arXiv subjects

Lewis Wright

Publications and source records attributed to Lewis Wright.

6 recordsLinked to original sources

arXiv2026

Scalable, self-verifying variational quantum eigensolver using adiabatic warm starts

We study an adiabatic variant of the variational quantum eigensolver (VQE) in which VQE is performed iteratively for a sequence of Hamiltonians along an adiabatic path. We derive the conditions under which gradient-based optimization successfully prepares the adiabatic ground states. These conditions show that the barren plateau problem and local optima can be avoided. Additionally, we propose using energy-standard-deviation measurements at runtime to certify eigenstate accuracy and verify convergence to the global optimum.

quant-ph↗

arXiv2025

Quantum circuits for partial differential equations in Fourier space

For the solution of partial differential equations (PDEs), we show that the quantum Fourier transform (QFT) can enable the design of quantum circuits that are particularly simple, both conceptually and with regard to hardware requirements. This is shown by explicit circuit constructions for the incompressible advection, heat, isotropic acoustic wave, and Poisson's equations as canonical examples. We utilize quantum singular value transformation to develop circuits that are expected to be of optimal computational complexity. Additionally, we consider approximations suited for smooth initial conditions and describe circuits that make lower demands on hardware. The simple QFT-based circuits are efficient with respect to dimensionality and pave the way for current quantum computers to solve high-dimensional PDEs.

quant-ph↗

arXiv2024

Noisy intermediate-scale quantum simulation of the one-dimensional wave equation

We design and implement quantum circuits for the simulation of the one-dimensional wave equation on the Quantinuum H1-1 quantum computer. The circuit depth of our approach scales as $O(n^{2})$ for $n$ qubits representing the solution on $2^{n}$ grid points, and leads to infidelities of $O(2^{-4n} t^{2})$ for simulation time $t$ assuming smooth initial conditions. By varying the qubit count we study the interplay between the algorithmic and physical gate errors to identify the optimal working point of minimum total error. Our approach to simulating the wave equation can be used with appropriate state preparation algorithms across different quantum processors and serve as an application-oriented benchmark.

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arXiv2022

Improvements to Gradient Descent Methods for Quantum Tensor Network Machine Learning

Tensor networks have demonstrated significant value for machine learning in a myriad of different applications. However, optimizing tensor networks using standard gradient descent has proven to be difficult in practice. Tensor networks suffer from initialization problems resulting in exploding or vanishing gradients and require extensive hyperparameter tuning. Efforts to overcome these problems usually depend on specific network architectures, or ad hoc prescriptions. In this paper we address the problems of initialization and hyperparameter tuning, making it possible to train tensor networks using established machine learning techniques. We introduce a `copy node' method that successfully initializes arbitrary tensor networks, in addition to a gradient based regularization technique for bond dimensions. We present numerical results that show that the combination of techniques presented here produces quantum inspired tensor network models with far fewer parameters, while improving generalization performance.

cs.LG↗

arXiv2021

Matrix Product State Pre-Training for Quantum Machine Learning

Hybrid Quantum-Classical algorithms are a promising candidate for developing uses for NISQ devices. In particular, Parametrised Quantum Circuits (PQCs) paired with classical optimizers have been used as a basis for quantum chemistry and quantum optimization problems. Training PQCs relies on methods to overcome the fact that the gradients of PQCs vanish exponentially in the size of the circuits used. Tensor network methods are being increasingly used as a classical machine learning tool, as well as a tool for studying quantum systems. We introduce a circuit pre-training method based on matrix product state machine learning methods, and demonstrate that it accelerates training of PQCs for both supervised learning, energy minimization, and combinatorial optimization.

quant-ph↗

arXiv2020

Automatic Post-selection by Ancillae Thermalisation

Tasks such as classification of data and determining the groundstate of a Hamiltonian cannot be carried out through purely unitary quantum evolution. Instead, the inherent non-unitarity of the measurement process must be harnessed. Post-selection and its extensions provide a way to do this. However they make inefficient use of time resources -- a typical computation might require $O(2^m)$ measurements over $m$ qubits to reach a desired accuracy. We propose a method inspired by the eigenstate thermalisation hypothesis, that harnesses the induced non-linearity of measurement on a subsystem. Post-selection on $m$ ancillae qubits is replaced with tracing out $O(\log\epsilon / \log(1-p))$ (where p is the probability of a successful measurement) to attain the same accuracy as the post-selection circuit. We demonstrate this scheme on the quantum perceptron and phase estimation algorithm. This method is particularly advantageous on current quantum computers involving superconducting circuits.

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