arXiv subjects

Nicholas J. Mayhall

Publications and source records attributed to Nicholas J. Mayhall.

At least 19 recordsLinked to original sources

arXiv2026

Efficient computation of real-time correlators using Pauli Propagation

Pauli propagation has shown promise for classically simulating quantum dynamics by evolving observables directly in the Heisenberg picture. In this work, we investigate its use for computing real-time two-point time-ordered correlators in one- and two-dimensional quantum systems. One major limitation of Pauli propagation is the rapid growth in the number of Pauli strings beyond short times. We overcome this limitation by combining accurate short-time Pauli-propagation data with time extension methods based on a positivity condition and the observation that the dynamics are often dominated by a small number of characteristic frequencies. This combined approach extends correlation functions far beyond the directly accessible time window while avoiding the exponential proliferation of Pauli operators. We demonstrate that the resulting correlators retain the relevant dynamical and spectral information. Our results broaden the regime in which classical methods can reliably probe the real-time dynamics of interacting quantum many-body systems.

quant-ph↗

arXiv2026

How to really measure operator gradients in ADAPT-VQE

ADAPT-VQE is a leading variational quantum algorithm as it circumvents the choice-of-ansatz conundrum by iteratively growing compact and arbitrarily accurate problem-tailored ansätze. However, for molecular Hamiltonians and hardware-efficient operator pools, the gradient-measurement step of the algorithm requires the estimation of $\mathcal{O}(N^8)$ observables, which may represent a bottleneck for relevant system sizes on real devices. We present an efficient strategy for measuring the gradients of the three best-performing hardware-efficient operator pools by partitioning the required observables into $\mathcal{O}(N^3)$-sized sets of commuting Paulis that can be simultaneously measured with an at most $N-3$ CNOT overhead. We argue that our approach is robust to shot-noise effects and show that measuring the pool gradients is, in fact, not $\mathcal{O}(N^4)$, but only about $4N$ times as expensive as measuring the energy once. Our proposed measurement strategy significantly ameliorates the measurement overhead of ADAPT-VQE and brings us one step closer to practical implementations on real devices.

quant-ph↗

arXiv2026

Pauli propagation enables fast classical simulation of strongly correlated quantum systems

Ground state energy estimation for strongly correlated quantum systems remains a central challenge in computational physics and chemistry. While tensor network methods like DMRG provide efficient solutions for one-dimensional systems, higher-dimensional problems remain difficult. Here we present a variational double bracket flow (vDBF) algorithm that leverages Pauli Propagation, a technique originally developed for classical simulation of quantum circuits, to efficiently approximate ground state energies. By combining greedy operator selection with coefficient-based fluctuation truncation and energy-variance extrapolation, we obtain results with sub-1% relative accuracy compared to DMRG benchmarks for the Heisenberg and Hubbard models in one and two dimensions. For a 10x10 Heisenberg lattice (100 qubits), vDBF obtains accurate results in approximately 1 minute on a single CPU thread, compared to over 50 hours on 64 threads for DMRG. For the 8x8 half-filled Hubbard model, corresponding to 128 qubits, vDBF reaches the 1% error regime in less than one hour, while our DMRG calculations required more than 10 hours on 64 threads. We further test vDBF on the 84-qubit π-valence active space of hexabenzocoronene, where the tighter-threshold calculations achieve sub-1% agreement with DMRG. These results demonstrate that classical simulation techniques developed in the context of quantum advantage benchmarking can provide practical tools for many-body physics.

quant-ph↗

arXiv2026

TIMES-ADAPT: A Quantum algorithm for real-time evolution in low-energy subspaces using fixed-depth circuits

We propose a new variational quantum algorithm, which we refer to as TIMES-ADAPT, that prepares time-evolved states in a low-energy or symmetric subspace of a time-independent Hamiltonian on a quantum computer. Using a specially trained unitary that diagonalizes the Hamiltonian in a subspace, we construct fixed-depth circuits for real-time evolution in the subspace, where time only enters as a circuit parameter. We present two versions of the algorithm depending on whether the initial state is specified in the energy eigenbasis or computational basis. We consider two important applications of our methods: wave packet evolution and energy transport in spin systems. We benchmark our algorithms using variants of the Heisenberg XXZ model.

