arXiv subjects

Alex J. W. Thom

Publications and source records attributed to Alex J. W. Thom.

At least 19 recordsLinked to original sources

arXiv2026

Explaining the magnitude of Chirality-Induced Spin Selectivity via electron-electron exchange

Chiral molecular structure can couple to electron spin, leading to unexpected spin polarization effects. This Chirality-Induced Spin Selectivity (CISS) was first reported for DNA molecules adsorbed on gold but its microscopic origin remains unclear. We demonstrated though simulation that the exchange arising from electron-electron Coulomb interactions within the self-consistent mean field (Hartree--Fock) approximation can yield significant ($\sim 2\%$) spin polarisation for $3$-methylcyclohexanone adsorbed on Cu(111) amplifying a much smaller ($\sim 0.0014\%$) initial bias, consistent with experiment. Symmetry considerations ensure the result is physically meaningful, while its ab-initio nature ensures all parameters are physically realistic. This amplification is connected to existing studies on spin-symmetry breaking in Hartree--Fock, providing a new pathway for understanding the magnitude of CISS as an emergent phenomenon of interacting electrons.

quant-ph↗

arXiv2026

Shallow Electronic State Preparation for Quantum Chemistry with Quantum Monte Carlo Pre-Selection

Quantum computers hold great promise for molecular simulation, but noise remains a fundamental obstacle. We introduce a Quantum Monte Carlo (QMC) pre-screening procedure that constructs compact, physically motivated Givens rotation ansätze tailored to realistic quantum hardware. By identifying the most important wavefunction contributions early in a QMC simulation, we build circuits that are shallower that conventional alternatives while preserving number symmetry. Benchmarked on Quantinuum System Model H1, QMC-prescreened circuits outperform more complex ansätze under realistic noise conditions. The method offers a practical path toward chemical accuracy on quantum devices, by providing an adjustable trade-off between expressivity and circuit depth to generate shallow circuits suited to current high-noise devices, as well as deeper, more expressive circuits that can be deployed on future lower-noise devices.

quant-ph↗

arXiv2024

Natural Orbital Non-Orthogonal Configuration Interaction

Non-orthogonal configuration interaction (NOCI) is a generalization of the standard orthogonal configuration interaction (CI) method and offers a highly flexible framework for describing ground and excited electronic states. However, this flexibility also comes with challenges, as there is still no clear or generally accepted approach for constructing a compact and accurate state basis for NOCI. In this work, we take a step toward addressing this challenge by introducing a novel NOCI approach designed with three primary objectives: (1) ensuring the method is systematic, (2) achieving a compact NOCI expansion, and (3) treating all electronic states of interest on equal footing. The development of our approach is presented step by step, with each building block evaluated and validated through applications to simple model systems, demonstrating its effectiveness and potential.

physics.chem-ph↗

arXiv2024

Shallow Quantum Scalar Products with Phase Information

The measurement of scalar products between two vectors is a common task in scientific computing and, by extension, in quantum computing. In this work, we introduce two alternative quantum circuits for computing scalar products with phase information, combining the structure of the swap test, the vacuum test, and the Hadamard test. These novel frameworks, called the zero-control and one-control tests, present different trade-offs between circuit depth and qubit count for accessing the scalar product between two quantum states. We demonstrate that our approach significantly reduces the gate count for large numbers of qubits and decreases the scaling of quantum requirements compared to the Hadamard test.

quant-ph↗

arXiv2024

On the characteristics of helium filled nano-pores in amorphous silicon thin films

The properties of helium-filled nanopores in amorphous silicon are elucidated by combining theoretical knowledge of helium electronic structure with the results of Scanning Transmission electron microscopy/electron energy loss spectroscopy (STEM/EELS). Two of the properties determined are the density and pressure of the confined helium, these being key properties which are needed for application. The experimental data consists, firstly of the shift of the helium 1s^2-> 1s2p(^1P) excitation energy from that of a free atom upon entering a condensed phase, and secondly, the intensities of both the elastically and inelastically scattered electron beams. Analysis uniting theory with the STEM/EELS measurements for both the helium-filled pores and earlier similar studies of helium encapsulated as bubbles in solid silicon is combined with fully trustworthy and closely related data for helium in its bulk condensed phases. The non-empirical theory used, containing no free parameters, is validated by the excellent agreement between the energy shifts predicted for bulk condensed helium with the entirely independently measured values. The above comparisons between the pores and bubbles with the bulk material show that the helium behaviour is essentially the same in all three of these environments. This means that, although the pressure is clearly temperature dependent, the other important properties are governed solely by the helium density. Although the energy of the electron beam used for the pore measurements differs from that in the bubble experiments, it is shown that scaling the results of either the pore or bubbles results using standard scattering theory almost exactly reproduces the experimental results for the other system. This provides confirmatory evidence that the behaviour of the helium in the pores is essentially the same as that in the bubbles.

