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

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.

arXiv comment14 pages, 8 figures

References in corpus (25)

• Quantum Computing in the NISQ era and beyond
• A variational eigenvalue solver on a quantum processor
• Barren plateaus in quantum neural network training landscapes
• Quantum Circuit Learning
• Parameterized quantum circuits as machine learning models
• Evaluating analytic gradients on quantum hardware
• Quantum algorithms: an overview
• Circuit-centric quantum classifiers
• Open Quantum Systems. An Introduction
• Efficient variational quantum simulator incorporating active error minimisation
• Ballistic spreading of entanglement in a diffusive nonintegrable system
• Quantum Computation as Geometry
• Quantum autoencoders for efficient compression of quantum data
• Quantum Natural Gradient
• A simple all-microwave entangling gate for fixed-frequency superconducting qubits
• Theory of variational quantum simulation
• Chopped random-basis quantum optimization
• Hybrid Quantum-Classical Approach to Quantum Optimal Control
• Variational quantum algorithms for discovering Hamiltonian spectra
• Stochastic gradient descent for hybrid quantum-classical optimization
• Methodology for replacing indirect measurements with direct measurements
• Hamiltonian Simulation Using Linear Combinations of Unitary Operations
• Quantum gate learning in engineered qubit networks: Toffoli gate with always-on interactions
• Noise-Resilient Variational Hybrid Quantum-Classical Optimization
• Supervised learning of time-independent Hamiltonians for gate design

Cited by in corpus (50)

• General parameter-shift rules for quantum gradients
• Is quantum advantage the right goal for quantum machine learning?
• A variational toolbox for quantum multi-parameter estimation
• Quantum computing models for artificial neural networks
• An efficient quantum algorithm for the time evolution of parameterized circuits
• Quantum Machine Learning: from physics to software engineering
• Near-Term Quantum Computing Techniques: Variational Quantum Algorithms, Error Mitigation, Circuit Compilation, Benchmarking and Classical Simulation
• Biology and medicine in the landscape of quantum advantages
• The Variational Power of Quantum Circuit Tensor Networks
• Analytic gradients in variational quantum algorithms: Algebraic extensions of the parameter-shift rule to general unitary transformations
• Generalized quantum circuit differentiation rules
• Variational inference with a quantum computer
• Realising and compressing quantum circuits with quantum reservoir computing
• Variational quantum amplitude estimation
• Mitigating Barren Plateaus with Transfer-learning-inspired Parameter Initializations
• Fock State-enhanced Expressivity of Quantum Machine Learning Models
• Optimal control of families of quantum gates
• Variational quantum algorithm for experimental photonic multiparameter estimation
• Training variational quantum algorithms with random gate activation
• Here comes the SU(N): multivariate quantum gates and gradients
• Security Aspects of Quantum Machine Learning: Opportunities, Threats and Defenses
• Quantum Circuit Evolution on NISQ Devices
• A blueprint for a Digital-Analog Variational Quantum Eigensolver using Rydberg atom arrays
• Subspace methods for the simulation of molecular response properties on a quantum computer
• Boundary Treatment for Variational Quantum Simulations of Partial Differential Equations on Quantum Computers
• Optimizing Variational Quantum Algorithms with qBang: Efficiently Interweaving Metric and Momentum to Navigate Flat Energy Landscapes
• Single-component gradient rules for variational quantum algorithms
• Measurement-induced entanglement phase transitions in variational quantum circuits
• Stochastic approach for quantum metrology with generic Hamiltonians
• Multi-variable integration with a variational quantum circuit
• Qsun: an open-source platform towards practical quantum machine learning applications
• Random coordinate descent: a simple alternative for optimizing parameterized quantum circuits
• State preparation of lattice field theories using quantum optimal control
• Local, Expressive, Quantum-Number-Preserving VQE Ansatze for Fermionic Systems
• Towards Variational Quantum Algorithms for generalized linear and nonlinear transport phenomena
• Quantum gradient evaluation through quantum non-demolition measurements
• Random Natural Gradient
• Framework for Learning and Control in the Classical and Quantum Domains
• Towards Arbitrary QUBO Optimization: Analysis of Classical and Quantum-Activated Feedforward Neural Networks
• Iteration Complexity of Variational Quantum Algorithms
• Using gradient-based algorithms to determine ground state energies on a quantum computer
• Probing many-body Bell correlation depth with superconducting qubits
• More buck-per-shot: Why learning trumps mitigation in noisy quantum sensing
• Evolved Quantum Boltzmann Machines
• "Proper" Shift Rules for Derivatives of Perturbed-Parametric Quantum Evolutions
• Efficient Estimation and Sequential Optimization of Cost Functions in Variational Quantum Algorithms
• Quantum Noise Sensing by generating Fake Noise
• Quantum natural gradient with thermal-state initialization
• Robustness of a universal gate set implementation in transmon systems via Chopped Random Basis optimal control
• Efficient classical computation of the neural tangent kernel of quantum neural networks