arXiv subjects

Andrew G. Green

Publications and source records attributed to Andrew G. Green.

At least 19 recordsLinked to original sources

arXiv2026

Locally optimized variational evolution for quantum many-body systems

Conventional quantum advantage in many-body dynamics is based on avoiding the simulation cost on a classical computer that arises from the extensive exponential complexity of the global wavefunction. Local observables, however, do not inherit this extensive complexity and may instead be governed by an intrinsic local complexity that is independent of the total system size. This distinction is particularly relevant in thermalising systems, where local observables lose memory of microscopic details and relax towards equilibrium values determined by only a few parameters. Here we introduce a variational time-evolution principle that exploits this distinction by replacing global-state fidelity with a cost function defined on local reduced density matrices. The resulting evolution retains coherent short-time dynamics while exploiting the simplification produced by thermalisation at later times. The concrete algorithm we propose is based on locally optimising matrix-product states and admits closed-form equations of motion analogous to the time-dependent variational principle. We show that the same variational principle has a quantum-classical counterpart, combining quantum evaluation of the local cost with an optimisation strategy robust to both shot and hardware noise. Proof-of-principle implementations on Quantinuum H2 and IBM Heron processors recover the characteristic local dynamics.

quant-ph↗

arXiv2026

Quantum probe advantage in learning many-body systems

Which properties of a quantum many-body system are operationally accessible is a central question underlying spectroscopy, thermodynamics, and quantum information science. Conventional response theory answers this question within a system-only paradigm: one perturbs and measures the matter itself, obtaining susceptibility built from causally ordered nested commutators. Here we show that coherently controlled quantum probes, when measured at the end, define a strictly larger operational learning framework beyond that accessible from response theory. We establish this through a quantum-circuit description that unifies spectroscopy, probe microscopy, and probe-based quantum technologies within a common operational framework, from which we develop quantum protocols for learning many-body properties from probe readout only. This advantage arises because the reduced dynamics of quantum probes generically encode anti-commutator and mixed-order correlators of the target; therefore, measurements on the probe provide access to fluctuations, non-equilibrium structure, and entanglement entropy that are in general not accessible through response functions or a single probe alone. Moreover, we demonstrate that entangled probes can access many-body properties such as von Neumann entropy. We prove that the required probe resources scale with the complexity of the target correlations rather than with the size of the many-body system. Quantum probes are therefore not merely more sensitive sensors but provide a new way to learn many-body properties distinct from those of tomography or quantum simulation.

quant-ph↗

arXiv2026

Quantum trajectory simulation of two-dimensional non-equilibrium steady states with a trapped ion quantum processor

Digital quantum computers offer a promising route for studying complex many-body systems that are otherwise inaccessible by their classical counterparts. Capabilities including mid-circuit measurements and feedback allow for simulating the dynamics of interacting open quantum systems. Using the Quantinuum System Model H1 trapped-ion quantum computer, we experimentally realise quantum trajectories for a two-dimensional system of (interacting) particles-hard-core bosons or fermions-undergoing stochastic driving at a source and drain at opposite corners of a square lattice. We study the non-equilibrium steady state with persistent current resulting from the this in/out flow of particles. The particle statistics, presence of interactions, and introduction of a magnetic field produce measurable effects on the steady state. Our findings highlight the rich physics in this corner driven two-dimensional setup and showcases both the power and current limitations of quantum computers as a platform to study it.

quant-ph↗

arXiv2026

Fully optimised variational simulation of a dynamical quantum phase transition on a trapped-ion quantum computer

We time-evolve a translationally invariant quantum state on the Quantinuum H1-1 trapped-ion quantum processor, studying the dynamical quantum phase transition of the transverse field Ising model. This physics requires a delicate cancellation of phases in the many-body wavefunction and presents a tough challenge for current quantum devices. We follow the dynamics using a quantum circuit matrix product state ansatz, optimised for the time-evolution using a fidelity cost function. Sampling costs are mitigated by using the measured values of this circuit as stochastic corrections to a simple classical extrapolation of the ansatz parameters. Our results demonstrate the feasibility of variational quantum time-evolution and reveal a hitherto hidden simplicity of the evolution of the transverse-field Ising model through the dynamical quantum phase transition.

quant-ph↗

arXiv2025

An unbiased measure over the matrix product state manifold

Matrix product states are useful representations for a large variety of naturally occurring quantum states. Studying their typical properties is important for understanding universal behavior, including quantum chaos and thermalization, as well as the limits of classical simulations of quantum devices. We show that the usual ensemble of sequentially generated random matrix product states (RMPS) using local Haar random unitaries is not uniform when viewed as a restriction of the full Hilbert space. As a result, the entanglement across the chain exhibits an anomalous asymmetry under spatial inversion. We show how to construct an unbiased measure starting from the left-canonical form and design a Metropolis algorithm for sampling random states. Some properties of this new ensemble are investigated both analytically and numerically, such as the resulting resolution of identity over matrix product states and the typical entanglement spectrum, which is found to differ from the sequentially generated case.

