arXiv subjects

Lachlan P. Lindoy

Publications and source records attributed to Lachlan P. Lindoy.

At least 19 recordsLinked to original sources

arXiv2026

Long-lived memory effects in the defect bath of superconducting qubits

We reveal long-lived memory effects in the defect bath of a superconducting transmon qubit through electric-field tuning of two-level system (TLS) defects coupled to the qubit. Using a fast TLS mapping method we observe several hysteretic effects in the TLS environment with memory timescales of the order of seconds, far beyond the lifetimes of individual TLS defects. The observations can be explained by TLS coupling to electric field-polarised charge fluctuators in the defect bath. Our method enables detailed mapping of the dynamics of the bath's coupled microscopic degrees of freedom and the associated memory effects which can introduce temporally correlated noise. This information may be used to improve qubit-stabilisation and quantum error correction protocols.

quant-ph↗

arXiv2026

Preparing 100-qubit symmetry-protected topological order on a digital quantum computer

Symmetry-protected topological (SPT) phases extend the Landau paradigm of quantum matter by admitting distinct symmetry-preserving phases that lack any local order parameter. Demonstrating these phases at scale on programmable quantum processors is a key milestone in using quantum hardware to probe emergent many-body phenomena, yet it is impeded by the circuit depth normally required to capture non-trivial entanglement. Here we use a tensor network based approximate quantum compiling (AQC) protocol to construct shallow quantum circuits (18-39 CNOT depth), which prepare 100-site ground states of the spin-1/2 bond-alternating Heisenberg chain in both SPT phases, to 97.9-99.0% fidelity. Upon executing the circuits on IBM quantum hardware, the resulting states exhibit all defining signatures of SPT order including non-local string order for strings of up to length 20, characteristic degeneracies in the entanglement spectrum and clear evidence of symmetry-protected edge modes. The simultaneous observation of these independent diagnostics establishes current quantum computers as versatile platforms for large-scale studies of symmetry-protected quantum matter. More broadly, our results establish a practical foundation for probing non-equilibrium quench dynamics of such systems in regimes that challenge classical computational methods.

quant-ph↗

arXiv2025

Variational preparation of normal matrix product states on quantum computers

Preparing matrix product states (MPSs) on quantum computers is an essential routine in the simulation of many-body physics. However, widely-used schemes based on staircase circuits are often too deep to execute on current hardware. Here we demonstrate that MPSs with short-range correlations can be prepared with shallow circuits by leveraging heuristics from approximate quantum compiling (AQC). We achieve this with ADAPT-AQC, an adaptive-ansatz preparation algorithm, and introduce a generalised initialisation procedure for the existing AQC-Tensor algorithm. We first compare these methods for the task of preparing a molecular electronic structure ground state. We then use them to prepare an antiferromagnetic (AFM) ground state of the 50-site Heisenberg XXZ spin chain near the AFM-XY phase boundary. Through the execution of circuits with up to 59 CZ depth and 1251 CZ gates, we perform a global quench and observe the relaxation of magnetic ordering in a parameter regime previously inaccessible due to deep ground state preparation circuits. Our results demonstrate how the integration of quantum and classical resources can push the boundary of what can be studied on quantum computers.

quant-ph↗

arXiv2025

On the Discretization Error of the Discrete Generalized Quantum Master Equation

The transfer tensor method (TTM) [Cerrillo and Cao, Phys. Rev. Lett. 2014, 112, 110401] can be considered a discrete-time formulation of the Nakajima-Zwanzig quantum master equation (NZ-QME) for modeling non-Markovian quantum dynamics. A recent paper [Makri, J. Chem. Theory Comput. 2025, 21, 5037] raised concerns regarding the consistency of the TTM discretization, particularly a spurious term at the initial time $ t=0 $. This Communication presents a detailed analysis of the discretization structure of TTM, clarifying the origin of the initial-time correction and establishing a consistent relationship between the TTM discrete-time memory kernel $ K_N $, and the continuous-time NZ-QME kernel $ \mathcal{K}(NΔt) $. This relationship is validated numerically using the spin-boson model, demonstrating convergence of reconstructed memory kernels and accurate dynamical evolution as $ Δt \to 0 $. While TTM provides a consistent discretization, we note that alternative schemes are also viable, such as the midpoint derivative/midpoint integral scheme proposed in Makri's work. The relative performance of various schemes for either computing accurate $ \mathcal{K}(NΔt) $ from exact dynamics, or obtaining accurate dynamics from exact $ \mathcal{K}(NΔt) $, warrants further investigation.

