arXiv subjects

Francesco A. Evangelista

Publications and source records attributed to Francesco A. Evangelista.

At least 37 records · Page 2Linked to original sources

arXiv2023

Implementation of the Projective Quantum Eigensolver on a Quantum Computer

We study the performance of our previously proposed Projective Quantum Eigensolver (PQE) on IBM's quantum hardware in conjunction with error mitigation techniques. For a single qubit model of H$_2$, we find that we are able to obtain energies within 4 millihartree (2.5 kcal/mol) of the exact energy along the entire potential energy curve, with the accuracy limited by both stochastic error and inconsistent performance of the IBM devices. We find that an optimization algorithm using direct inversion of the iterative subspace can converge swiftly, even to excited states, but stochastic noise can cause large parameter updates. For the four-site transverse-field Ising model at the critical point, PQE with an appropriate application of qubit tapering can recover 99% of the correlation energy, even discarding several parameters. The large number of CNOT gates needed for the additional parameters introduces a concomitant error that, on the IBM devices, results in loss of accuracy, despite the increased expressivity of the trial state. Error extrapolation techniques and tapering or postselection are recommended to mitigate errors in PQE hardware experiments.

quant-ph↗

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

A benchmark study of core-excited states of organic molecules computed with the generalized active space driven similarity renormalization group

This work examines the accuracy and precision of X-ray absorption spectra computed with a multireference approach that combines generalized active space (GAS) references with the driven similarity renormalization group (DSRG). We employ the X-ray absorption benchmark of organic molecules (XABOOM) set, consisting of 116 transitions from mostly organic molecules [T. Fransson et al., J. Chem. Theory Comput. 17, 1618 (2021)]. Several approximations to a full-valence active space are examined and benchmarked. Absolute excitation energies and intensities computed with the GAS-DSRG truncated to second-order in perturbation theory are found to systematically underestimate experimental and reference theoretical values. Third-order perturbative corrections significantly improve the accuracy of GAS-DSRG absolute excitation energies, bringing the mean absolute deviation from experimental values down to 0.32 eV. The ozone molecule and glyoxylic acid are particularly challenging for second-order perturbation theory and are examined in detail to assess the importance of active space truncation and intruder states.

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↗

arXiv2022

AGP-based unitary coupled cluster theory for quantum computers

Electronic structure methods typically benefit from symmetry breaking and restoration, specially in the strong correlation regime. The same goes for Ansätze on a quantum computer. We develop a unitary coupled cluster method on the antisymmetrized geminal power (AGP) -- a state formally equivalent to the number-projected Bardeen--Cooper--Schrieffer wavefunction. We demonstrate our method for the single-band Fermi--Hubbard Hamiltonian in one and two dimensions. We also explore post-selection as a state preparation step to obtain correlated AGP and prove that it scales no worse than $\mathcal{O}(\sqrt{M})$ in the number of measurements, thereby making it a less expensive alternative to gauge integration to restore particle number symmetry.

quant-ph↗

arXiv2022

Leveraging small scale quantum computers with unitarily downfolded Hamiltonians

In this work, we propose a quantum unitary downfolding formalism based on the driven similarity renormalization group (QDSRG) that may be combined with quantum algorithms for both noisy and fault-tolerant hardware. The QDSRG is a classical polynomially-scaling downfolding method that avoids the evaluation of costly three- and higher-body reduced density matrices while retaining the accuracy of classical multireference many-body theories. We calibrate and test the QDSRG on several challenging chemical problems and propose a strategy for avoiding classical exponential-scaling steps in the QDSRG scheme. We report QDSRG computations of two chemical systems using the variational quantum eigensolver on IBM quantum devices: i) the dissociation curve of H$_2$ using a quintuple-$ζ$ basis and ii) the bicyclobutane isomerization reaction to $trans$-butadiene, demonstrating the reduction of problems that require several hundred qubits to a single qubit. Our work shows that the QDSRG is a viable approach to leverage near-term quantum devices for the accurate estimation of molecular properties.

