Multi-variable integration with a variational quantum circuit

Abstract

In this work we present a novel strategy to evaluate multi-variable integrals with quantum circuits. The procedure first encodes the integration variables into a parametric circuit. The obtained circuit is then derived with respect to the integration variables using the parameter shift rule technique. The observable representing the derivative is then used as the predictor of the target integrand function following a quantum machine learning approach. The integral is then estimated using the fundamental theorem of integral calculus by evaluating the original circuit. Embedding data according to a reuploading strategy, multi-dimensional variables can be easily encoded into the circuit's gates and then individually taken as targets while deriving the circuit. These techniques can be exploited to partially integrate a function or to quickly compute parametric integrands within the training hyperspace.

arXiv commentCode available at https://github.com/qiboteam/QiNNtegrate, version that appeared in journal

References in corpus (36)

• Adam: A Method for Stochastic Optimization
• Deep Learning in Neural Networks: An Overview
• Quantum Computing in the NISQ era and beyond
• An overview of gradient descent optimization algorithms
• Quantum Machine Learning
• Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms
• Quantum Circuit Learning
• An introduction to quantum machine learning
• Parameterized quantum circuits as machine learning models
• Evaluating analytic gradients on quantum hardware
• The CMA Evolution Strategy: A Tutorial
• Data re-uploading for a universal quantum classifier
• Quantum Natural Gradient
• The Path to Proton Structure at One-Percent Accuracy
• Quantum Simulation for High Energy Physics
• Weight optimization in multichannel Monte Carlo
• Adaptive Multidimensional Integration: VEGAS Enhanced
• Estimating the gradient and higher-order derivatives on quantum hardware
• The QICK (Quantum Instrumentation Control Kit): Readout and control for qubits and detectors
• Progress in the Determination of the Partonic Structure of the Proton
• Qibo: a framework for quantum simulation with hardware acceleration
• An Adaptive Optimizer for Measurement-Frugal Variational Algorithms
• Exploring phase space with Neural Importance Sampling
• Measuring Analytic Gradients of General Quantum Evolution with the Stochastic Parameter Shift Rule
• Gradients of parameterized quantum gates using the parameter-shift rule and gate decomposition
• One qubit as a Universal Approximant
• Determining the proton content with a quantum computer
• VegasFlow: accelerating Monte Carlo simulation across multiple hardware platforms
• Quantum simulation with just-in-time compilation
• Collider Events on a Quantum Computer
• Latency considerations for stochastic optimizers in variational quantum algorithms
• Multi-variable Integration with a Neural Network
• An open-source modular framework for quantum computing
• Characterization of a Transmon Qubit in a 3D Cavity for Quantum Machine Learning and Photon Counting
• Quantum gradient evaluation through quantum non-demolition measurements
• A Novel Approach to Reduce Derivative Costs in Variational Quantum Algorithms

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