quant-ph↗

arXiv2026

Co-Designed Adaptive Quantum State Preparation Protocols

We propose a co-designed variant of ADAPT-VQE (Co-ADAPT-VQE) where the quantum hardware is taken into account in the construction of the ansatz. This framework can be readily used to optimize state preparation circuits for any device, addressing shortcomings such as limited connectivity, short coherence times, and variable gate errors. We exemplify the impact of Co-ADAPT-VQE by creating state preparation circuits for devices with linear nearest-neighbor (LNN) connectivity. We show a reduction of the CNOT count of the final circuits by up to 97% for 12-14 qubit systems, with the impact being greater for larger and more strongly correlated systems. Surprisingly, the circuits created by Co-ADAPT-VQE provide an over 70% CNOT count reduction with respect to the original ADAPT-VQE in all-to-all connectivity, despite being restricted to LNN qubit interactions.

quant-ph↗

arXiv2025

TEPID-ADAPT: Adaptive variational method for simultaneous preparation of low-temperature Gibbs and low-lying eigenstates

Preparing Gibbs states, which describe systems in equilibrium at finite temperature, is of great importance, particularly at low temperatures. In this work, we propose a new method -- TEPID-ADAPT -- that prepares the thermal Gibbs state of a given Hamiltonian at low temperatures using a variational method that is partially adaptive and uses a purification with a minimal number of ancillary qubits. We also present an alternative implementation without ancillary qubits. A key technical innovation here is to use a mixed-state ansatz where the entropy can be efficiently calculated, with no computational overhead. Our algorithm uses a truncated, parametrized eigenspectrum of the Hamiltonian. Beyond preparing Gibbs states, this approach also straightforwardly gives us access to the truncated low-energy eigenspectrum of the Hamiltonian, making it also a method that prepares excited states simultaneously. As a result of this, we are also able to prepare thermal states at any lower temperature of the same Hamiltonian without further optimization.

quant-ph↗

arXiv2025

Computing Exchange Coupling constants in Transition metal complexes with Tensor Product Selected Configuration Interaction

Transition metal complexes present significant challenges for electronic structure theory due to strong electron correlation arising from partially filled $d$-orbitals. We compare our recently developed Tensor Product Selected Configuration Interaction (TPSCI) with Density Matrix Renormalization Group (DMRG) for computing exchange coupling constants in six transition metal systems, including dinuclear Cr, Fe, and Mn complexes and a tetranuclear Ni-cubane. TPSCI uses a locally correlated tensor product state basis to capture electronic structure efficiently while maintaining interpretability. From calculations on active spaces ranging from (22e,29o) to (42e,49o), we find that TPSCI consistently yields higher variational energies than DMRG due to truncation of local cluster states, but provides magnetic exchange coupling constants (J) generally within 10-30 cm$^{-1}$ of DMRG results. Key advantages include natural multistate capability enabling direct J extrapolation with smaller statistical errors, and computational efficiency for challenging systems. However, cluster state truncation represents a fundamental limitation requiring careful convergence testing, particularly for large local cluster dimensions. We identify specific failure cases where current truncation schemes break down, highlighting the need for improved cluster state selection methods and distributed memory implementations to realize TPSCI's full potential for strongly correlated systems.

physics.chem-ph↗

arXiv2025

Floquet-ADAPT-VQE: A Quantum Algorithm to Simulate Non-Equilibrium Physics in Periodically Driven Systems

Periodically driven quantum systems exhibit many fascinating phenomena absent in equilibrium systems, but their simulation is more challenging than that of static systems. Consequently, quantum simulation of these systems offers greater opportunity for achieving quantum advantage. To build the foundation for simulating time-periodic Hamiltonians, we utilize the Floquet-Hilbert space formalism to transform the Hamiltonian into a time-independent form and provide its Pauli decomposition. We propose a hybrid quantum-classical algorithm, Floquet-ADAPT-VQE, to simulate the non-equilibrium physics of periodically driven quantum systems. We define a cost function based on the square of the shifted extended Floquet Hamiltonian and show how to prepare Floquet states using Floquet-ADAPT-VQE. We also obtain a suitable auxiliary initial state whose squared Floquet energy is independent of the number of auxiliary qubits as well as the driving frequency, which leads to better convergence with fewer ADAPT iterations. Additionally, we provide a framework to calculate the time-dependent expectation value of observables in the Floquet state with fixed-depth quantum circuit. We demonstrate our algorithm by performing numerical simulations on a periodically driven XYZ model with a magnetic field. We also explore potential applications of our algorithm for studying various non-equilibrium phenomena in periodically driven systems.