quant-ph↗

arXiv2024

Zero-point energy of tensor fluctuations on the MPS manifold

This work presents a method for studying low-energy physics in highly correlated magnetic systems using the matrix product state (MPS) manifold. We adapt the spin-wave approach, which has been very successful in modeling certain low-entanglement magnetic materials, to systems where the ground state is better represented by an MPS, such as the S = 1 Affleck-Kennedy-Lieb-Tasaki (AKLT) model. We argue that the quasi-local action of tensor fluctuations and the natural Kähler structure of the MPS manifold facilitate a description in terms of bosonic modes. We apply this approach to compute fluctuation corrections to the bilinear-biquadratic Heisenberg model, whose ground state we expect to be close to the exact bond dimension 2 AKLT state in a certain parameter range. Our results show significant improvements in energy approximations, highlighting both the qualitative and quantitative potential of this paradigm for studying complex entangled systems. This approach paves the way for new insights into the low-energy physics of correlated materials and the development of effective field theories beyond traditional semiclassical methods.

quant-ph↗

arXiv2024

Entanglement growth from squeezing on the MPS manifold

Finding suitable characterizations of quantum chaos is a major challenge in many-body physics, with a central difficulty posed by the linearity of the Schrödinger equation. A possible solution for recovering non-linearity is to project the dynamics onto some variational manifold. The classical chaos induced via this procedure may be used as a signature of quantum chaos in the full Hilbert space. Here, we demonstrate analytically a previously heuristic connection between the Lyapunov spectrum from projection onto the matrix product state (MPS) manifold and the growth of entanglement. This growth occurs by squeezing a localized distribution on the variational manifold. The process qualitatively resembles the Cardy-Calabrese picture, where local perturbations to a moving MPS reference are interpreted as bosonic quasi-particles. Taking careful account of the number of distinct channels for these processes recovers the connection to the Lyapunov spectrum. Our results rigorously establish the physical significance of the projected Lyapunov spectrum, suggesting it as an alternative method of characterizing chaos in quantum many-body systems, one that is manifestly linked to classical chaos.

quant-ph↗

arXiv2023

Introducing fluctuation-driven order into density functional theory using the quantum order-by-disorder framework

Density functional theory in the local or semi-local density approximation is a powerful tool for materials simulation, yet it struggles in many cases to describe collective electronic order that is driven by electronic interactions. In this work it is shown how arbitrary, fluctuation-driven electronic order may be introduced into density functional theory using the quantum order-by-disorder framework. This is a method of calculating the free energy correction due to collective spin and charge fluctuations about a state that hosts static order, in a self-consistent manner. In practical terms, the quantum order-by-disorder method is applied to the Kohn-Sham auxiliary system of density functional theory to give an order-dependent correction to the exchange-correlation functional. Calculation of fluctuation propagators within density functional theory renders the result fully first-principles. Two types of order are considered as examples -- fluctuation-driven superconductivity and spin nematic order -- and implementation schemes are presented in each case.

cond-mat.str-el↗

arXiv2023

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 $O(\logε/ \log(1-p))$ (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.

quant-ph↗

arXiv2022

Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer

We optimise a translationally invariant, sequential quantum circuit on a superconducting quantum device to simulate the groundstate of the quantum Ising model through its quantum critical point. We further demonstrate how the dynamical quantum critical point found in quenches of this model across its quantum critical point can be simulated. Our approach avoids finite-size scaling effects by using sequential quantum circuits inspired by infinite matrix product states. We provide efficient circuits and a variety of error mitigation strategies to implement, optimise and time-evolve these states.

quant-ph↗

arXiv2022

Crossing a topological phase transition with a quantum computer

Quantum computers promise to perform computations beyond the reach of modern computers with profound implications for scientific research. Due to remarkable technological advances, small scale devices are now becoming available for use. One of the most apparent applications for such a device is the study of complex many-body quantum systems, where classical computers are unable to deal with the generic exponential complexity of quantum states. Even zero-temperature equilibrium phases of matter and the transitions between them have yet to be fully classified, with topologically protected phases presenting major difficulties. We construct and measure a continuously parametrized family of states crossing a symmetry protected topological phase transition on the IBM Q quantum computers. We present two complementary methods for measuring string order parameters that reveal the transition, and additionally analyse the effects of noise in the device using simple error models. The simulation that we perform is easily scalable and is a practical demonstration of the utility of near-term quantum computers for the study of quantum phases of matter and their transitions.

