arXiv subjects

Ilias Magoulas

Publications and source records attributed to Ilias Magoulas.

14 recordsLinked to original sources

arXiv2026

Spin-Adapted Fermionic Unitaries: From Lie Algebras to Compact Quantum Circuits

Conservation of symmetries is crucial for reliable quantum simulations of molecular systems, yet compact circuit implementations of fully symmetry-adapted fermionic unitaries have remained elusive beyond the simplest excitation classes. Here we address this issue for the set of singlet spin-adapted generalized singles and doubles operators (saGSD). Using the Wei--Norman approach, we derive exact product formulas that express spin-adapted fermionic unitaries as products of elementary spin-orbital unitaries. To obtain closed-form parameters in the more challenging 28- and 84-dimensional dynamical Lie algebras, we develop a computational discovery-and-verification protocol combining numerical optimization, parameter-structure identification, closed-form inference, and exact validation against reduced Wei--Norman equations. We also introduce an algorithm for constructing closed-form fermionic unitary transformations on Krylov subspaces and extend the fermionic-excitation-based circuit formalism to generators consisting of an anti-Hermitian fermionic string multiplied by arbitrary linear combinations of number-operator products. Together, these developments yield the most compact circuits to date for exact implementation of saGSD unitaries. Finally, for non fully spin-polarized systems, we identify a compact universal symmetry-adapted subset of saGSD that further reduces the quantum resources required for chemically relevant simulations.

quant-ph↗

arXiv2025

Symmetry Dilemmas in Quantum Computing for Chemistry: A Comprehensive Analysis

Symmetry adaptation, universality, and gate efficiency are central but often competing requirements in quantum algorithms for electronic structure and many-body physics. For example, fully symmetry-adapted universal operator pools typically generate long and deep quantum circuits, gate-efficient universal operator pools generally break symmetries, and gate-efficient fully symmetry-adapted operator pools may not be universal. In this work, we analyze such symmetry dilemmas both theoretically and numerically. On the theory side, we prove that the popular, gate-efficient operator pool consisting of singlet spin-adapted singles and perfect-pairing doubles is not universal when spatial symmetry is enforced. To demonstrate the strengths and weaknesses of the three types of pools, we perform numerical simulations using an adaptive algorithm paired with operator pools that are (i) fully symmetry-adapted and universal, (ii) fully symmetry-adapted and non-universal, and (iii) breaking a single symmetry and are universal. Our numerical simulations encompass three physically relevant scenarios in which the target state is (i) the global ground state, (ii) the ground state crossed by a state differing in multiple symmetry properties, and (iii) the ground state crossed by a state differing in a single symmetry property. Our results show when symmetry-breaking but universal pools can be used safely, when enforcing at least one distinguishing symmetry suffices, and when a particular symmetry must be rigorously preserved to avoid variational collapse. Together, the formal and numerical analysis provides a practical guide for designing and benchmarking symmetry-adapted operator pools that balance universality, resource requirements, and robust state targeting in quantum simulations for chemistry.

quant-ph↗

arXiv2025

Clifford Transformations for Fermionic Quantum Systems: From Paulis to Majoranas to Fermions

Clifford gates and transformations, which map products of elementary Pauli or Majorana operators to other such products, are foundational in quantum computing, underpinning the stabilizer formalism, error-correcting codes, magic state distillation, quantum communication and cryptography, and qubit tapering. Moreover, circuits composed entirely of Clifford gates are classically simulatable, highlighting their computational significance. In this work, we extend the concept of Clifford transformations to fermionic systems. We demonstrate that fermionic Clifford transformations are generated by half-body and pair operators, providing a systematic framework for their characterization. Additionally, we establish connections with fermionic mean-field theories and applications in qubit tapering, offering insights into their broader implications in quantum computing.

quant-ph↗

arXiv2025

Closed-Form Expressions for Unitaries of Spin-Adapted Fermionic Operators

One of the open challenges in quantum computing simulations of problems of chemical interest is the proper enforcement of spin symmetry. Efficient quantum circuits implementing unitaries generated by spin-adapted operators remain elusive, while naïve Trotterization schemes break spin symmetry. In this work, we analyze the mathematical structure of spin-adapted operators and derive closed-form expressions for unitaries generated by singlet spin-adapted generalized single and double excitations. These results represent significant progress toward the economical enforcement of spin symmetry in quantum simulations.

quant-ph↗

arXiv2025

Exact closed-form unitary transformations of fermionic operators

Unitary transformations play a fundamental role in many-body physics, and except for special cases, they are not expressible in closed form. We present closed-form expressions for unitary transformations generated by a single fermionic operator for Hermitian and anti-Hermitian generators. We demonstrate the usefulness of these expressions in formal analyses of unitary transformations and numerical applications involving block-diagonalization and Heisenberg dynamics. This work paves the way for new analytical treatments of unitary transformations and numerical many-body methods for fermions.