quant-ph↗

arXiv2025

Reducing the Resources Required by ADAPT-VQE Using Coupled Exchange Operators and Improved Subroutines

Adaptive variational quantum algorithms arguably offer the best prospects for quantum advantage in the Noisy Intermediate-Scale Quantum era. Since the inception of the first such algorithm, the Adaptive Derivative-Assembled Problem-Tailored Variational Quantum Eigensolver (ADAPT-VQE), many improvements have appeared in the literature. We combine the key improvements along with a novel operator pool -- which we term Coupled Exchange Operator (CEO) pool -- to assess the cost of running state-of-the-art ADAPT-VQE on hardware in terms of measurement counts and circuit depth. We show a dramatic reduction of these quantum computational resources compared to the early versions of the algorithm: CNOT count, CNOT depth and measurement costs are reduced by up to 88%, 96% and 99.6%, respectively, for molecules represented by 12 to 14 qubits (LiH, H6 and BeH2). We also find that our state-of-the-art CEO-ADAPT-VQE outperforms the Unitary Coupled Cluster Singles and Doubles ansatz, the most widely used static VQE ansatz, in all relevant metrics, and offers a five order of magnitude decrease in measurement costs as compared to other static ansätze with competitive CNOT counts.

quant-ph↗

arXiv2025

Qubit-efficient quantum chemistry with the ADAPT variational quantum eigensolver and double unitary downfolding

In this work, we combine the recently developed double unitary coupled cluster (DUCC) theory with the adaptive, problem-tailored variational quantum eigensolver (ADAPT-VQE) to explore accuracy of unitary downfolded Hamiltonians for quantum simulation of chemistry. We benchmark the ability of DUCC effective Hamiltonians to recover dynamical correlation energy outside of an active space. We consider the effects of strong correlation, commutator truncation, higher-body terms, and approximate external amplitudes on the accuracy of these effective Hamiltonians. When combining these DUCC Hamiltonians with ADAPT-VQE, we observe similar convergence of the ground state as compared to bare active space Hamiltonians, demonstrating that DUCC Hamiltonians provide increased accuracy without increasing the load on the quantum processor.

quant-ph↗

arXiv2024

Reducing measurement costs by recycling the Hessian in adaptive variational quantum algorithms

Adaptive protocols enable the construction of more efficient state preparation circuits in variational quantum algorithms (VQAs) by utilizing data obtained from the quantum processor during the execution of the algorithm. This idea originated with ADAPT-VQE, an algorithm that iteratively grows the state preparation circuit operator by operator, with each new operator accompanied by a new variational parameter, and where all parameters acquired thus far are optimized in each iteration. In ADAPT-VQE and other adaptive VQAs that followed it, it has been shown that initializing parameters to their optimal values from the previous iteration speeds up convergence and avoids shallow local traps in the parameter landscape. However, no other data from the optimization performed at one iteration is carried over to the next. In this work, we propose an improved quasi-Newton optimization protocol specifically tailored to adaptive VQAs. The distinctive feature in our proposal is that approximate second derivatives of the cost function are recycled across iterations in addition to parameter values. We implement a quasi-Newton optimizer where an approximation to the inverse Hessian matrix is continuously built and grown across the iterations of an adaptive VQA. The resulting algorithm has the flavor of a continuous optimization where the dimension of the search space is augmented when the gradient norm falls below a given threshold. We show that this inter-optimization exchange of second-order information leads the Hessian in the state of the optimizer to better approximate the exact Hessian. As a result, our method achieves a superlinear convergence rate even in situations where the typical quasi-Newton optimizer converges only linearly. Our protocol decreases the measurement costs in implementing adaptive VQAs on quantum hardware as well as the runtime of their classical simulation.

