Ptychographic estimation of pure multiqubit states in a quantum device

TL;DR

This paper explores quantum ptychography for estimating pure multiqubit states on IBM quantum processors, demonstrating high fidelity results with optimized measurements and discussing scalability for noisy devices.

Contribution

It introduces a ptychographic estimation method tailored for multiqubit states, utilizing efficient measurements and approximate Fourier transforms to improve scalability on noisy quantum hardware.

Findings

High estimation fidelities achieved for up to four qubits

Separable unitaries work well for separable states

Approximate QFT enhances scalability on noisy devices

Abstract

Quantum ptychography is a method for estimating an unknown pure quantum state by subjecting it to overlapping projections, each one followed by a projective measurement on a single prescribed basis. Here, we present a comprehensive study of this method applied for estimating $n$-qubit states in a circuit-based quantum computer, including numerical simulations and experiments carried out on an IBM superconducting quantum processor. The intermediate projections are implemented through Pauli measurements on one qubit at a time, which sets the number of ptychographic circuits to $3n$ (in contrast to the $3^n$ circuits for standard Pauli tomography); the final projective measurement in the computational basis is preceded by the quantum Fourier transform (QFT). Due to the large depth and number of two-qubit gates of the QFT circuit, which is unsuitable for noisy devices, we also test the approximate QFT (AQFT) and separable unitary operations. Using the QFT and AQFT of degree $2$, we obtained high estimation fidelities in all tests with separable and entangled states for up to three and four qubits, respectively; on the other hand, the separable unitaries in this scenario provided good estimations only for separable states, in general. Our results compare favorably with recent results in the literature and we discuss further alternatives to make the ptychographic method scalable for the current noisy devices.