quant-ph↗

arXiv2024

Fermionic Mean-Field Theory as a Tool for Studying Spin Hamiltonians

The Jordan--Wigner transformation permits one to convert spin $1/2$ operators into spinless fermion ones, or vice versa. In some cases, it transforms an interacting spin Hamiltonian into a noninteracting fermionic one which is exactly solved at the mean-field level. Even when the resulting fermionic Hamiltonian is interacting, its mean-field solution can provide surprisingly accurate energies and correlation functions. Jordan--Wigner is, however, only one possible means of interconverting spin and fermionic degrees of freedom. Here, we apply several such techniques to the XXZ and $J_1\text{--}J_2$ Heisenberg models, as well as to the pairing or reduced BCS Hamiltonian, with the aim of discovering which of these mappings is most useful in applying fermionic mean-field theory to the study of spin Hamiltonians.

cond-mat.str-el↗

arXiv2023

Unitary Coupled Cluster: Seizing the Quantum Moment

Shallow, CNOT-efficient quantum circuits are crucial for performing accurate computational chemistry simulations on current noisy quantum hardware. Here, we explore the usefulness of non-iterative energy corrections, based on the method of moments of coupled-cluster theory, for accelerating convergence toward full configuration interaction. Our preliminary numerical results relying on iteratively constructed ansätze suggest that chemically accurate energies can be obtained with substantially more compact circuits, implying enhanced resilience to gate and decoherence noise.

physics.chem-ph↗

arXiv2023

Linear-Scaling Quantum Circuits for Computational Chemistry

We have recently constructed compact, CNOT-efficient, quantum circuits for fermionic and qubit excitations of arbitrary many-body rank [I. Magoulas and F.A. Evangelista, J. Chem. Theory Comput. 19, 822 (2023)]. Here, we present approximations to these circuits that substantially reduce the CNOT counts even further. Our preliminary numerical data, using the selected projective quantum eigensolver approach, demonstrate that there is practically no loss of accuracy in the energies compared to the parent implementation while the ensuing symmetry breaking is essentially negligible.

physics.chem-ph↗

arXiv2022

CNOT-Efficient Circuits for Arbitrary Rank Many-Body Fermionic and Qubit Excitations

Efficient quantum circuits are necessary for realizing quantum algorithms on noisy intermediate-scale quantum devices. Fermionic excitations entering unitary coupled-cluster (UCC) ansätze give rise to quantum circuits containing CNOT "staircases" whose number scales exponentially with the excitation rank. Recently, Yordanov et al. [Phys. Rev. A 102, 062612 (2020); Commun. Phys. 4, 228 (2021)] constructed CNOT-efficient quantum circuits for both fermionic- (FEB) and qubit-excitation-based (QEB) singles and doubles and illustrated their usefulness in adaptive derivative-assembled pseudo-Trotterized variational quantum eigensolver (ADAPT-VQE) simulations. In this work, we extend these CNOT-efficient quantum circuits to arbitrary excitation ranks. To illustrate the benefits of these compact FEB and QEB quantum circuits, we perform numerical simulations using the recently developed selected projective quantum eigensolver (SPQE) approach, which relies on an adaptive UCC ansatz built from arbitrary-order particle-hole excitation operators. We show that both FEB- and QEB-SPQE decrease the number of CNOT gates compared to traditional SPQE by factors as large as 15. At the same time, QEB-SPQE requires, in general, more ansatz parameters than FEB-SPQE, in particular those corresponding to higher-than-double excitations, resulting in quantum circuits with larger CNOT counts. Although ADAPT-VQE generates quantum circuits with fewer CNOTs than SPQE, SPQE requires orders of magnitude less residual element evaluations than gradient element evaluations in ADAPT-VQE.

quant-ph↗

arXiv2021

Addressing Strong Correlation by Approximate Coupled-Pair Methods with Active-Space and Full Treatments of Three-Body Clusters

When the number of strongly correlated electrons becomes larger, the single-reference coupled-cluster (CC) CCSD, CCSDT, etc. hierarchy displays an erratic behavior, while traditional multi-reference approaches may no longer be applicable due to enormous dimensionalities of the underlying model spaces. These difficulties can be alleviated by the approximate coupled-pair (ACP) theories, in which selected $(T_2)^2$ diagrams in the CCSD amplitude equations are removed, but there is no generally accepted and robust way of incorporating connected triply excited ($T_3$) clusters within the ACP framework. It is also not clear if the specific combinations of $(T_2)^2$ diagrams that work well for strongly correlated minimum-basis-set model systems are optimum when larger basis sets are employed. This study explores these topics by considering a few novel ACP schemes with the active-space and full treatments of $T_3$ correlations and schemes that scale selected $(T_2)^2$ diagrams by factors depending on the numbers of occupied and unoccupied orbitals. The performance of the proposed ACP approaches is illustrated by examining the symmetric dissociations of the $\text{H}_6$ and $\text{H}_{10}$ rings using basis sets of the triple- and double-$ζ$ quality and the $\text{H}_{50}$ linear chain treated with a minimum basis, for which the conventional CCSD and CCSDT methods fail.

