Quantum benefit of the quantum equation of motion for the strongly coupled many-body problem

Physical review. C, Journal Year: 2024, Volume and Issue: 109(1)

Published: Jan. 2, 2024

We investigate the quantum equation of motion (qEOM), a hybrid quantum-classical algorithm for computing excitation properties fermionic many-body system, with particular emphasis on strong-coupling regime. The method is designed as stepping stone towards building more accurate solutions strongly coupled systems, such medium-heavy nuclei, using algorithms to surpass current barrier in classical computation. Approximations increasing accuracy exact solution Lipkin-Meshkov-Glick Hamiltonian $N=8$ particles are studied digital simulators and IBM devices. Improved achieved by applying operators growing complexity generate excitations above correlated ground state, which determined variational eigensolver. demonstrate explicitly that qEOM exhibits benefit due independence number required measurements from configuration complexity. Postprocessing examination shows device errors amplified coupling strength. A detailed error analysis presented, mitigation based zero noise extrapolation implemented.

Language: Английский

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Subspace Methods for the Simulation of Molecular Response Properties on a Quantum Computer

Journal of Chemical Theory and Computation, Journal Year: 2024, Volume and Issue: 20(9), P. 3729 - 3740

Published: May 1, 2024

We explore Davidson methods for obtaining excitation energies and other linear response properties within the recently developed quantum self-consistent (q-sc-LR) method. Davidson-type allow only a few selected without explicitly constructing electronic Hessian since they require ability to perform Hessian-vector multiplications. apply method calculate of hydrogen chains (up H10) analyze aspects statistical noise computing on simulators. Additionally, we such as static polarizabilities H2, LiH, H2O, OH–, NH3, show that unitary coupled cluster outperforms classical projected molecular systems with strong correlation. Finally, formulate damped (complex) response, application nitrogen K-edge X-ray absorption ammonia, C6 coefficients NH3.

Language: Английский

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Electronic excited states from a variance-based contracted quantum eigensolver

Physical review. A/Physical review, A, Journal Year: 2023, Volume and Issue: 108(2)

Published: Aug. 25, 2023

Electronic excited states of molecules are central to many physical and chemical processes, yet they typically more difficult compute than ground states. In this paper we leverage the advantages quantum computers develop an algorithm for highly accurate calculation We solve a contracted Schr\"odinger equation (CSE)---a contraction (projection) onto space two electrons---whose solutions correspond identically equation. While recent algorithms solving CSE, known as eigensolvers (CQEs), have focused on states, CQE based variance that is designed optimize rapidly or state. apply ${\mathrm{H}}_{2}, {\mathrm{H}}_{4}$, BH.

Language: Английский

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Measurement Optimization Techniques for Excited Electronic States in Near-Term Quantum Computing Algorithms

Journal of Chemical Theory and Computation, Journal Year: 2023, Volume and Issue: 19(11), P. 3184 - 3193

Published: May 24, 2023

The variational quantum eigensolver (VQE) remains one of the most popular near-term algorithms for solving electronic structure problem. Yet, its practicality, main challenge to overcome is improving measurement efficiency. Numerous techniques have been developed recently, but it unclear how these state-of-the-art will perform in extensions VQE obtaining excited states. Assessing techniques' performance state crucial because requirements are typically much greater than ground VQE, as must measure expectation value multiple observables addition that Hamiltonian. Here, we adapt various two widely used algorithms: multistate contraction and subspace expansion. Then, each technique numerically compared. We find best methods ones utilizing Hamiltonian data wave function information minimize number measurements. In contrast, randomized more appropriate expansion, with many vastly different energy scales measure. Nevertheless, when possible algorithm considered, significantly fewer measurements required

Language: Английский

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Quantum Davidson algorithm for excited states

Quantum Science and Technology, Journal Year: 2024, Volume and Issue: 9(3), P. 035012 - 035012

Published: April 4, 2024

Abstract Excited state properties play a pivotal role in various chemical and physical phenomena, such as charge separation light emission. However, the primary focus of most existing quantum algorithms has been ground state, seen phase estimation variational eigensolver (VQE). Although VQE-type methods have extended to explore excited states, these grapple with optimization challenges. In contrast, Krylov subspace (QKS) method introduced address both positioning itself cost-effective alternative estimation. conventional QKS methodologies depend on pre-generated through real or imaginary-time evolutions. This is inherently expansive can be plagued issues like slow convergence numerical instabilities, often leading relatively deep circuits. Our research presents an economic algorithm, which we term Davidson (QDavidson) algorithm. innovation hinges iterative expansion incorporation pre-conditioner within framework. By using residues eigenstates expand subspace, manage formulate compact that aligns closely exact solutions. paves way for more rapid comparison other techniques, Lanczos. Using simulators, employ novel QDavidson algorithm delve into systems, spanning from Heisenberg spin model molecules. Compared methods, not only converges swiftly but also demands significantly shallower circuit. efficiency establishes pragmatic tool elucidating computing platforms.