quant-ph↗

arXiv2025

Fast-tracking and disentangling of qubit noise fluctuations using minimal-data averaging and hierarchical discrete fluctuation auto-segmentation

Qubit noise and fluctuations of the noise over time are key factors limiting the performance of quantum computers. Characterising them with high temporal resolution is challenging due to multiple overlapping stochastic processes such as discrete jumps and continuous drifts. Hence, experiments typically probe individual sources of fluctuations rather than concurrent fluctuations caused by multiple sources. To overcome this limitation we develop a framework comprising a noise characterisation method with minimal measurements allowing high temporal resolution, combined with a hierarchical discrete fluctuation auto-segmentation tool to disentangle the overlapping fluctuations without human intervention, enabling their characterisation and tracking over long times. We show that on transmon qubits the method can track and disentangle qubit frequency fluctuations with temporal resolution of a few tens of milliseconds over hours. This enables us to identify the origins of the fluctuations as overlapping charge parity and two-level-systems switching. Beyond insights into the fluctuation origins, our method also provides information that can be used to improve qubit calibration, error mitigation and error correction.

quant-ph↗

arXiv2024

Anderson impurity solver integrating tensor network methods with quantum computing

Solving the Anderson impurity model typically involves a two-step process, where one first calculates the ground state of the Hamiltonian, and then computes its dynamical properties to obtain the Green's function. Here we propose a hybrid classical/quantum algorithm where the first step is performed using a classical computer to obtain the tensor network ground state as well as its quantum circuit representation, and the second step is executed on the quantum computer to obtain the Green's function. Our algorithm exploits the efficiency of tensor networks for preparing ground states on classical computers, and takes advantage of quantum processors for the evaluation of the time evolution, which can become intractable on classical computers. We demonstrate the algorithm using 24 qubits on a quantum computing emulator for SrVO$_3$ with a multi-orbital Anderson impurity model within the dynamical mean field theory. The tensor network based ground state quantum circuit preparation algorithm can also be performed for up to 60 qubits with our available computing resources, while the state vector emulation of the quantum algorithm for time evolution is beyond what is accessible with such resources. We show that, provided the tensor network calculation is able to accurately obtain the ground state energy, this scheme does not require a perfect reproduction of the ground state wave function on the quantum circuit to give an accurate Green's function. This hybrid approach may lead to quantum advantage in materials simulations where the ground state can be computed classically, but where the dynamical properties cannot.

quant-ph↗

arXiv2024

Reply to "Comment on "Unified Framework for Open Quantum Dynamics with Memory""

We present our response to the commentary piece by Makri {\it et al.} [arXiv:2410.08239], which raises critiques of our work [Nat. Commun. 15, 8087 (2024)]. In our paper, we considered various settings of open-quantum system dynamics, including non-commuting, non-diagonalizable system-bath coupling, and bosonic/spin/fermionic baths. For these, we showed a direct and explicit relationship between the discrete-time memory kernel ($\mathcal K$) of the generalized quantum master equation (GQME) and the discrete-time influence functions ($I$) of the path integrals. As an application of this, we showed one can construct $\mathcal K$ without projection-free dynamics inputs that conventional methods require, and we also presented a quantum sensing protocol that characterizes the bath spectral density from reduced system dynamics. As the Comment focused on the relationship between ($\mathcal K$) and $I$ in one specific setup (i.e., commuting, diagonalizable system-bath coupling with a bosonic bath), we focus on that aspect in this response. In summary, we could not find a set of equations that explicitly connect $I$ and $\mathcal K$ from Makri's 2020 paper [J. Chem. Theory Comput. 16, 4038 (2020)]. Furthermore, while our analysis is specific to the choice of discretization of path-integral and GQME, we have not found issues with the GQME discretization employed. As per critiques on citations, in our paper, we note that we had acknowledged Makri's driven SMatPI work and Wang and Cai's tree-based SMatPI work for the number of Dyck paths needed for the computation of the memory kernel.

