Process Tomography on a 7-Qubit Quantum Processor via Tensor Network Contraction Path Finding

TL;DR

This paper introduces an efficient tensor network-based quantum process tomography method tailored for a 7-qubit IBM quantum processor, significantly reducing measurement requirements while accurately reconstructing quantum channels.

Contribution

It combines tensor network contraction path finding with unsupervised learning for scalable quantum process tomography on arbitrary topologies, extending beyond linear circuits.

Findings

Achieved 0.89 fidelity in process reconstruction

Reduced measurements by over five orders of magnitude compared to traditional QPT

Successfully characterized a 7-qubit quantum process on IBM hardware

Abstract

Quantum process tomography (QPT), where a quantum channel is reconstructed through the analysis of repeated quantum measurements, is an important tool for validating the operation of a quantum processor. We detail the combined use of an existing QPT approach based on tensor networks (TNs) and unsupervised learning with TN contraction path finding algorithms in order to use TNs of arbitrary topologies for reconstruction. Experiments were conducted on the 7-qubit IBM Quantum Falcon Processor ibmq_casablanca, where we demonstrate this technique by matching the topology of the tensor networks used for reconstruction with the topology of the processor, allowing us to extend past the characterisation of linear nearest neighbour circuits. Furthermore, we conduct single-qubit gate set tomography (GST) on each individual qubit to correct for separable errors during the state preparation and measurement phases of QPT, which are separate from the channel under consideration but may negatively impact the quality of its reconstruction. We are able to report a fidelity of 0.89 against the ideal unitary channel of a single-cycle random quantum circuit performed on ibmq_casablanca, after obtaining just $1.1 \times 10^5$ measurements for the reconstruction of this 7-qubit process. This represents more than five orders of magnitude fewer total measurements than the number needed to conduct full, traditional QPT on a 7-qubit process.