arXiv subjects

Alexis Ralli

Publications and source records attributed to Alexis Ralli.

17 recordsLinked to original sources

arXiv2026

Quantum-Accelerated Self-Consistent Field: A Hybrid Algorithm

We present the Grover adaptive search self-consistent field (GAS-SCF) algorithm. GAS-SCF leverages quantum arithmetic to construct an efficient oracle that marks target states (Fock states) which improve upon some initial classical energy estimate. Amplitude amplification then increases the probability of measuring these states. This approach offers a theoretical quadratic speed-up for the optimization problem encountered in SCF quantum chemistry and establishes a baseline against which structured optimization algorithms, such as QAOA and DQI may be compared. In this work, we classically simulate three examples as proofs of concept of the algorithm, the largest consisting of 26 qubits. We then extend our analysis to two larger systems, with O3 representing the largest case at 330 qubits. These examples are chosen to probe classically challenging SCF regimes. Achieving chemically relevant applications of GAS-SCF will require large-scale, fault-tolerant quantum hardware.

quant-ph↗

arXiv2025

Towards Compact Wavefunctions from Quantum-Selected Configuration Interaction

A recent direction in quantum computing for molecular electronic structure sees the use of quantum devices as configuration sampling machines integrated within high-performance computing (HPC) platforms. This appeals to the strengths of both the quantum and classical hardware; where state-sampling is classically hard, the quantum computer can provide computational advantage in the selection of high quality configuration subspaces, while the final molecular energies are evaluated by solving an interaction matrix on HPC and is therefore not corrupted by hardware noise. In this work, we present an algorithm that leverages stochastic Hamiltonian time evolution in Quantum-Selected Configuration Interaction (QSCI), with multireference perturbation theory capturing missed correlations outside the configuration subspace. The approach is validated through a hardware demonstration utilising 42 qubits of an IQM superconducting device to calculate the potential energy curve of the inorganic silane molecule, SiH4 using a 6-31G atomic orbital basis set, under a stretching of the Si-H bond length. We assess the resulting wavefunctions for compactness, a point on which QSCI has previously been criticised. At large separations, where static correlation dominates, we find a configuration space more than 200 times smaller than that obtained from a conventional SCI selection criterion yields comparable energies. We also compare against the best-in-class Heatbath Configuration Interaction algorithm and observe similar wavefunction compactness at convergence. This result is achieved with a configuration sampling scheme that uses the experimental orbital occupancies of a time-evolved quantum state to predict likely single and double excitations away from existing configurations to bias the subspace expansion procedure.

quant-ph↗

arXiv2025

The Renormalized Yukawa Hamiltonian: Spectrum, Parton Distribution Functions, and Resource Estimates for Quantum Simulation

We apply the Renormalization Group Procedure for Effective Particles (RGPEP) to the front form Yukawa Hamiltonian, yielding a renormalized (effective) Hamiltonian, accurate up to second order in the coupling strength. Subsequently, we examine the spectrum and parton distribution functions produced by the renormalized Hamiltonian, and show that the addition of counterterms leads to finite results. Resource estimates for quantum simulation are calculated for a single `Ladder Operator Block Encoding' (LOBE), and show that the cost to block encode the renormalized Hamiltonian is comparable to block encoding the bare Hamiltonian.

hep-th↗

arXiv2025

Noncontextual Pauli Hamiltonians

Contextuality is a key feature of quantum mechanics, and identification of noncontextual subtheories of quantum mechanics is of both fundamental and practical importance. Recently, noncontextual Pauli Hamiltonians have been defined in the setting of variational quantum algorithms. In this work we rigorously establish a number of properties of noncontextual Pauli Hamiltonians. We prove that these Hamiltonians can be composed of more Pauli operators than diagonal Hamiltonians. This establishes that noncontextual Hamiltonians are able to describe a greater number of physical interactions. We then show that the eigenspaces admit an efficient classical description. We analyse the eigenspace of these Hamiltonians and prove that for every eigenvalue there exists an associated eigenvector whose stabilizer rank scales linearly with the number of qubits. We prove that further structure in these Hamiltonians allow us to derive where degeneracies in the eigenspectrum can arise. We thus open the field to a new class of efficiently simulatable states.

quant-ph↗

arXiv2025

Simulating the Antiferromagnetic Heisenberg Model on a Spin-Frustrated Kagome Lattice with the Contextual Subspace Variational Quantum Eigensolver

