Rigorous quantum state tomography for distributed quantum computing

TL;DR

This paper introduces a distributed quantum state tomography protocol that enables accurate quantum state estimation across multiple processors using only local operations and classical communication, with rigorous error bounds.

Contribution

It extends projected least-squares tomography to distributed systems without requiring remote entanglement as a primitive, providing explicit error bounds and validation through simulations.

Findings

Non-asymptotic trace-norm error bounds with exponential dependence on number of nodes.

Certified error bounds for entanglement negativity estimation.

Numerical validation for systems up to seven qubits across multiple devices.

Abstract

Distributed quantum computing offers a promising approach to scaling quantum devices by networking multiple quantum processors. We present a quantum state tomography protocol tailored for distributed quantum computers that avoids assuming remote entanglement as a primitive resource. The protocol extends projected least-squares (PLS) tomography based on projective 2-designs to systems composed of multiple quantum processors, using only local operations within each processor and classical communication between nodes. Assuming entanglement within each individual quantum processor is trusted, the protocol can be executed using mutually unbiased bases. We derive rigorous, non-asymptotic trace-norm error bounds for the PLS estimator, with explicit exponential dependence on the number of nodes. In addition, we establish certified error bounds for estimating entanglement negativity from the PLS estimator. Numerical simulations for systems of up to seven qubits distributed across several devices validate the theoretical error bounds.