Towards quantum simulations in particle physics and beyond on noisy intermediate-scale quantum devices

We review two algorithmic advances that bring us closer to reliable quantum simulations of model systems in high-energy physics and beyond on noisy intermediate-scale quantum (NISQ) devices. The first method is the dimensional expressivity analysis of quantum circuits, which allows for constructing minimal but maximally expressive quantum circuits. The second method is an efficient mitigation of readout errors on quantum devices. Both methods can lead to significant improvements in quantum simulations, e.g. when variational quantum eigensolvers are used. This article is part of the theme issue ‘Quantum technologies in particle physics’.

Survey of NISQ Era Hybrid Quantum-Classical Machine Learning Research

Quantum computing is a rapidly growing field that has received a significant amount of support in the past decade in industry and academia. Several physical quantum computers are now freely available to use through cloud services, with some implementations supporting upwards of hundreds of qubits. These advances mark the beginning of the Noisy Intermediate-Scale Quantum (NISQ) era of quantum computing, paving the way for hybrid quantum-classical systems. This work provides an introductory overview of gate-model quantum computing through the Visual IoT/Robotics Programming Language Environment and a survey of recent applications of NISQ era quantum computers to hybrid quantum-classical machine learning.

Noise-induced barren plateaus in variational quantum algorithms

Variational Quantum Algorithms (VQAs) may be a path to quantum advantage on Noisy Intermediate-Scale Quantum (NISQ) computers. A natural question is whether noise on NISQ devices places fundamental limitations on VQA performance. We rigorously prove a serious limitation for noisy VQAs, in that the noise causes the training landscape to have a barren plateau (i.e., vanishing gradient). Specifically, for the local Pauli noise considered, we prove that the gradient vanishes exponentially in the number of qubits n if the depth of the ansatz grows linearly with n. These noise-induced barren plateaus (NIBPs) are conceptually different from noise-free barren plateaus, which are linked to random parameter initialization. Our result is formulated for a generic ansatz that includes as special cases the Quantum Alternating Operator Ansatz and the Unitary Coupled Cluster Ansatz, among others. For the former, our numerical heuristics demonstrate the NIBP phenomenon for a realistic hardware noise model.

Qubit-excitation-based adaptive variational quantum eigensolver

Molecular simulations with the variational quantum eigensolver (VQE) are a promising application for emerging noisy intermediate-scale quantum computers. Constructing accurate molecular ansätze that are easy to optimize and implemented by shallow quantum circuits is crucial for the successful implementation of such simulations. Ansätze are, generally, constructed as series of fermionic-excitation evolutions. Instead, we demonstrate the usefulness of constructing ansätze with "qubit-excitation evolutions”, which, contrary to fermionic excitation evolutions, obey "qubit commutation relations”. We show that qubit excitation evolutions, despite the lack of some of the physical features of fermionic excitation evolutions, accurately construct ansätze, while requiring asymptotically fewer gates. Utilizing qubit excitation evolutions, we introduce the qubit-excitation-based adaptive (QEB-ADAPT)-VQE protocol. The QEB-ADAPT-VQE is a modification of the ADAPT-VQE that performs molecular simulations using a problem-tailored ansatz, grown iteratively by appending evolutions of qubit excitation operators. By performing classical numerical simulations for small molecules, we benchmark the QEB-ADAPT-VQE, and compare it against the original fermionic-ADAPT-VQE and the qubit-ADAPT-VQE. In terms of circuit efficiency and convergence speed, we demonstrate that the QEB-ADAPT-VQE outperforms the qubit-ADAPT-VQE, which to our knowledge was the previous most circuit-efficient scalable VQE protocol for molecular simulations.

Clinical Data Classification With Noisy Intermediate Scale Quantum Computers

Quantum machine learning has experienced a significant progress in both software and hardware development in the recent years and has emerged as an applicable area of near-term quantum computers. In this work, we investigate the feasibility of utilizing quantum machine learning (QML) on real clinical datasets. We propose two QML algorithms for data classification on IBM quantum hardware: a quantum distance classifier (qDS) and a simplified quantum-kernel support vector machine (sqKSVM). We utilize these different methods using the linear time quantum data encoding technique (\({\text{log}}_{2}N\)) for embedding classical data into quantum states and estimating the inner product on 15-qubit IBMQ Melbourne quantum computer. We match the predictive performance of our QML approaches with prior QML methods and with their classical counterpart algorithms for three open-access clinical datasets. Our results imply that the qDS in small sample and feature count datasets outperforms kernel-based methods. In contrast, quantum kernel approaches outperform qDS in high sample and feature count datasets. We demonstrate that the \({\text{log}}_{2}N\) encoding increases predictive performance with up to +2% area under the receiver operator characteristics curve across all quantum machine learning approaches, thus, making it ideal for machine learning tasks executed in Noisy Intermediate Scale Quantum computers.