quant-ph↗

arXiv2024

Quantum subspace expansion approach for simulating dynamical response functions of Kitaev spin liquids

We develop a quantum simulation-based approach for studying properties of strongly correlated magnetic materials at increasing scale. We consider a paradigmatic example of a quantum spin liquid (QSL) state hosted by the honeycomb Kitaev model, and use a trainable symmetry-guided ansatz for preparing its ground state. Applying the tools of quantum subspace expansion (QSE), Hamiltonian operator approximation, and overlap measurements, we simulate the QSL at zero temperature and finite magnetic field, thus moving outside of the symmetric subspace. Next, we implement a protocol for quantum subspace expansion-based measurement of spin-spin correlation functions. Finally, we perform QSE-based simulation of the dynamical structure factor obtained from Green's functions of the finite field Kitaev model. Our results show that quantum simulators offer an insight to quasiparticle properties of strongly correlated magnets and can become a valuable tool for studying material science.

quant-ph↗

arXiv2024

Correlation Functions From Tensor Network Influence Functionals: The Case of the Spin-Boson Model

We investigate the application of matrix product state (MPS) representations of the influence functionals (IF) for the calculation of real-time equilibrium correlation functions in open quantum systems. Focusing specifically on the unbiased spin-boson model, we explore the use of IF-MPSs for complex time propagation, as well as IF-MPSs for constructing correlation functions in the steady state. We examine three different IF approaches: one based on the Kadanoff-Baym contour targeting correlation functions at all times, one based on a complex contour targeting the correlation function at a single time, and a steady state formulation which avoids imaginary or complex times, while providing access to correlation functions at all times. We show that within the IF language, the steady state formulation provides a powerful approach to evaluate equilibrium correlation functions.

physics.chem-ph↗

arXiv2024

Unified Framework for Open Quantum Dynamics with Memory

Studies of the dynamics of a quantum system coupled to baths are typically performed by utilizing the Nakajima-Zwanzig memory kernel (${\mathcal{K}}$) or the influence functions ($\mathbf{I}$), especially when the dynamics exhibit memory effects (i.e., non-Markovian). Despite their significance, the formal connection between the memory kernel and the influence functions has not been explicitly made. We reveal their relation by inspecting the system propagator for a broad class of problems where an $N$-level system is linearly coupled to Gaussian baths (bosonic, fermionic, and spin.) With this connection, we also show how approximate path integral methods can be understood in terms of approximate memory kernels. For a certain class of open quantum system problems, we devised a non-perturbative, diagrammatic approach to construct ${\mathcal{K}}$ from $\mathbf{I}$ for (driven) systems interacting with Gaussian baths without the use of any projection-free dynamics inputs required by standard approaches. Lastly, we demonstrate a Hamiltonian learning procedure to extract the bath spectral density from a set of reduced system trajectories obtained experimentally or by numerically exact methods, opening new avenues in quantum sensing and engineering. The insights we provide in this work will significantly advance the understanding of non-Markovian dynamics, and they will be an important stepping stone for theoretical and experimental developments in this area.

quant-ph↗

arXiv2024

Investigating the Collective Nature of Cavity Modified Chemical Kinetics under Vibrational Strong Coupling

In this paper we develop quantum dynamical methods capable of treating the dynamics of chemically reacting systems in an optical cavity in the vibrationally strong-coupling (VSC) limit at finite temperatures and in the presence of a dissipative solvent in both the few and many molecule limits. In the context of two simple models we demonstrate how reactivity in the {\em collective} VSC regime does not exhibit altered rate behavior in equilibrium, but may exhibit resonant cavity modification of reactivity when the system is explicitly out of equilibrium. Our results suggest experimental protocols that may be used to modify reactivity in the collective regime and point to features not included in the models studied which demand further scrutiny.

