Coherence-Sensitive Readout Models for Quantum Devices: Beyond the Classical Assignment Matrix

TL;DR

This paper introduces a generalized readout error model for quantum devices that accounts for quantum coherences, extending beyond classical models that assume measurement noise is purely classical and diagonal in the measurement basis.

Contribution

It derives a comprehensive framework incorporating quantum coherences into measurement error models, capturing interference effects ignored by traditional classical assignment matrices.

Findings

The observed measurement probabilities depend on both populations and coherences.

Classical models are insufficient when POVM elements have off-diagonal components.

The coherence-response matrix quantifies accessible information about quantum coherences.

Abstract

Readout error models for noisy quantum devices almost universally assume that measurement noise is classical: the measurement statistics are obtained from the ideal computational-basis populations by a column-stochastic assignment matrix $A$. This description is equivalent to assuming that the effective positive-operator-valued measurement (POVM) is diagonal in the measurement basis, and therefore completely insensitive to quantum coherences. We relax this assumption and derive a fully general expression for the observed measurement probabilities under arbitrary completely positive trace-preserving (CPTP) noise preceding a computational-basis measurement. Writing the ideal post-circuit stat $\tilde{\rho}$ in terms of its populations $x$ and coherences $y$, we show that the observed probability vector $z$ satisfies $z = A x + C y$, where $A$ is the familiar classical assignment matrix and $C$ is a coherence-response matrix constructed from the off-diagonal matrix elements of the effective POVM in the computational basis. The classical model $z = A x$ arises if and only if all POVM elements are diagonal; in this sense $C$ quantifies accessible information about coherent readout distortions and interference between computational-basis states, all of which are invisible to models that retain only $A$. This work therefore provides a natural, fully general framework for coherence-sensitive readout modeling on current and future quantum devices.