cond-mat.mes-hall↗

arXiv2024

Folded Spectrum VQE : A quantum computing method for the calculation of molecular excited states

The recent developments of quantum computing present potential novel pathways for quantum chemistry, as the increased computational power of quantum computers could be harnessed to naturally encode and solve electronic structure problems. Theoretically exact quantum algorithms for chemistry have been proposed (e.g. Quantum Phase Estimation) but the limited capabilities of current noisy intermediate scale quantum devices (NISQ) motivated the development of less demanding hybrid algorithms. In this context, the Variational Quantum Eigensolver (VQE) algorithm was successfully introduced as an effective method to compute the ground state energy of small molecules. The current study investigates the Folded Spectrum (FS) method as an extension to the VQE algorithm for the computation of molecular excited states. It provides the possibility of directly computing excited states around a selected target energy, using the same ansatz as for the ground state calculation. Inspired by the variance-based methods from the Quantum Monte Carlo literature, the FS method minimizes the energy variance, thus requiring a computationally expensive squared Hamiltonian. We alleviate this potentially poor scaling by employing a Pauli grouping procedure, identifying sets of commuting Pauli strings that can be evaluated simultaneously. This allows for a significant reduction of the computational cost. We apply the FS-VQE method to small molecules (H$_2$,LiH), obtaining all electronic excited states with chemical accuracy on ideal quantum simulators.

quant-ph↗

arXiv2023

Optimised Baranyai partitioning of the second quantised Hamiltonian

Simultaneous measurement of multiple Pauli strings (tensor products of Pauli matrices) is the basis for efficient measurement of observables on quantum computers by partitioning the observable into commuting sets of Pauli strings. We present the implementation and optimisation of the Baranyai grouping method for second quantised Hamiltonian partitioning in molecules up to CH$_4$ (cc-pVDZ, 68 qubits) and efficient construction of the diagonalisation circuit in $O(N)$ quantum gates, compared to $O(N^2)$, where $N$ is the number of qubits. We show that this method naturally handles sparsity in the Hamiltonian and produces a $O(1)$ number of groups for linearly scaling Hamiltonians, such as those formed by molecules in a line; rising to $O(N^3)$ for fully connected two-body Hamiltonians. While this is more measurements than some other schemes it allows for the flexibility to move Pauli strings and optimise the variance. We also present an explicit optimisation for spin-symmetry which reduces the number of groups by a factor of $8$, without extra computational effort.

quant-ph↗

arXiv2023

Non-unitary Trotter circuits for imaginary time evolution

We propose an imaginary time equivalent of the well-established Pauli gadget primitive for Trotter-decomposed real time evolution, using mid-circuit measurements on a single ancilla qubit. Imaginary time evolution (ITE) is widely used for obtaining the ground state of a system on classical hardware, computing thermal averages, and as a component of quantum algorithms that perform non-unitary evolution. Near-term implementations on quantum hardware rely on heuristics, compromising their accuracy. As a result, there is growing interest in the development of more natively quantum algorithms. Since it is not possible to implement a non-unitary gate deterministically, we resort to the implementation of probabilistic imaginary time evolution (PITE) algorithms, which rely on a unitary quantum circuit to simulate a block encoding of the ITE operator - that is, they rely on successful ancillary measurements to evolve the system non-unitarily. Compared with previous PITE proposals, the suggested block encoding in this paper results in shorter circuits and is simpler to implement, requiring only a slight modification of the Pauli gadget primitive. This scheme was tested on the transverse Ising model and the fermionic Hubbard model and is demonstrated to converge to the ground state of the system.