In this work we investigate the ground state properties of a candidate quantum spin liquid using a superconducting Noisy Intermediate-Scale Quantum (NISQ) device. Specifically, we study the antiferromagnetic Heisenberg model on a Kagome lattice, a geometrically frustrated structure that gives rise to a highly degenerate energy spectrum. To successfully simulate this system, we employ a qubit reduction strategy leveraging the Contextual Subspace methodology, significantly reducing the problem size prior to execution on the quantum device. We improve the quality of these subspaces by using the wavefunctions obtained from low bond dimension Density Matrix Renormalization Group (DMRG) calculations to bias the subspace stabilizers through a symplectic approximate symmetry generator extraction algorithm. Reducing the Hamiltonian size allows us to implement tiled circuit ensembles and deploy the Variational Quantum Eigensolver (VQE) to estimate the ground state energy. We adopt a hybrid quantum error mitigation strategy combining Readout Error Mitigation (REM), Symmetry Verification (SV) and Zero Noise Extrapolation (ZNE). This approach yields high-accuracy energy estimates, achieving error rates on the order of 0.01% and thus demonstrating the potential of near-term quantum devices for probing frustrated quantum materials.

quant-ph↗

arXiv2025

Bridging Quantum Chemistry and MaxCut: Classical Performance Guarantees and Quantum Algorithms for the Hartree-Fock Method

In quantum chemistry, self-consistent field (SCF) algorithms define a nonlinear optimization problem, with both continuous and discrete components. In this work, we derive Hartree-Fock-inspired SCF algorithms that can be exactly written as a sequence of Quadratic Unconstrained Spin/Binary Optimization problems (QUSO/QUBO). We reformulate the optimization problem as a series of MaxCut graph problems, which can be efficiently solved using semi-definite programming techniques. This procedure provides performance guarantees at each SCF step, irrespective of the complexity of the optimization landscape. We numerically demonstrate the QUBO-SCF and MaxCut-SCF methods by studying the hydroxide anion OH- and molecular Nitrogen N2. The largest problem addressed in this study involves a system comprised of 220 qubits (equivalently, spin-orbitals). Our results show that QUBO-SCF and MaxCut-SCF suffer much less from internal instabilities compared with conventional SCF calculations. Additionally, we show that the new SCF algorithms can enhance single-reference methods, such as configuration interaction. Finally, we explore how quantum algorithms for optimization can be applied to the QUSO problems arising from the Hartree-Fock method. Four distinct hybrid-quantum classical approaches are introduced: GAS-SCF, QAOA-SCF, QA-SCF and DQI-SCF.

quant-ph↗

arXiv2025

Extending Quantum Computing through Subspace, Embedding and Classical Molecular Dynamics Techniques

The advent of hybrid computing platforms consisting of quantum processing units integrated with conventional high-performance computing brings new opportunities for algorithm design. By strategically offloading select portions of the workload to classical hardware where tractable, we may broaden the applicability of quantum computation in the near term. In this perspective, we review techniques that facilitate the study of subdomains of chemical systems with quantum computers and present a proof-of-concept demonstration of quantum-selected configuration interaction deployed within a multiscale/multiphysics simulation workflow leveraging classical molecular dynamics, projection-based embedding and qubit subspace tools. This allows the technology to be utilised for simulating systems of real scientific and industrial interest, which not only brings true quantum utility closer to realisation but is also relevant as we look forward to the fault-tolerant regime.

quant-ph↗

arXiv2025

Ladder Operator Block-Encoding

We describe and analyze LOBE (Ladder Operator Block-Encoding), a framework for block-encoding ladder operators that act upon fermionic and bosonic modes. In this framework, we achieve efficient block-encodings by applying the desired action of the operator onto the quantum state and pushing any undesired effects outside of the encoded subspace. This direct approach avoids any overhead caused by expanding the operators in another basis. We numerically benchmark these constructions using models arising in quantum field theories including the quartic harmonic oscillator, and $\phi^4$ and Yukawa Hamiltonians on the light front. These benchmarks show that LOBE often produces block-encodings with fewer non-Clifford operations, fewer block-encoding ancillae and overall number of qubits, and lower rescaling factors for various operators as compared to frameworks that expand the ladder operators in the Pauli basis. LOBE constructions also demonstrate favorable scaling with respect to key parameters, including the maximum occupation of bosonic modes, the total number of fermionic and bosonic modes, and the locality of the operators. LOBE is implemented as an open-source python package to enable further applications.

