Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session F02: Towards Discovery in Chemistry with Quantum Computers IIIFocus Recordings Available

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Sponsoring Units: DCP Chair: Mekena Metcalf, LBNL Room: McCormick Place W175C 
Tuesday, March 15, 2022 8:00AM  8:36AM 
F02.00001: Exploiting nonorthogonality in quantum algorithms for calculations of molecular electronic states Invited Speaker: Birgitta Whaley Quantum algorithms for the calculation of electronic states of molecules on nearterm quantum computers are primarily hybrid, involving iterative schemes that alternate quantum and classical processing components. Repeatedly interfacing quantum and classical steps increases the measurement costs and leads to a tradeoff between requirements of viable coherence and a feasible number of circuit repetitions. I shall present new options for electronic structure quantum algorithms based on the use of nonorthogonal methods that allow a different cut between quantum and classical processing components to be made. Applications to strongly correlated systems and scaling of computational resources for these will be discussed, together with an outlook for nearterm realizations. 
Tuesday, March 15, 2022 8:36AM  8:48AM 
F02.00002: State preparation and evolution in quantum computing: a perspective from Hamiltonian moments. Bo Peng The nonnegligible gate error present on NISQ devices impedes the implementation of conventional quantum algorithms. Practical strategies usually exploit hybrid quantumclassical algorithms to demonstrate potentially useful applications of quantum computing in the NISQ era. Recent efforts highlight the development of quantum algorithms based upon quantum computed Hamiltonian moments with respect to a given trial quantum state. In this talk, we will briefly introduce these quantum algorithms with focuses on the typical ways of computing Hamiltonian moments using quantum hardware and improving the accuracy of the estimated state energies. We will present an example to show how we can measure and compute the Hamiltonian moments of a foursite Heisenberg model, and compute the energy and magnetization of the model utilizing the imaginary time evolution on the real IBMQ NISQ hardware. We will further discuss some practical issues associated with these algorithms, and conclude this talk by discussing some possible developments and applications in this direction in the near future. 
Tuesday, March 15, 2022 8:48AM  9:00AM 
F02.00003: Fast state preparation for molecular simulation by direct pulse optimization: ctrlVQE Nicholas Mayhall, Oinam R Meitei, David Pappas, Bryan T Gard, George S Barron, Edwin Barnes, Sophia Economou The variational quantum eigensolver (VQE) is a hybrid quantumclassical algorithm to simulate stationary states of molecular systems, which classically optimizes a parameterized quantum circuit to minimize the expectation value of a molecular Hamiltonian. Due to the ability of the variational principle to absorb circuit errors, VQE is uniquely positioned for deployment on NISQ devices. However, in order to obtain sufficiently accurate results, the depth of the parameterized circuits can easily exceed what is experimentally realizable within device coherence times. In this talk, I will discuss recent progress we have made which dramatically reduces the coherence time demands by replacing the parameterized quantum circuit component with a direct pulse optimization. Compared to UCCSD, direct pulse optimization achieves 1000x faster state preparation for LiH molecule on four qubits. 
Tuesday, March 15, 2022 9:00AM  9:12AM 
F02.00004: Leakage reduces device coherence demands for molecular simulations with pulselevel VQE Ayush Asthana, Sophia Economou, Edwin Barnes, Nicholas Mayhall Variational Quantum Eigensolver (VQE) algorithms have generally involved the optimization of a series of parameterized quantum gates designed to approximate the quantum state of a molecule. While this has many attractive features such as robustness to noise, the limited coherence times and frequent gate errors limit the number of these gates in nearterm quantum devices. Our team's proposed method (ctrlVQE) uses a pulse shaping routine to prepare the final state by variationally optimizing the pulse parameters directly instead of using a parameterized circuit. Through numerical simulations, we have observed reductions in the coherence time required of multiple orders of magnitude. Consequently, ctrlVQE may extend the applicability of quantum algorithms for nearterm quantum devices to highly entangled systems, such as strongly correlated molecules. In this talk, I will discuss recent results related to the behaviour of ctrlVQE at the minimum time of evolution. When constraining the pulse to within some experimentally convenient bounds, we reveal the emergence of bangbang shapes of optimal pulses, consistent with Pontryagin's Principle. Interestingly, we observe that leakage outside computational space using qudits with access to more than two states (something that is usually considered disadvantageous) actually speeds up the state preparation, which ultimately further reduces device coherence time demands. 
