Differentiable quantum computational chemistry with PennyLane

Arrazola, Juan Miguel; Jahangiri, Soran; Delgado, Alain; Ceroni, Jack; Izaac, Josh; Száva, Antal; Azad, Utkarsh; Lang, Robert A.; Niu, Zeyue; Matteo, Olivia Di; Moyard, Romain; Soni, Jay; Schuld, Maria; Vargas-Hernández, Rodrigo A.; Tamayo-Mendoza, Teresa; Lin, Cedric Yen-Yu; Aspuru‐Guzik, Alán; Killoran, Nathan

doi:10.48550/arxiv.2111.09967

Cited by 5 publications

(6 citation statements)

References 42 publications

(52 reference statements)

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“…where θ is used to indicate that the derivatives in (11) act only on the right hand side of the overlap. After solving (9) for θ the parameters are updated according to θ(τ + ∆τ ) = θ(τ ) + ∆τ θ where ∆τ acts like a learning rate parameter.…”

Section: Variational Quantum Imaginary Time Evolutionmentioning

confidence: 99%

“…The Pennylane quantum computing framework [8] has extensive built-in automatic differentiation capability mainly focused on machine learning applications. However, quantum automatic differentiation does have applications in scientific computations [9,10] and will be used here as it vastly simplifies the use of variational quantum imaginary time evolution.…”

Section: Introductionmentioning

confidence: 99%

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Demonstrating quantum computing with the quark model

Woloshyn¹

2023

Preprint

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The use of quantum computing to solve a problem in quantum mechanics is illustrated, step by step, by calculating energies and transition amplitudes in a nonrelativistic quark model. The quantum computations feature the use of variational quantum imaginary time evolution implemented using automatic differentiation to determine ground and excited states of charmonium. The calculation of transition amplitudes is illustrated utilizing the Hadamard test. Examples of readout and gate error mitigation are included

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Section: Variational Quantum Imaginary Time Evolutionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Demonstrating quantum computing with the quark model

Woloshyn¹

2023

Preprint

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“…Differentiable programming is a programming paradigm in which the computational flow of a program can be explicitly differentiated with respect to its parameters, thereby allowing gradient-descent optimisation of those parameters. The approach is widely used as a backbone of machine learning tools [30] and has been applied to variational problems in quantum many-body physics [31][32][33][34] and quantum technology [35][36][37].…”

Section: Variational Optimisation By Differentiable Programmingmentioning

confidence: 99%

Finite-Volume Pionless Effective Field Theory for Few-Nucleon Systems with Differentiable Programming

Sun¹,

Detmold²,

Luo³

et al. 2022

Preprint

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Finite-volume pionless effective field theory provides an efficient framework for the extrapolation of nuclear spectra and matrix elements calculated at finite volume in lattice QCD to infinite volume, and to nuclei with larger atomic number. In this work, it is demonstrated how this framework may be implemented via a set of correlated Gaussian wavefunctions optimised using differentiable programming and via solution of a generalised eigenvalue problem. This approach is shown to be significantly more efficient than a stochastic implementation of the variational method based on the same form of correlated Gaussian wavefunctions, yielding comparably accurate representations of the ground-state wavefunctions with an order of magnitude fewer terms. The efficiency of representation allows such calculations to be extended to larger systems than in previous work. The method is demonstrated through calculations of the binding energies of nuclei with atomic number A ∈ {2, 3, 4} in finite volume, matched to lattice QCD calculations at quark masses corresponding to mπ = 806 MeV, and infinite-volume effective field theory calculations of A ∈ {2, 3, 4, 5, 6} systems based on this matching.

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“…are the one and two-electron integrals yielded from a set of molecular orbitals φ p (r), usually obtained by using the Hartree-Fock method [31]. Note that these molecular orbitals depend implicitly on R. of the energy Hessian -the matrix of second-order energy derivatives with respect to each of the nuclear coordinates,…”

Section: Numerical Examplesmentioning

confidence: 99%

“…We use the PennyLane library for quantum differentiable programming [31,32] to simulate an adaptive circuit-building procedure, followed by VQE, to compute approximate ground-state energies at the equilibrium geometry. More specifically, we run an adaptive gate selection procedure using a pool of gates composed of all admissible single and double excitation gates for each particular molecule [30], and optimize the resulting circuit by minimizing the energy expectation value of the Hamiltonian, at geometry R 0 , with gradient descent.…”

Section: Numerical Examplesmentioning

confidence: 99%

Tailgating quantum circuits for high-order energy derivatives

Ceroni¹,

Delgado²,

Jahangiri³

et al. 2022

Preprint

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To understand the chemical properties of molecules, it is often important to study derivatives of energies with respect to nuclear coordinates or external fields. Quantum algorithms for computing energy derivatives have been proposed, but only limited work has been done to address the specific challenges that arise in this context, where calculations are more complicated and involve more stringent requirements on accuracy compared to single-point energy calculations. In this work, we introduce a technique to improve the performance of variational quantum circuits calculating energy derivatives. The method, which we refer to as tailgating, is an adaptive procedure that selects gates based on their gradient with respect to the expectation value of Hamiltonian derivatives. These gates are then added at the end of a quantum circuit originally designed to calculate ground-or excited-state energies. A distinguishing feature of this approach is that the appended gates do not need to be optimized: their parameters can be set to zero and varied only for the purpose of computing energy derivatives, via calculating derivatives with respect to circuit parameters. We support the validity of this method by establishing sufficient conditions for a circuit to compute accurate energy gradients. This is achieved through a connection between energy derivatives and eigenstates of Taylor approximations of the Hamiltonian. We illustrate the advantages of the tailgating approach by performing simulations calculating the vibrational modes of beryllium hydride and water: quantities that depend on second-order energy derivatives.

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Differentiable quantum computational chemistry with PennyLane

Cited by 5 publications

References 42 publications

Demonstrating quantum computing with the quark model

Demonstrating quantum computing with the quark model

Finite-Volume Pionless Effective Field Theory for Few-Nucleon Systems with Differentiable Programming

Tailgating quantum circuits for high-order energy derivatives

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