quant-ph↗

arXiv2022

Automatic derivation of fermionic many-body theories based on general Fermi vacua

This paper describes Wick&d, an implementation of the algebra of second-quantized operators normal ordered with respect to general correlated references and the corresponding Wick theorem [W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 107, 432 (1997)]. Wick&d employs a compact representation of operators and a backtracking algorithm to efficiently evaluate Wick contractions. Since Wick&d can handle both fully and partially contracted terms, it can be applied to both projective and Fock-space many-body formalisms. To demonstrate the usefulness of Wick&d, we use it to evaluate the single-reference coupled cluster equations up to octuple excitations and report an automated derivation and implementation of the second-order driven similarity renormalization group multireference perturbation theory (DSRG-MRPT2).

physics.chem-ph↗

arXiv2021

Analytic energy gradients for the driven similarity renormalization group multireference second-order perturbation theory

We derive analytic energy gradients of the driven similarity renormalization group (DSRG) multireference second-order perturbation theory (MRPT2) using the method of Lagrange multipliers. In the Lagrangian, we impose constraints for a complete-active-space self-consistent-field reference wave function and the semicanonical orthonormal molecular orbitals. Solving the associated Lagrange multipliers is found to share the same asymptotic scaling of a single DSRG-MRPT2 energy computation. A pilot implementation of the DSRG-MRPT2 analytic gradients is used to optimize the geometry of the singlet and triplet states of p-benzyne. The equilibrium bond lengths and angles are similar to those computed via other MRPT2s and Mukherjee's multireference coupled cluster theory. An approximate DSRG-MRPT2 method that neglects the contributions of three-body density cumulant is found to introduce negligible errors in the geometry of p-benzyne, lending itself to a promising low-cost approach for molecular geometry optimizations using large active spaces.

physics.chem-ph↗

arXiv2021

Spin-free formulation of the multireference driven similarity renormalization group: A benchmark study of first-row diatomic molecules and spin-crossover energetics

We report a spin-free formulation of the multireference (MR) driven similarity renormalization group (DSRG) by employing the ensemble normal ordering of Mukherjee and Kutzelnigg [W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 107, 432 (1997)]. This ensemble averages over all microstates for a given total spin quantum number and, therefore, it is invariant with respect to SU(2) transformations. As such, all equations may be reformulated in terms of spin-free quantities and they closely resemble those of spin-adapted closed-shell coupled cluster (CC) theory. The current implementation is used to assess the accuracy of various truncated MR-DSRG methods (perturbation theory up to third order and iterative methods with single and double excitations) in computing the constants of thirty-three first-row diatomic molecules. The accuracy trends for these first-row diatomics are consistent with our previous benchmark on a small subset of closed-shell diatomic molecules. We then present the first MR-DSRG application on transition-metal complexes by computing the spin splittings of the [Fe(H$_2$O)$_6$]$^{2+}$ and [Fe(NH$_3$)$_6$]$^{2+}$ molecules. Focal point analysis (FPA) shows that third-order perturbative corrections are essential to achieve reasonably converged energetics. A FPA based on the linearized MR-DSRG theory with one- and two-body operators and up to a quintuple-$ζ$ basis set predicts the spin splittings of [Fe(H$_2$O)$_6$]$^{2+}$ and [Fe(NH$_3$)$_6$]$^{2+}$ to be $-35.7$ and $-17.1$ kcal mol$^{-1}$, respectively, showing good agreement with results of local CC theory with singles, doubles, and perturbative triples.

physics.chem-ph↗

arXiv2021

QForte: an efficient state simulator and quantum algorithms library for molecular electronic structure