quant-ph↗

arXiv2025

Carleman-lattice-Boltzmann quantum circuit with matrix access oracles

We apply Carleman linearization of the Lattice Boltzmann (CLB) representation of fluid flows to quantum emulate the dynamics of a 2D Kolmogorov-like flow. We assess the accuracy of the result and find a relative error of the order of $10^{-3}$ with just two Carleman iterates, for a range of the Reynolds number up to a few hundreds. We first define a gate-based quantum circuit for the implementation of the CLB method and then exploit the sparse nature of the CLB matrix to build a quantum circuit based on block-encoding techniques which makes use of matrix oracles. It is shown that the gate complexity of the algorithm is thereby dramatically reduced, from exponential to quadratic. However, due to the need of employing up to seven ancilla qubits, the probability of success of the corresponding circuit for a single time step is too low to enable multi-step time evolution. Several possible directions to circumvent this problem are briefly outlined.

quant-ph↗

arXiv2024

Accurately Simulating the Time Evolution of an Ising Model with Echo Verified Clifford Data Regression on a Superconducting Quantum Computer

We present an error mitigation strategy composed of Echo Verification (EV) and Clifford Data Regression (CDR), the combination of which allows one to learn the effect of the quantum noise channel to extract error mitigated estimates for the expectation value of Pauli observables. We analyse the behaviour of the method under the depolarizing channel and derive an estimator for the depolarization rate in terms of the ancilla purity and postselection probability. We also highlight the sensitivity of this probability to noise, a potential bottleneck for the technique. We subsequently consider a more general noise channel consisting of arbitrary Pauli errors, which reveals a linear relationship between the error rates and the estimation of expectation values, suggesting the learnability of noise in EV by regression techniques. Finally, we present a practical demonstration of Echo Verified Clifford Data Regression (EVCDR) on a superconducting quantum computer and observe accurate results for the time evolution of an Ising model over spin-lattices consisting of up to 35 sites and circuit depths up to 173 entangling layers.

quant-ph↗

arXiv2023

Contextual Subspace Variational Quantum Eigensolver Calculation of the Dissociation Curve of Molecular Nitrogen on a Superconducting Quantum Computer

In this work we present an experimental demonstration of the Contextual Subspace Variational Quantum Eigensolver on superconducting quantum hardware. In particular, we compute the potential energy curve for molecular nitrogen, where a dominance of static correlation in the dissociation limit proves challenging for many conventional quantum chemistry techniques. Our quantum simulations retain good agreement with the full configuration interaction energy in the chosen STO-3G basis, outperforming all benchmarked single-reference wavefunction techniques in capturing the bond-breaking appropriately. Moreover, our methodology is competitive with several multiconfigurational approaches, but at a considerable saving of quantum resource, meaning larger active spaces can be treated for a fixed qubit allowance. To achieve this result we deploy an error mitigation/suppression strategy comprised of dynamical decoupling, measurement-error mitigation and zero-noise extrapolation, in addition to circuit parallelization that not only provides passive averaging of noise but improves the effective shot-yield to reduce the measurement overhead. Furthermore, we introduce a modification to previous adaptive ansatz construction algorithms that incorporates hardware-awareness into our variational circuits to minimize the transpilation cost for the target qubit topology.

quant-ph↗

arXiv2023

Calculating the Single-Particle Many-body Green's Functions via the Quantum Singular Value Transform Algorithm

The Quantum Singular Value Transformation (QSVT) is a technique that provides a unified framework for describing many of the quantum algorithms discovered to date. We implement a noise-free simulation of the technique to investigate how it can be used to perform matrix inversion, which is an important step in calculating the single-particle Green's function in the Lehmann representation. Due to the inverse function not being defined at zero, we explore the effect of approximating f(x)=1/x with a polynomial. This is carried out by calculating the single-particle Green's function of the two-site single-impurity Anderson model. We also propose a new circuit construction for the linear combination of unitaries block encoding technique, that reduces the number of single and two-qubit gates required.

quant-ph↗

arXiv2023

Benchmarking Noisy Intermediate Scale Quantum Error Mitigation Strategies for Ground State Preparation of the HCl Molecule

Due to numerous limitations including restrictive qubit topologies, short coherence times and prohibitively high noise floors, few quantum chemistry experiments performed on existing noisy intermediate-scale quantum hardware have achieved the high bar of chemical precision, namely energy errors to within 1.6 mHa of full configuration interaction. To have any hope of doing so, we must layer contemporary resource reduction techniques with best-in-class error mitigation methods; in particular, we combine the techniques of qubit tapering and the contextual subspace variational quantum eigensolver with several error mitigation strategies comprised of measurement-error mitigation, symmetry verification, zero-noise extrapolation and dual-state purification. We benchmark these strategies across a suite of eight 27-qubit IBM Falcon series quantum processors, taking preparation of the HCl molecule's ground state as our testbed.