quant-ph↗

arXiv2023

Modelling non-Markovian noise in driven superconducting qubits

Non-Markovian noise can be a significant source of errors in superconducting qubits. We develop gate sequences utilising mirrored pseudoidentities that allow us to characterise and model the effects of non-Markovian noise on both idle and driven qubits. We compare three approaches to modelling the observed noise: (i) a Markovian noise model, (ii) a model including interactions with a two-level system (TLS), (iii) a model utilising the post Markovian master equation (PMME), which we show to be equivalent to the qubit-TLS model in certain regimes. When running our noise characterisation circuits on a superconducting qubit device we find that purely Markovian noise models cannot reproduce the experimental data. Our model based on a qubit-TLS interaction, on the other hand, is able to closely capture the observed experimental behaviour for both idle and driven qubits. We investigate the stability of the noise properties of the hardware over time, and find that the parameter governing the qubit-TLS interaction strength fluctuates significantly even over short time-scales of a few minutes. Finally, we evaluate the changes in the noise parameters when increasing the qubit drive pulse amplitude. We find that although the hardware noise parameters fluctuate significantly over different days, their drive pulse induced relative variation is rather well defined within computed uncertainties: both the phase error and the qubit-TLS interaction strength change significantly with the pulse strength, with the phase error changing quadratically with the amplitude of the applied pulse. Since our noise model can closely describe the behaviour of idle and driven qubits, it is ideally suited to be used in the development of quantum error mitigation and correction methods.

quant-ph↗

arXiv2022

Quantum Dynamics of Vibrational Polariton Chemistry

We employ an exact quantum mechanical simulation technique to investigate a model of cavity-modified chemical reactions in the condensed phase. The model contains the coupling of the reaction coordinate to a generic solvent, cavity coupling to either the reaction coordinate or a non-reactive mode, and the coupling of the cavity to lossy modes. Thus, many of the most important features needed for realistic modeling of the cavity modification of chemical reactions are included. We find that when a molecule is coupled to an optical cavity it is essential to treat the problem quantum mechanically in order to obtain a quantitative account of alterations to reactivity. We find sizable and sharp changes in the rate constant that are associated with quantum mechanical state splittings and resonances. The features that emerge from our simulations are closer to those observed in experiments than are previous calculations, even for realistically small values of coupling and cavity loss. This work highlights the importance of a fully quantum treatment of vibrational polariton chemistry.

quant-ph↗

arXiv2022

Resonant Cavity Modification of Ground State Chemical Kinetics

Recent experiments have suggested that ground state chemical kinetics can be suppressed or enhanced by coupling the vibrational degrees of freedom of a molecular system with a radiation mode inside an optical cavity. Experiments show that the chemical rate is strongly modified when the photon frequency is close to characteristic vibrational frequencies. The origin of this remarkable effect remains unknown. In this work, we develop an analytical rate theory for cavity-modified ground state chemical kinetics based on the Pollak-Grabert-Hänggi rate theory. Unlike previous work, our theory covers the complete range of solvent friction values, from the energy-diffusion limited to the spatial-diffusion limited regimes. We show that the chemical reaction rate can either be enhanced or suppressed depending on the bath friction; when bath friction is weak chemical kinetics is enhanced as opposed to the case of strong bath friction, where chemical kinetics is suppressed. Further, we show that the photon frequency at which maximum modification of chemical rate is achieved is close to the reactant well, and hence resonant rate modification occurs. In the strong friction limit the {\it resonant} photon frequency is instead close to the barrier frequency, as obtained using the Grote-Hynes rate theory. Finally, we observe that the rate changes (as a function of photon frequency) are much sharper and more sizable in the weak friction limit than in the strong friction limit, and become increasingly sharp with decreasing well frequency.

physics.chem-ph↗

arXiv2021

Time Evolution of ML-MCTDH Wavefunctions I: Gauge Conditions, Basis Functions, and Singularities

