Hybrid quantum-classical optimization algorithms represent one of the most promising application for near-term quantum computers. In these algorithms the goal is to optimize an observable quantity with respect to some classical parameters, using feedback from measurements performed on the quantum device. Here we study the problem of estimating the gradient of the function to be optimized directly from quantum measurements, generalizing and simplifying some approaches present in the literature, such as the so-called parameter-shift rule. We derive a mathematically exact formula that provides a stochastic algorithm for estimating the gradient of any multi-qubit parametric quantum evolution, without the introduction of ancillary qubits or the use of Hamiltonian simulation techniques. The gradient measurement is possible when the underlying device can realize all Pauli rotations in the expansion of the Hamiltonian whose coefficients depend on the parameter. Our algorithm continues to work, although with some approximations, even when all the available quantum gates are noisy, for instance due to the coupling between the quantum device and an unknown environment.

Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule / Banchi, Leonardo; Crooks, Gavin E.. - In: QUANTUM. - ISSN 2521-327X. - ELETTRONICO. - 5:(2021), pp. 386-399. [10.22331/q-2021-01-25-386]

Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule

Banchi, Leonardo
;
2021

Abstract

Hybrid quantum-classical optimization algorithms represent one of the most promising application for near-term quantum computers. In these algorithms the goal is to optimize an observable quantity with respect to some classical parameters, using feedback from measurements performed on the quantum device. Here we study the problem of estimating the gradient of the function to be optimized directly from quantum measurements, generalizing and simplifying some approaches present in the literature, such as the so-called parameter-shift rule. We derive a mathematically exact formula that provides a stochastic algorithm for estimating the gradient of any multi-qubit parametric quantum evolution, without the introduction of ancillary qubits or the use of Hamiltonian simulation techniques. The gradient measurement is possible when the underlying device can realize all Pauli rotations in the expansion of the Hamiltonian whose coefficients depend on the parameter. Our algorithm continues to work, although with some approximations, even when all the available quantum gates are noisy, for instance due to the coupling between the quantum device and an unknown environment.
2021
5
386
399
Banchi, Leonardo; Crooks, Gavin E.
File in questo prodotto:
File Dimensione Formato  
q-2021-01-25-386.pdf

accesso aperto

Tipologia: Pdf editoriale (Version of record)
Licenza: Open Access
Dimensione 1.34 MB
Formato Adobe PDF
1.34 MB Adobe PDF

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/1227060
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 57
  • ???jsp.display-item.citation.isi??? 49
social impact