Ensemble Engineering to Overcome Destructive Cancellation in Quantum Measurements

Abstract

On noisy intermediate-scale quantum (NISQ) devices, expectation values of many observables are obtained through sampling-based approximations to trace-like quantities. A central limitation of this approach is destructive cancellation under near-uniform ensembles, which can render physically relevant signals effectively unresolvable. Here we show that this limitation is not simply statistical, but reflects a structural mismatch between ensemble weights and the operator-dependent sign structure of the measured correlator. We introduce a general framework for mitigating this effect through quantum ensemble engineering, in which the sampling distribution is encoded directly in the prepared quantum state. By reformulating correlators in a basis-resolved representation, we make the origin of cancellation explicit and derive strategies for aligning ensemble weights with operator structure. We realize this approach using two complementary circuit constructions: a Grover-type amplitude amplification protocol that provides a structure-aligned benchmark, and an oracle-free shallow circuit designed for near-term hardware constraints. Using the infinite-temperature correlation function as a representative setting, we combine noiseless numerical simulations with demonstrations on IBM Quantum hardware using circuits with up to 20 qubits, showing that engineered ensembles expose operator-resolved contributions that are strongly suppressed under uniform averaging. We identify a practical tradeoff between amplification strength and noise robustness, extend the framework to multi-qubit diagonal observables, and outline a path toward non-diagonal generalizations. These results position ensemble engineering as a new tool for improving measurement efficiency in near-term quantum algorithms.

22 pages, 13 figures

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