Quantum circuit cutting with maximum-likelihood tomography

Michael A Perlin,Zain H Saleem,Martin Suchara,James C Osborn

doi:10.1038/s41534-021-00390-6

Abstract

We introduce maximum-likelihood fragment tomography (MLFT) as an improved circuit cutting technique for running clustered quantum circuits on quantum devices with a limited number of qubits. In addition to minimizing the classical computing overhead of circuit cutting methods, MLFT finds the most likely probability distribution for the output of a quantum circuit, given the measurement data obtained from the circuit’s fragments. We demonstrate the benefits of MLFT for accurately estimating the output of a fragmented quantum circuit with numerical experiments on random unitary circuits. Finally, we show that circuit cutting can estimate the output of a clustered circuit with higher fidelity than full circuit execution, thereby motivating the use of circuit cutting as a standard tool for running clustered circuits on quantum hardware.

Highlights

The advent of noisy intermediate-scale quantum (NISQ) technologies[1] makes quantum processors with increasing numbers of qubits available to the quantum computing community for experimentation
In the spirit of maximum-likelihood state tomography (MLST)[23], one would like to determine the ‘most likely’ probability distribution that is consistent with available fragment data. We find this “most likely” probability distribution by generalizing MLST and introducing maximum-likelihood fragment tomography (MLFT), the use of which guarantees that reconstructed probability distributions are non-negative and normalized
We have introduced improved circuit cutting methods by minimizing associated classical computing costs, and by using MLFT to reconstruct the “most likely” probability distribution defined by a quantum circuit, given the measurement data obtained from its fragments

Summary

INTRODUCTION

The advent of noisy intermediate-scale quantum (NISQ) technologies[1] makes quantum processors with increasing numbers of qubits available to the quantum computing community for experimentation. The above splitting method relies on the capability to project qubit n onto state jbi while preserving phase information Such capability is possible when running classical simulations of a circuit, but is not possible on quantum computing hardware. In a circuit with K cuts, this postprocessing reduces the number of tensor products that must be computed during recombination from 16K to 4K, which is an case of channels (processes) with mixed (quantum/classical) inputs and outputs. 16 involves 8K tensor products, rather than 16K, because it consolidates “measurement” condigenerally have Qi “quantum input” and Qo “quantum output” qubits at the locations of cuts We refer to these inputs and outputs as “quantum” because characterizing the fragment for circuit reconstruction will require performing full quantum tions, but not “preparation” conditions, which is equivalent to tomography on the corresponding degrees of freedom.

RESULTS

DISCUSSION

CODE AVAILABILITY