quant-ph↗

arXiv2024

Physically motivated improvements of Variational Quantum Eigensolvers

The Adaptive Derivative-Assembled Pseudo-Trotter Variational Quantum Eigensolver (ADAPT-VQE) has emerged as a pivotal promising approach for electronic structure challenges in quantum chemistry with noisy quantum devices. Nevertheless, to surmount existing technological constraints, this study endeavors to enhance ADAPT-VQE's efficacy. Leveraging insights from electronic structure theory, we concentrate on optimizing state preparation without added computational burden and guiding ansatz expansion to yield more concise wavefunctions with expedited convergence toward exact solutions. These advancements culminate in shallower circuits and, as demonstrated, reduced measurement requirements. This research delineates these enhancements and assesses their performance across mono, di, and tridimensional arrangements of H4 models, as well as in the water molecule. Ultimately, this work attests to the viability of physically-motivated strategies in fortifying ADAPT-VQE's efficiency, marking a significant stride in quantum chemistry simulations.

quant-ph↗

arXiv2024

Minimal evolution times for fast, pulse-based state preparation in silicon spin qubits

Standing as one of the most significant barriers to reaching quantum advantage, state-preparation fidelities on noisy intermediate-scale quantum processors suffer from quantum-gate errors, which accumulate over time. A potential remedy is pulse-based state preparation. We numerically investigate the minimal evolution times (METs) attainable by optimizing (microwave and exchange) pulses on silicon hardware. We investigate two state preparation tasks. First, we consider the preparation of molecular ground states and find the METs for H$_2$, HeH$^+$, and LiH to be 2.4 ns, 4.4 ns, and 27.2 ns, respectively. Second, we consider transitions between arbitrary states and find the METs for transitions between arbitrary four-qubit states to be below 50 ns. For comparison, connecting arbitrary two-qubit states via one- and two-qubit gates on the same silicon processor requires approximately 200 ns. This comparison indicates that pulse-based state preparation is likely to utilize the coherence times of silicon hardware more efficiently than gate-based state preparation. Finally, we quantify the effect of silicon device parameters on the MET. We show that increasing the maximal exchange amplitude from 10 MHz to 1 GHz accelerates the METs, e.g., for H$_2$ from 84.3 ns to 2.4 ns. This demonstrates the importance of fast exchange. We also show that increasing the maximal amplitude of the microwave drive from 884 kHz to 56.6 MHz shortens state transitions, e.g., for two-qubit states from 1000 ns to 25 ns. Our results bound both the state-preparation times for general quantum algorithms and the execution times of variational quantum algorithms with silicon spin qubits.

quant-ph↗

arXiv2024

Restricted Open-shell cluster Mean-Field theory for Strongly Correlated Systems

The cluster-based Mean Field method (cMF) and it's second order perturbative correction[1], was introduced by Jiménez-Hoyos and Scuseria to reduce the cost of modeling strongly correlated systems by dividing an active space up into small clusters, which are individually solved in the mean-field presence of each other. In that work, clusters with unpaired electrons are treated naturally, by allowing the $α$ and $β$ orbitals to spin polarize. While that provided significant energetic stabilization, the resulting cMF wavefunction was spin-contaminated, making it difficult to use as a reference state for spin-pure post-cMF methods. In this work, we propose the Restricted Open-shell cMF (RO-cMF) method, extending the cMF approach to systems with open-shell clusters, while not permitting spin-polarization. While the resulting RO-cMF energies are necessarily higher in energy than the unrestricted orbital cMF, the new RO-cMF provides a simple reference state for post-cMF methods that recover the missing inter-cluster correlations. We provide a detailed explanation of the method, and report demonstrative calculations of exchange coupling constants for three systems: a di-iron complex, a di-chromium complex, and a dimerized organic radical. We also report the first perturbatively corrected RO-cMF-PT2 results as well.

physics.chem-ph↗

arXiv2024

Accurate and Interpretable Representation of Correlated Electronic Structure via Tensor Product Selected CI