quant-ph↗

arXiv2022

Unitary Partitioning and the Contextual Subspace Variational Quantum Eigensolver

The contextual subspace variational quantum eigensolver (CS-VQE) is a hybrid quantum-classical algorithm that approximates the ground-state energy of a given qubit Hamiltonian. It achieves this by separating the Hamiltonian into contextual and noncontextual parts. The ground-state energy is approximated by classically solving the noncontextual problem, followed by solving the contextual problem using VQE, constrained by the noncontextual solution. In general, computation of the contextual correction needs fewer qubits and measurements compared with solving the full Hamiltonian via traditional VQE. We simulate CS-VQE on different tapered molecular Hamiltonians and apply the unitary partitioning measurement reduction strategy to further reduce the number of measurements required to obtain the contextual correction. Our results indicate that CS-VQE combined with measurement reduction is a promising approach to allow feasible eigenvalue computations on noisy intermediate-scale quantum devices. We also provide a modification to the CS-VQE algorithm; the CS-VQE algorithm previously could cause an exponential increase in Hamiltonian terms, but with this modification now at worst will scale quadratically.

quant-ph↗

arXiv2022

A stabilizer framework for Contextual Subspace VQE and the noncontextual projection ansatz

Quantum chemistry is a promising application for noisy intermediate-scale quantum (NISQ) devices. However, quantum computers have thus far not succeeded in providing solutions to problems of real scientific significance, with algorithmic advances being necessary to fully utilise even the modest NISQ machines available today. We discuss a method of ground state energy estimation predicated on a partitioning the molecular Hamiltonian into two parts: one that is noncontextual and can be solved classically, supplemented by a contextual component that yields quantum corrections obtained via a Variational Quantum Eigensolver (VQE) routine. This approach has been termed Contextual Subspace VQE (CS-VQE), but there are obstacles to overcome before it can be deployed on NISQ devices. The problem we address here is that of the ansatz - a parametrized quantum state over which we optimize during VQE. It is not initially clear how a splitting of the Hamiltonian should be reflected in our CS-VQE ans\"atze. We propose a 'noncontextual projection' approach that is illuminated by a reformulation of CS-VQE in the stabilizer formalism. This defines an ansatz restriction from the full electronic structure problem to the contextual subspace and facilitates an implementation of CS-VQE that may be deployed on NISQ devices. We validate the noncontextual projection ansatz using a quantum simulator, with results obtained herein for a suite of trial molecules.

quant-ph↗

arXiv2022

A Scalable Approach to Quantum Simulation via Projection-based Embedding

Owing to the computational complexity of electronic structure algorithms running on classical digital computers, the range of molecular systems amenable to simulation remains tightly circumscribed even after many decades of work. Quantum computers hold the promise of transcending such limitations although in the current era the size and noise of these devices militates against significant progress. Here we describe a new and chemically intuitive approach that permits a subdomain of the electronic structure of a molecule to be calculated accurately on a quantum device, while the rest of the molecule is described at a lower level of accuracy using density functional theory running on a classical computer. We demonstrate that our method produces improved results for molecules that cannot be simulated fully on quantum computers but which can be resolved classically at a lower level of approximation. Our algorithm is tunable, so that the size of the quantum simulation can be adjusted to run on available quantum resources. Therefore, as quantum devices become larger, our method will enable increasingly large subdomains to be studied accurately.

quant-ph↗

arXiv2020

Implementation of Measurement Reduction for the Variational Quantum Eigensolver

One limitation of the variational quantum eigensolver algorithm is the large number of measurement steps required to estimate different terms in the Hamiltonian of interest. Unitary partitioning reduces this overhead by transforming the problem Hamiltonian into one containing fewer terms. We explore two different circuit constructions of the transformation required - one built by a sequence of rotations and the other a linear combination of unitaries (LCU). To assess performance, we simulated chemical Hamiltonians and studied the ground states of H2 and LiH. Both implementations are successful even in the presence of noise. The sequence of rotations realization offers the greatest benefit to calculations, whereas the probabilistic nature of LCU reduces its effectiveness. To our knowledge, this work also demonstrates the first experimental implementation of LCU on quantum hardware.

quant-ph↗