physics.chem-ph↗

arXiv2021

Controlling quantum interference between virtual and dipole two-photon optical excitation pathways using phase-shaped laser pulses

Two-photon excitation (TPE) proceeds via a "virtual" pathway, which depends on the accessibility of one or more intermediate states, and, in the case of non-centrosymmetric molecules, an additional "dipole" pathway involving the off-resonance dipole-allowed one-photon transitions and the change in the permanent dipole moment between the initial and final states. Here, we control the quantum interference between these two optical excitation pathways by using phase-shaped femtosecond laser pulses. We find enhancements by a factor of up to 1.75 in the two-photon-excited fluorescence of the photobase FR0-SB in methanol after taking into account the longer pulse duration of the shaped laser pulses. Simulations taking into account the different responses of the virtual and dipole pathways to external fields and the effect of pulse shaping on two-photon transitions are found to be in good agreement with our experimental measurements. The observed quantum control of TPE in condensed phase may lead to enhanced signal at a lower intensity in two-photon microscopy, multiphoton-excited photoreagents, and novel spectroscopic techniques that are sensitive to the magnitude of the contributions from the virtual and dipole pathways to multiphoton excitations.

physics.chem-ph↗

arXiv2021

Is Externally Corrected Coupled Cluster Always Better than the Underlying Truncated Configuration Interaction?

The short answer to the question in the title is 'no'. We identify classes of truncated configuration interaction (CI) wave functions for which the externally corrected coupled-cluster (ec-CC) approach using the three-body ($T_{3}$) and four-body ($T_{4}$) components of the cluster operator extracted from CI does not improve the results of the underlying CI calculations. Implications of our analysis, illustrated by numerical examples, for the ec-CC computations using truncated and selected CI methods are discussed. We also introduce a novel ec-CC approach using the $T_{3}$ and $T_{4}$ amplitudes obtained with the selected CI scheme abbreviated as CIPSI, correcting the resulting energies for the missing $T_{3}$ correlations not captured by CIPSI with the help of moment expansions similar to those employed in the completely renormalized CC methods.

physics.chem-ph↗

arXiv2020

Isoenergetic Two-Photon Excitation Enhances Solvent-to-Solute Excited-State Proton Transfer

Two-photon excitation is an attractive means for controlling chemistry in both space and time. Isoenergetic one- and two-photon excitations (OPE and TPE) in non-centrosymmetric molecules are often assumed to reach the same excited state and, hence, to produce similar excited-state reactivity. We compare the solvent-to-solute excited-state proton transfer of the super photobase FR0-SB following isoenergetic OPE and TPE. We find up to 62 % increased reactivity following TPE compared to OPE. From steady-state spectroscopy, we rule out the involvement of different excited states and find that OPE and TPE spectra are identical in non-polar solvents but not in polar ones. We propose that differences in the matrix elements that contribute to the two-photon absorption cross sections lead to the observed enhanced isoenergetic reactivity, consistent with the predictions of our high-level coupled-cluster-based computational protocol. We find that polar solvent configurations favor greater dipole moment change between ground and excited states, which enters the probability for two-photon excitations as the absolute value squared. This, in turn, causes a difference in the Franck-Condon region reached via TPE compared to OPE. We conclude that a new method has been found for controlling chemical reactivity via the matrix elements that affect two-photon cross sections, which may be of great utility for spatial and temporal precision chemistry.

physics.chem-ph↗

arXiv2020

The Ground State Electronic Energy of Benzene

We report on the findings of a blind challenge devoted to determining the frozen-core, full configuration interaction (FCI) ground state energy of the benzene molecule in a standard correlation-consistent basis set of double-$ζ$ quality. As a broad international endeavour, our suite of wave function-based correlation methods collectively represents a diverse view of the high-accuracy repertoire offered by modern electronic structure theory. In our assessment, the evaluated high-level methods are all found to qualitatively agree on a final correlation energy, with most methods yielding an estimate of the FCI value around $-863$ m$E_{\text{H}}$. However, we find the root-mean-square deviation of the energies from the studied methods to be considerable (1.3 m$E_{\text{H}}$), which in light of the acclaimed performance of each of the methods for smaller molecular systems clearly displays the challenges faced in extending reliable, near-exact correlation methods to larger systems. While the discrepancies exposed by our study thus emphasize the fact that the current state-of-the-art approaches leave room for improvement, we still expect the present assessment to provide a valuable community resource for benchmark and calibration purposes going forward.

physics.chem-ph↗