cond-mat.str-el↗

arXiv2022

Error measurements for a quantum annealer using the one-dimensional Ising model with twisted boundaries

A finite length ferromagnetic chain with opposite spin polarisation imposed at its two ends is one of the simplest frustrated spin models. In the clean classical limit the domain wall inserted on account of the boundary conditions resides with equal probability on any one of the bonds, and the degeneracy is precisely equal to the number of bonds. If quantum mechanics is introduced via a transverse field, the domain wall will behave as a particle in a box, and prefer to be nearer the middle of the chain rather than the ends. A simple characteristic of a real quantum annealer is therefore which of these limits obtains in practice. Here we have used the ferromagnetic chain with antiparallel boundary spins to test a real flux qubit quantum annealer and discover that contrary to both expectations, the domain walls found are non-uniformly distributed on account of effective random longitudinal fields present notwithstanding tuning carried out to zero out such fields when the couplings between qubits are nominally zero. We present a simple derivation of the form of the distribution function for the domain walls, and show also how the effect we have discovered can be used to determine the strength of the effective random fields (noise) characterising the annealer. The noise measured in this fashion is smaller than what is seen during the single qubit tuning process, but nonetheless qualitatively affects the outcome of the simulation performed by the annealer.

quant-ph↗

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↗

arXiv2021

Parallel Quantum Simulation of Large Systems on Small Quantum Computers

Tensor networks permit computational and entanglement resources to be concentrated in interesting regions of Hilbert space. Implemented on NISQ machines they allow simulation of quantum systems that are much larger than the computational machine itself. This is achieved by parallelising the quantum simulation. Here, we demonstrate this in the simplest case; an infinite, translationally invariant quantum spin chain. We provide Cirq and Qiskit code that translate infinite, translationally invariant matrix product state (iMPS) algorithms to finite-depth quantum circuit machines, allowing the representation, optimisation and evolution arbitrary one-dimensional systems. Illustrative simulated output of these codes for achievable circuit sizes is given.

quant-ph↗

arXiv2020

Dissipative failure of adiabatic quantum transport as a dynamical phase transition

Entanglement is the central resource in adiabatic quantum transport. Dephasing affects the availability of that resource by biasing trajectories, driving transitions between success and failure. This depletion of entanglement is important for the practical implementation of quantum technologies. We present a new perspective on the failure of adiabatic computation by understanding the failure of adiabatic transport as a dynamical phase transition. These ideas are demonstrated in a toy model of adiabatic quantum transport in a two spin system.

quant-ph↗

arXiv2020

Real- and imaginary-time evolution with compressed quantum circuits

The current generation of noisy intermediate scale quantum computers introduces new opportunities to study quantum many-body systems. In this paper, we show that quantum circuits can provide a dramatically more efficient representation than current classical numerics of the quantum states generated under non-equilibrium quantum dynamics. For quantum circuits, we perform both real- and imaginary-time evolution using an optimization algorithm that is feasible on near-term quantum computers. We benchmark the algorithms by finding the ground state and simulating a global quench of the transverse field Ising model with a longitudinal field on a classical computer. Furthermore, we implement (classically optimized) gates on a quantum processing unit and demonstrate that our algorithm effectively captures real time evolution.

quant-ph↗

arXiv2018

Hierarchical quantum classifiers

Quantum circuits with hierarchical structure have been used to perform binary classification of classical data encoded in a quantum state. We demonstrate that more expressive circuits in the same family achieve better accuracy and can be used to classify highly entangled quantum states, for which there is no known efficient classical method. We compare performance for several different parameterizations on two classical machine learning datasets, Iris and MNIST, and on a synthetic dataset of quantum states. Finally, we demonstrate that performance is robust to noise and deploy an Iris dataset classifier on the ibmqx4 quantum computer.

quant-ph↗

arXiv2018

Compact Neural Networks based on the Multiscale Entanglement Renormalization Ansatz

This paper demonstrates a method for tensorizing neural networks based upon an efficient way of approximating scale invariant quantum states, the Multi-scale Entanglement Renormalization Ansatz (MERA). We employ MERA as a replacement for the fully connected layers in a convolutional neural network and test this implementation on the CIFAR-10 and CIFAR-100 datasets. The proposed method outperforms factorization using tensor trains, providing greater compression for the same level of accuracy and greater accuracy for the same level of compression. We demonstrate MERA layers with 14000 times fewer parameters and a reduction in accuracy of less than 1% compared to the equivalent fully connected layers, scaling like O(N).

cs.NE↗