conditions under which these contributions vanish at low orders in propagation time. We use this structure to develop finite-order error estimates and state-dependent selection rules. We further prove that retaining the symmetry-preserving part of a weak perturbation eliminates first-order expectation-value errors under suitable symmetry conditions. By revealing how approximation errors affect the desired expectation value, our framework provides a basis for more informative error analysis and the development of readout-aware simulation strategies.
Abstract:Classical methods for computing quantum expectation values often propagate observables in the Heisenberg picture. To remain tractable, these methods rely on approximations that discard operator components during evolution. Yet the magnitude of these components alone does not determine the resulting expectation-value error, which also depends on their subsequent evolution and the input state. We develop \emph{generalized Pauli propagation}, a common algebraic framework encompassing Pauli propagation, Lie-algebraic simulation, and Krylov subspace methods. Using weighted commutator graphs, we derive exact identities that relate approximation errors to the signed contributions of omitted and discarded operator components. Our central result establishes \emph{delayed observability}, identifying conditions under which these contributions vanish at low orders in propagation time. We use this structure to develop finite-order error estimates and state-dependent selection rules. We further prove that retaining the symmetry-preserving part of a weak perturbation eliminates first-order expectation-value errors under suitable symmetry conditions. By revealing how approximation errors affect the desired expectation value, our framework provides a basis for more informative error analysis and the development of readout-aware simulation strategies.
arXiv:2610.26222 [quant-ph]
(or arXiv:2610.26222v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2610.26222 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 261 words