We introduce a novel open-source software package QForte, a comprehensive development tool for new quantum simulation algorithms. QForte incorporates functionality for handling molecular Hamiltonians, fermionic encoding, ansatz construction, time evolution, and state-vector simulation, requiring only a classical electronic structure package as a dependency. QForte also contains black-box implementations of a wide variety of quantum algorithms including (but not limited to): variational and projective quantum eigensolvers, adaptive eigensolvers, quantum imaginary time evolution, quantum Krylov methods, and quantum phase estimation. We highlight two features of QForte: i) how the Python class structure of QForte enables the facile implementation of new algorithms, and ii) how existing algorithms can be executed in just a few lines of code.

quant-ph↗

arXiv2021

Simulating Many-Body Systems with a Projective Quantum Eigensolver

We present a new hybrid quantum-classical algorithm for optimizing unitary coupled-cluster (UCC) wave functions deemed the projective quantum eigensolver (PQE), amenable to near-term noisy quantum hardware. Contrary to variational quantum algorithms, PQE optimizes a trial state using residuals (projections of the Schrödinger equation) rather than energy gradients. We show that the residuals may be evaluated by simply measuring two energy expectation values per element. We also introduce a selected variant of PQE (SPQE) that uses an adaptive ansatz built from arbitrary-order particle-hole operators, offering an alternative to gradient-based selection procedures. PQE and SPQE are tested on a set of molecular systems covering both the weak and strong correlation regimes, including hydrogen clusters with 4-10 atoms and the BeH$_2$ molecule. When employing a fixed ansatz, we find that PQE can converge disentangled (factorized) UCC wave functions to essentially identical energies as variational optimization while requiring fewer computational resources. A comparison of SPQE and adaptive variational quantum algorithms shows that - for ansätze containing the same number of parameters - the two methods yield results of comparable accuracy. Finally, we show that SPQE performs similar to, and in some cases, better than selected configuration interaction and the density matrix renormalization group on 1-3 dimensional strongly correlated H$_{10}$ systems in terms of energy accuracy for a given number of variational parameters.

quant-ph↗

arXiv2020

Correlating AGP on a quantum computer

For variational algorithms on the near term quantum computing hardware, it is highly desirable to use very accurate ansatze with low implementation cost. Recent studies have shown that the antisymmetrized geminal power (AGP) wavefunction can be an excellent starting point for ansatze describing systems with strong pairing correlations, as those occurring in superconductors. In this work, we show how AGP can be efficiently implemented on a quantum computer with circuit depth, number of CNOTs, and number of measurements being linear in system size. Using AGP as the initial reference, we propose and implement a unitary correlator on AGP and benchmark it on the ground state of the pairing Hamiltonian. The results show highly accurate ground state energies in all correlation regimes of this model Hamiltonian.

quant-ph↗

arXiv2020

Exploring Hilbert space on a budget: Novel benchmark set and performance metric for testing electronic structure methods in the regime of strong correlation

This work explores the ability of classical electronic structure methods to efficiently represent (compress) the information content of full configuration interaction (FCI) wave functions. We introduce a benchmark set of four hydrogen model systems of different dimensionality and distinctive electronic structures: a 1D chain, a 1D ring, a 2D triangular lattice, and a 3D close-packed pyramid. To assess the ability of a computational method to produce accurate and compact wave functions, we introduce the accuracy volume, a metric that measures the number of variational parameters necessary to achieve a target energy error. Using this metric and the hydrogen models, we examine the performance of three classical deterministic methods: i) selected configuration interaction (sCI) realized both via an a posteriori and variational selection of the most important determinants, ii) rank-reduced FCI, obtained by an a posteriori singular value decomposition of the FCI tensor (SVD-FCI), and iii) the matrix product state representation obtained via the density matrix renormalization group (DMRG). We find that DMRG generally gives the most efficient wave function representation for all systems, particularly in the 1D chain with a localized basis. For the 2D and 3D systems, all methods perform best with a delocalized basis, and the efficiency of sCI is closer to that of DMRG, with the former having and accuracy volume approximately twice as large in the strong correlation regime. Compared to sCI, the SVD-FCI scheme is generally found to require a slightly larger number of parameters to achieve the same energy accuracy.