quant-ph↗

arXiv2023

Corrected Density Functional Theory and the Random Phase Approximation: Improved Accuracy at Little Extra Cost

We recently introduced an efficient methodology to perform density-corrected Hartree-Fock density functional theory (DC(HF)-DFT) calculations and an extension to it we called "corrected" HF DFT (C(HF)-DFT). In this work, we take a further step and combine C(HF)-DFT, augmented with a straightforward orbital energy correction, with the random phase approximation (RPA). We refer to the resulting methodology as corrected HF RPA (C(HF)-RPA). We evaluate the proposed methodology across various RPA methods: direct RPA (dRPA), RPA with an approximate exchange kernel (RPA-AXK), and RPA with second-order screened exchange (RPA-SOSEX). C(HF)-dRPA, in particular, demonstrates very promising performance; for RPA with exchange methods we find over-corrections for certain chemical problems.

physics.chem-ph↗

arXiv2023

A hybrid stochastic configuration interaction-coupled cluster approach for multireference systems

The development of multireference coupled cluster (MRCC) techniques has remained an open area of study in electronic structure theory for decades due to the inherent complexity of expressing a multi-configurational wavefunction in the fundamentally single-reference coupled cluster framework. The recently developed multireference coupled cluster Monte Carlo (mrCCMC) technique uses the formal simplicity of the Monte Carlo approach to Hilbert space quantum chemistry to avoid some of the complexities of conventional MRCC, but there is room for improvement in terms of accuracy and, particularly, computational cost. In this paper we explore the potential of incorporating ideas from conventional MRCC - namely the treatment of the strongly correlated space in a configuration interaction formalism - to the mrCCMC framework, leading to a series of methods with increasing relaxation of the reference space in the presence of external amplitudes. These techniques offer new balances of stability and cost against accuracy, as well as a means to better explore and better understand the structure of solutions to the mrCCMC equations.

physics.chem-ph↗

arXiv2023

A simple and efficient route towards improved energetics within the framework of density-corrected density functional theory

The crucial step in density-corrected Hartree-Fock density functional theory (DC(HF)-DFT) is to decide whether the density produced by the density functional for a specific calculation is erroneous and hence should be replaced by, in this case, the HF density. We introduce an indicator, based on the difference in non-interacting kinetic energies between DFT and HF calculations, to determine when the HF density is the better option. Our kinetic energy indicator directly compares the self-consistent density of the analysed functional with the HF density, is size-intensive, reliable, and most importantly highly efficient. Moreover, we present a procedure that makes best use of the computed quantities necessary for DC(HF)-DFT by additionally evaluating a related hybrid functional and, in that way, not only "corrects" the density but also the functional itself; we call that procedure corrected Hartree-Fock density functional theory (C(HF)-DFT).

physics.chem-ph↗

arXiv2023

Global descriptors of a water molecule for machine learning of potential energy surfaces

Machine learning of multi-dimensional potential energy surfaces, from purely ab initio datasets, has seen substantial progress in the past years. Gaussian processes, a popular regression method, have been very successful at producing realistic potential energy surfaces from sparse datasets allowing to reduce the computational cost of highly accurate models. However, there are many choices one has to take in the design of the kernel and the feature space which can substantially change the performance and the characteristic of the model. In this study we explore different Gaussian processes set ups and, more specifically, how the permutational invariance of the target surface is controlled through the feature space selection.

physics.chem-ph↗

arXiv2023

Studies on the Transcorrelated Method

We investigate the possibility of using a transcorrelated Hamiltonian to describe electron correlation. Amethod to obtain transcorrelatedwavefunctionswas developed based on the mathematical framework of the bi-variational principle. This involves the construction of an effective transcorrelated Hamiltonian matrix which can be solved in a self-consistent manner. This was optimised using a method we call Second Order Moment (SOM) minimisation to give highly accurate energies for some closed-shell atoms and helium-like ions. The effect of certain correlator terms on the description of electron-electron and electron-nuclear cusps were also examined graphically and some transcorrelated wavefunctions were compared against near-exact Hylleraas wavefunctions.

