A hybrid quantum-classical algorithm for Bayes-optimal quantum state discrimination using the source code

TL;DR

This paper introduces a hybrid quantum-classical algorithm that reformulates quantum state discrimination problems using source code access, enabling efficient solutions for complex quantum tasks.

Contribution

It presents a novel reduction of the semidefinite program for state discrimination using source code, facilitating scalable quantum data processing.

Findings

Efficiently constructs reduced SDP from quantum source code.

Characterizes optimal identification in quantum changepoint problems.

Enables tractable quantum error classification for large systems.

Abstract

Quantum state discrimination is a fundamental primitive in quantum information processing, underpinning tasks in quantum communication, sensing, and learning. We consider the general Bayes framework, as introduced by Helstrom, for state discrimination when, instead of a classical description of the candidate states, one has access to their \emph{source code}: the quantum circuit that prepares them. We show that the semidefinite program (SDP) for the discrimination problem can be reformulated in terms of the Gram matrix of these states, reducing the SDP variable dimensions from $dL$ to $NL$, where $d$ is the Hilbert space dimension, $N$ is the number of candidate states, and $L$ is the number of possible guesses. Importantly, we further introduce a quantum pre-processing procedure which efficiently constructs the reduced semidefinite program from the source code, enabling our method to operate directly on quantum data. We consider two applications. First, we characterize the optimal identifications for quantum changepoint problems under several reward structures, including multiple-changepoint settings that were previously computationally inaccessible. Second, we consider a quantum error classification problem and show how our reduction makes it tractable for systems of hundreds of qubits.