Tuesday, March 15, 2022 9:12AM  9:48AM 
F02.00005: Dynamical Quantum Algorithms For Chemistry and Materials Invited Speaker: Nathan Fitzpatrick We present a series of dynamical quantum computing algorithms for use in quantum chemistry and materials. With application to a range of time and frequency dependent problems, and also eigenvalue decompositions. We show how dynamical algorithms are naturally well suited to quantum computers and may be a promising route to quantum advantage. One example we present is the Jaynes Cumming model for fermionboson dynamics using the Holstein Primakov qubit mapping transformation to the Pauli spin operators, which has application to nuclearelectron dynamics in molecules. Another important application of dynamical algorithms are Green’s functions. We demonstrate quantum algorithms for Green’s functions within the EUMEN quantum chemistry and materials package. Furthermore we use these quantum algorithms for Green’s functions in quantum embedding methods such as Dynamical Mean Field Theory (DMFT). Finally, we present a low depth formulation of the recently developed Variational Phase Estimation (VPE) method, which can be thought of as a generalized eigenvalue decomposition in a time evolved basis. We therefore aim to show that time dependant algorithms are a powerful subroutine in near and intermediate scale quantum algorithms for quantum chemistry and materials. 
Tuesday, March 15, 2022 9:48AM  10:00AM 
F02.00006: Multiscale Electronic Structure Calculations via Projection Based Quantum Embedding Alexis P Ralli, Peter V Coveney, Michael Williams Simulation of matter at the molecular scale on quantum computers has been restricted by the limitations of current hardware. As a result, only small chemical systems  such as H_{2}  have been studied to date. To move calculations towards more complex molecular systems, we propose utilizing a projection based embedding theory. This allows an electronic structure problem to be split into conventional density functional theory calculations and a wave function problem. We propose solving the latter on a quantum device and the remainder using conventional computers. As there is freedom to choose the size of the quantum problem, we show how this embedding procedure can generate molecular Hamiltonians requiring fewer quantum resources to simulate. 
Tuesday, March 15, 2022 10:00AM  10:12AM Withdrawn 
F02.00007: Symmetryadapted factorized unitary coupled cluster ansatz for quantum computer Avijit Shee For variational quantum eigensolver (VQE) algorithm exploitation of Hamiltonian symmetry enables us to search through a limited size of the Hilbert space and reach correct eigenstate protected by symmetry. We will use unitary coupled cluster as a state preparation ansatz for VQE, where cluster operators will be adapted to a particular spin symmetry. Furthermore, each spinadapted operators will be factorized using the Cartan decomposition to get an ansatz which can be easily utilized within a quantum algorithm. We will apply this method to various low lying states of openshell molecules, where non spinadapted ansatz will face trouble to converge to a correct eigenstate. 
Tuesday, March 15, 2022 10:12AM  10:24AM 
F02.00008: Unitary Selective Coupled Cluster Method Dmitry A Fedorov, Yuri Alexeev, Stephen K Gray, Matthew Otten Variational quantum eigensolver is one of the promising methods to simulate quantum systems by utilizing nearterm quantum computers. Unitary coupled cluster (UCC) is one of the most promising ways of representing electronic wave function on a quantum computer. Although UCC is a chemistryinspired ansatz, which only explores chemically relevant parts of the Hilbert space, it often contains too many fermionic operators with nearly zero contribution to the correlation energy of a molecule. We demonstrate that molecular symmetries can be leveraged to prescreen the excitation operators in the ansatz. Our approach allows us to significantly reduce the number of excitation operators in ansatz. For highly symmetric molecules, this reduction can be up to 8090%. Moreover, we propose a unitary selective coupled cluster, an iterative method, which can construct a unitary coupled cluster (UCC) ansatz with excitation operators of arbitrary order. We demonstrate its performance on a set of small molecules and discuss the method's potential for simulations of chemical systems on quantum computers. 
Tuesday, March 15, 2022 10:24AM  11:00AM 
F02.00009: DMRGbased methods for largescale applications in strongly correlated quantum chemistry Invited Speaker: Libor Veis Quantum chemical version of the density matrix renormalization group approach (QCDMRG) is a method of choice for accurate calculations of strongly correlated molecular systems requiring very large active spaces. It is also one of the methods, which will in the early stage help to benchmark the NISQ devices. 
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