physics.chem-ph↗

arXiv2023

Optimised Morse transform of a Gaussian process feature space

Morse projections are well-known in chemistry and allow one, within a Morse potential approximation, to redefine the potential in a simple quadratic form. The latter, being a non-linear transform, is also very helpful for machine learning methods as they improve the performance of models by projecting the feature space onto more well-suited coordinates. Usually, the Morse projection parameters are taken from numerical benchmarks. We investigate the effect of changing these parameters latter on the model learning, as well as using the machine learning method itself to make the parameters decision. We find that learning is not necessarily improved by the latter and that general Morse projections are extremely susceptible to changes in the training data.

physics.chem-ph↗

arXiv2022

Modified noise kernels in Gaussian process modelling of energy surfaces

We explore the use of non homogenous noise kernels in Gaussian process modelling to improve the potential energy curve models describing stochastic electronic structure data. We use the same noise kernels on energy curves describing deterministic electronic structure data by creating non-homogenous noise model. We observe, as well as agreement between the noise of the model and the stochastic data, a strong regularisation of the curves when using artificial noises on deterministic data which improves Gaussian processes in the over fitting regime.

physics.chem-ph↗

arXiv2022

Reducing Unitary Coupled Cluster Circuit Depth by Classical Stochastic Amplitude Pre-Screening

Unitary Coupled Cluster (UCC) approaches are an appealing route to utilising quantum hardware to perform quantum chemistry calculations, as quantum computers can in principle perform UCC calculations in a polynomially scaling fashion, as compared to the exponential scaling required on classical computers. Current noisy intermediate scale quantum (NISQ) computers are limited by both hardware capacity in number of logical qubits and the noise introduced by the deep circuits required for UCC calculations using the Variational Quantum Eigensolver (VQE) approach. We present a combined classical--quantum approach where a stochastic classical UCC pre-processing step is used to determine the important excitations in the UCC ansatz. The reduced number of selected excitations are then used in a UCC-based VQE calculation. This approach gives a systematically improvable approximation, and we show that significant reductions in quantum resources can be achieved, with simulations on the CH$_2$, N$_2$ and N$_2$H$_2$ molecules giving sub-milliHartree errors.

quant-ph↗

arXiv2022

On Symmetry and the Reality of Holomorphic Hartree--Fock Wavefunctions

The coalescence and disappearance of Hartree--Fock (HF) solutions as the molecular structure varies have been a common source of criticism for the breakdown of the HF approximation to the potential energy surfaces. However, recent developments in holomorphic HF theory show that this disappearing behavior is only a manifestation of the way conventional HF equations prevent solutions from being analytically continued, but it is unclear what factors govern the existence and the locations of these disappearances. In this work, we explore some of these factors from the perspective of spatial symmetry by introducing a classification for symmetry constraints on electronic-structure calculations. This forms a framework for us to systematically investigate several analytic holomorphic HF solutions of a model $\textrm{[H}_4\textrm{]}^{2+}$ system in STO-3G and demonstrate that, under appropriate conditions, spatial symmetry imposes strict requirements on the reality of certain solutions. The implications for self-consistent-field HF search algorithms are then discussed. Throughout this article, the term reality means the quality of a holomorphic HF solution having real molecular orbitals.

physics.chem-ph↗

arXiv2021

Localised Spin Rotations: A Size-Consistent Approach to Non-Orthogonal Configuration Interaction

Current Non-Orthogonal Configuration Interaction (NOCI) methods often use a set of Self-Consistent Field (SCF) states selected based on chemical intuition. However, it may be challenging to track these SCF states across a dissociation profile and the NOCI states recovered may be spin contaminated. In this paper, we propose a method of applying spin rotation on symmetry broken UHF (sb-UHF) states to generate a basis for NOCI. The dissociation of ethene was examined by localising spin rotation on each resulting carbene fragment. We show that this gives a size-consistent description of its dissociation and results in spin-pure states at all geometries. The dissociation was also studied with different orbitals, namely canonical UHF and Absolutely Localised Molecular Orbitals (ALMO). Furthermore, we demonstrate that the method can be used to restore spin symmetry of symmetry broken SCF wavefunctions for molecules of various sizes, marking an improvement over existing NOCI methods.

physics.chem-ph↗