Language: Английский

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Nonadiabatic Molecular Dynamics with Fermionic Subspace-Expansion Algorithms on Quantum Computers

Journal of Chemical Theory and Computation, Journal Year: 2024, Volume and Issue: 20(14), P. 5951 - 5963

Published: July 5, 2024

We introduce a novel computational framework for excited-state molecular quantum dynamics simulations driven by quantum-computing-based electronic-structure calculations. This leverages the fewest-switches surface-hopping method simulating nuclear and calculates required transition properties with different flavors of subspace expansion equation-of-motion algorithms. apply our to simulate collision reaction between hydrogen atom molecule. For this system, we critically compare accuracy efficiency algorithms show that only methods can capture both weak strong electron correlation effects properly describe nonadiabatic tune reactive event.

Language: Английский

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Self-consistent Quantum Linear Response with a Polarizable Embedding Environment

The Journal of Physical Chemistry A, Journal Year: 2025, Volume and Issue: unknown

Published: Jan. 23, 2025

Quantum computing presents a promising avenue for solving complex problems, particularly in quantum chemistry, where it could accelerate the computation of molecular properties and excited states. This work focuses on excitation energies with hybrid quantum-classical algorithms near-term devices, combining linear response (qLR) method polarizable embedding (PE) environment. We employ self-consistent operator manifold (q-sc-LR) top unitary coupled cluster (UCC) wave function combination Davidson solver. The latter removes need to construct entire electronic Hessian, improving computational efficiency when going toward larger molecules. introduce new superposition-state-based technique compute Hessian-vector products show that this approach is more resilient noise than our earlier gradient-based approach. demonstrate performance PE-UCCSD model systems such as butadiene para-nitroaniline water find delivers comparable accuracy classical PE-CCSD methods simple closed-shell systems. also explore challenges posed by hardware propose error mitigation techniques maintain accurate results noisy computers.

Language: Английский

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Cheaper and more noise-resilient quantum state preparation using eigenvector continuation

Physical review. A/Physical review, A, Journal Year: 2025, Volume and Issue: 111(3)

Published: March 10, 2025

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Determination of Molecular Symmetry Adapted Eigenroots in the Variational Quantum Eigensolver Framework

International Journal of Quantum Chemistry, Journal Year: 2025, Volume and Issue: 125(7)

Published: March 28, 2025

ABSTRACT Variational Quantum Eigensolver (VQE) provides a lucrative platform to determine molecular energetics in near‐term quantum devices. While the VQE is traditionally tailored ground state wavefunction with underlying Rayleigh‐Ritz principle, for molecules characterized by given point group symmetry, we propose unify framework treat lowest energy states of any irreducible representation and spin‐multiplicity. The method relies on construction symmetry adapted multi determinantal reference where constituent determinants are entangled through appropriate Clebsch‐Gordan coefficients ensure desired unitary operator, defined terms totally symmetric spin‐free generators, safeguards against variational collapse broken solutions. We also an sorting based adaptive ansatz algorithm starting from pool generators come up dynamically optimal ansatz. proposed methodology allows us build further search algorithms within reduced dimensional symmetry‐adapted sub‐Hilbert‐space. With highly compact circuit structure, it expected be realized devices study emerging chemical phenomena exploration novel space.

Language: Английский

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Equation-of-motion internally contracted multireference unitary coupled-cluster theory

The Journal of Chemical Physics, Journal Year: 2025, Volume and Issue: 162(15)

Published: April 16, 2025

The accurate computation of excited states remains a challenge in electronic structure theory, especially for systems with ground state that requires multireference treatment. In this work, we introduce novel equation-of-motion (EOM) extension the internally contracted unitary coupled-cluster framework (ic-MRUCC), termed EOM-ic-MRUCC. EOM-ic-MRUCC follows transform-then-diagonalize approach, analogy to its non-unitary counterpart [Datta and Nooijen, J. Chem. Phys. 137, 204107 (2012)]. By employing projective approach optimize state, method retains additive separability proper scaling system size. We show excitation energies are size-intensive if EOM operator satisfies “killer” conditions. Furthermore, propose represent changes reference upon electron via projected many-body operators span active orbitals equations formulated way invariant respect orbital rotations. test truncated single double excitations by computing potential energy curves several BeH2 model system, HF molecule, water undergoing symmetric dissociation. Across these systems, our delivers within 5 mEh (∼0.14 eV) from full configuration interaction. find truncating Baker–Campbell–Hausdorff series fourfold commutators contributes negligible errors (on order 10−5Eh or less), offering practical route highly excited-state calculations reduced computational overhead.

Language: Английский

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