We derive a family of equations of motion (EOMs) for evolving multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) wavefunctions that, unlike the standard ML-MCTDH EOMs, never require the evaluation of the inverse of singular matrices. All members of this family of EOMs make use of alternative static gauge conditions than that used for standard ML-MCTDH. These alternative conditions result in an expansion of the wavefunction in terms of a set of potentially arbitrary orthonormal functions, rather than in terms of a set of non-orthonormal and potentially linearly dependent functions, as is the case for standard ML-MCTDH. We show that the EOMs used in the projector splitting integrator (PSI) and the invariant EOMs approaches are two special cases of this family obtained from different choices for the dynamic gauge condition, with the invariant EOMs making use of a choice that introduces potentially unbounded operators into the EOMs. As a consequence, all arguments for the existence of parallelizable integration schemes for the invariant EOMs can also be applied to the PSI EOMs.

physics.chem-ph↗

arXiv2021

Time Evolution of ML-MCTDH Wavefunctions II: Application of the Projector Splitting Integrator

The multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) approach suffers from numerical instabilities whenever the wavefunction is weakly entangled. These instabilities arise from singularities in the equations of motion (EOMs) and necessitate the use of a regularization parameter. The Projector Splitting Integrator (PSI) has previously been presented as an approach for evolving ML-MCTDH wavefunctions that is free of singularities. Here we will discuss the implementation of the multi-layer PSI with a particular focus on how the steps required relate to those required to implement standard ML-MCTDH. We demonstrate the efficiency and stability of the PSI for large ML-MCTDH wavefunctions containing up to hundreds of thousands of nodes by considering a series of spin-boson models with up to $10^6$ bath modes, and find that for these problems the PSI requires roughly 3-4 orders of magnitude fewer Hamiltonian evaluations and 2-3 orders of magnitude fewer Hamiltonian applications than standard ML-MCTDH, and 2-3/1-2 orders of magnitude fewer evaluations/applications than approaches that use improved regularization schemes. Finally, we consider a series of significantly more challenging multi-spin-boson models that require much larger numbers of single-particle functions with wavefunctions containing up to $\sim 1.3\times 10^9$ parameters to obtain accurate dynamics.

physics.chem-ph↗

arXiv2021

Spin relaxation in radical pairs from the stochastic Schrödinger equation

We show that the stochastic Schrödinger equation (SSE) provides an ideal way to simulate the quantum mechanical spin dynamics of radical pairs. Electron spin relaxation effects arising from fluctuations in the spin Hamiltonian are straightforward to include in this approach, and their treatment can be combined with a highly efficient stochastic evaluation of the trace over nuclear spin states that is required to compute experimental observables. These features are illustrated in example applications to a flavin-tryptophan radical pair of interest in avian magnetoreception, and to a problem involving spin-selective radical pair recombination along a molecular wire. In the first of these examples, the SSE is shown to be both more efficient and more widely applicable than a recent stochastic implementation of the Lindblad equation, which only provides a valid treatment of relaxation in the extreme-narrowing limit. In the second, the exact SSE results are used to assess the accuracy of a recently-proposed combination of Nakajima-Zwanzig theory for the spin relaxation and Schulten-Wolynes theory for the spin dynamics, which is applicable to radical pairs with many more nuclear spins. An appendix analyses the efficiency of trace sampling in some detail, highlighting the particular advantages of sampling with SU(N) coherent states.

quant-ph↗

arXiv2020

Quantum mechanical spin dynamics of a molecular magnetoreceptor

Radical pair recombination reactions are known to be sensitive to extremely weak magnetic fields, and can therefore be said to function as molecular magnetoreceptors. The classic example is a carotenoid-porphyrin-fullerene (C+PF-) radical pair that has been shown to provide a "proof-of-principle" for the operation of a chemical compass [K. Maeda et al., Nature 453, 387 (2008)]. Previous simulations of this radical pair have employed semiclassical approximations, which are routinely applicable to its 47 coupled electronic and nuclear spins. However, calculating the exact quantum mechanical spin dynamics presents a significant challenge, and has not been possible before now. Here we use a recently developed method to perform numerically converged simulations of the C+PF- quantum mechanical spin dynamics, including all coupled spins. Comparison of these quantum mechanical simulations with various semiclassical approximations reveals that, while it is not perfect, the best semiclassical approximation does capture essentially all of the relevant physics in this problem.

physics.chem-ph↗