physics.chem-ph↗

arXiv2020

Connected three-body terms in single-reference unitary many-body theories: Iterative and perturbative approximations

This work introduces various approaches to include connected three-body terms in unitary many-body theories, focusing a representative example on the driven similarity renormalization group (DSRG). Starting from the least approximate method - the linearized DSRG truncated to one-, two-, and three-body operators [LDSRG(3)] - we develop several approximate LDSRG(3) models with reduced computational cost. Through a perturbative analysis, we motivate a family of iterative LDSRG(3)-$n$ and -$n'$ ($n=1,2,3,4$) methods that contain a subset of the LDSRG(3) diagrams. Among these variants, the LDSRG(3)-2 scheme has the same computational complexity of coupled cluster theory with singles, doubles, and triples (CCSDT), but it outperforms CCSDT in the accuracy of the predicted correlation energies. We also propose and implement two perturbative triples corrections based on the linearized DSRG truncated to one- and two-body operators augmented with recursive quadratic commutators [qDSRG(2)]. The resulting qDSRG(2)+(T) approach matches the accuracy of the "gold-standard" coupled cluster theory with singles, doubles, and perturbative triples model on the energetics of twenty-eight closed-shell atoms and small molecules.

physics.chem-ph↗

arXiv2019

A Multireference Quantum Krylov Algorithm for Strongly Correlated Electrons

We introduce a multireference selected quantum Krylov (MRSQK) algorithm suitable for quantum simulation of many-body problems. MRSQK is a low-cost alternative to the quantum phase estimation algorithm that generates a target state as a linear combination of non-orthogonal Krylov basis states. This basis is constructed from a set of reference states via real-time evolution avoiding the numerical optimization of parameters. An efficient algorithm for the evaluation of the off-diagonal matrix elements of the overlap and Hamiltonian matrices is discussed and a selection procedure is introduced to identify a basis of orthogonal references that ameliorates the linear dependency problem. Preliminary benchmarks on linear H$_6$, H$_8$, and BeH$_2$ indicate that MRSQK can predict the energy of these systems accurately using very compact Krylov bases.

physics.chem-ph↗

arXiv2019

Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory

A formal analysis is conducted on the exactness of various forms of unitary coupled cluster (UCC) theory based on particle-hole excitation and de-excitation operators. Both the conventional single exponential UCC parameterization and a disentangled (factorized) version are considered. We formulate a differential cluster analysis to determine the UCC amplitudes corresponding to a general quantum state. The exactness of conventional UCC (ability to represent any state) is explored numerically and it is formally shown to be determined by the structure of the critical points of the UCC exponential mapping. A family of disentangled UCC wave functions are shown to exactly parameterize any state, thus showing how to construct Trotter-error-free parameterizations of UCC for applications in quantum computing. From these results, we derive an exact disentangled UCC parameterization that employs an infinite sequence of particle-hole or general one- and two-body substitution operators.

physics.chem-ph↗

arXiv2019

Time Dependent Adaptive Configuration Interaction Applied to Attosecond Charge Migration

In this work, we present a time-dependent (TD) selected configuration interaction method based on our recently-introduced adaptive configuration interaction (ACI). We show that ACI, in either its ground or excited state formalisms, is capable of building a compact basis for use in real-time propagation of wave functions for computing electron dynamics. TD-ACI uses an iteratively selected basis of determinants in real-time propagation capable of capturing strong correlation effects in both ground and excited states, all with an accuracy---and associated cost---tunable by the user. We apply TD-ACI to study attosecond-scale migration of charge following ionization in small molecules. We first compute attosecond charge dynamics in a benzene model to benchmark and understand the utility of TD-ACI with respect to an exact solution. Finally, we use TD-ACI to reproduce experimentally determined ultrafast charge migration dynamics in iodoacetylene. TD-ACI is shown to be a valuable benchmark theory for electron dynamics, and it represents an important step towards accurate and affordable time-dependent multireference methods.

physics.chem-ph↗