The task of computing wavefunctions that are accurate, yet simple enough mathematical objects to use for reasoning has long been a challenge in quantum chemistry. The difficulty in drawing physical conclusions from a wavefunction is often related to the generally large number of configurations with similar weights. In Tensor Product Selected CI, we use a locally correlated tensor product state basis, which has the effect of concentrating the weight of a state onto a smaller number of physically interpretable degrees of freedom. In this paper, we apply TPSCI to a series of three molecular systems ranging in separability, one of which is the first application of TPSCI to an open-shell bimetallic system. For each of these systems, we obtain accurate solutions to large active spaces, and analyze the resulting wavefunctions through a series of different approaches including (i) direct inspection of the TPS basis coefficients, (ii) construction of Bloch effective Hamiltonians, and (iii) computation of cluster correlation functions.

physics.chem-ph↗

arXiv2023

Scaling adaptive quantum simulation algorithms via operator pool tiling

Adaptive variational quantum simulation algorithms use information from the quantum computer to dynamically create optimal trial wavefunctions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator pool from which trial wavefunctions are constructed. Finding suitable pools is critical for the efficiency of the algorithm as the problem size increases. Here, we present a technique called operator pool tiling that facilitates the construction of problem-tailored pools for arbitrarily large problem instances. By first performing an ADAPT-VQE calculation on a smaller instance of the problem using a large, but computationally inefficient operator pool, we extract the most relevant operators and use them to design more efficient pools for larger instances. We demonstrate the method here on strongly correlated quantum spin models in one and two dimensions, finding that ADAPT automatically finds a highly effective ansatz for these systems. Given that many problems, such as those arising in condensed matter physics, have a naturally repeating lattice structure, we expect the pool tiling method to be a widely applicable technique apt for such systems.

quant-ph↗

arXiv2023

Generalization of the tensor product selected CI method for molecular excited states

In a recent paper [JCTC, 2020, 16, 6098], we introduced a new approach for accurately approximating full CI ground states in large electronic active-spaces, called Tensor Product Selected CI (TPSCI). In TPSCI, a large orbital active space is first partitioned into disjoint sets (clusters) for which the exact, local many-body eigenstates are obtained. Tensor products of these locally correlated many-body states are taken as the basis for the full, global Hilbert space. By folding correlation into the basis states themselves, the low-energy eigenstates become increasingly sparse, creating a more compact selected CI expansion. While we demonstrated that this approach can improve accuracy for a variety of systems, there is even greater potential for applications to excited states, particularly those which have some excited state character. In this paper, we report on the accuracy of TPSCI for excited states, including a far more efficient implementation in the Julia programming language. In traditional SCI methods that use a Slater determinant basis, accurate excitation energies are obtained only after a linear extrapolation and at a large computational cost. We find that TPSCI with perturbative corrections provides accurate excitation energies for several excited states of various polycyclic aromatic hydrocarbons (PAH) with respect to the extrapolated result (i.e. near exact result). Further, we use TPSCI to report highly accurate estimates of the lowest 31 eigenstates for a tetracene tetramer system with an active space of 40 electrons in 40 orbitals, giving direct access to the initial bright states and the resulting 18 doubly excited (biexcitonic) states.

physics.chem-ph↗

arXiv2023

How Much Entanglement Do Quantum Optimization Algorithms Require?

Many classical optimization problems can be mapped to finding the ground states of diagonal Ising Hamiltonians, for which variational quantum algorithms such as the Quantum Approximate Optimization Algorithm (QAOA) provide heuristic methods. Because the solutions of such classical optimization problems are necessarily product states, it is unclear how entanglement affects their performance. An Adaptive Derivative-Assembled Problem-Tailored (ADAPT) variation of QAOA improves the convergence rate by allowing entangling operations in the mixer layers whereas it requires fewer CNOT gates in the entire circuit. In this work, we study the entanglement generated during the execution of ADAPT-QAOA. Through simulations of the weighted Max-Cut problem, we show that ADAPT-QAOA exhibits substantial flexibility in entangling and disentangling qubits. By incrementally restricting this flexibility, we find that a larger amount of entanglement entropy at earlier stages coincides with faster convergence at later stages. In contrast, while the standard QAOA quickly generates entanglement within a few layers, it cannot remove excess entanglement efficiently. Our results demonstrate that the role of entanglement in quantum optimization is subtle and provide guidance for building favorable features into quantum optimization algorithms.

quant-ph↗