Bulletin of the American Physical Society
APS March Meeting 2021
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session P34: Quantum Computing Algorithms IFocus Live

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Sponsoring Units: DQI Chair: Yuval Sanders, Macquarie University 
Wednesday, March 17, 2021 3:00PM  3:36PM Live 
P34.00001: The Power of Adiabatic Quantum Computation with No Sign Problem Invited Speaker: Matthew Hastings : Interference is an essential part of quantum mechanics. However, an important class of Hamiltonians considered are those with "no sign problem", where all offdiagonal matrix elements of the Hamiltonian are nonnegative. This means that the ground state wave function can be chosen to have all amplitudes real and positive. In a sense, no destructive interference is possible for these Hamiltonians so that they are "almost classical", and there are several simulation algorithms which work well in practice on classical computers today. In this talk, I'll discuss what happens when one considers adiabatic evolution of such Hamiltonians, and show that they still have some power that cannot be efficiently simulated on a classical computer; to be precise and formal, I'll show this "relative to an oracle", which I will explain. I'll discuss implications for simulation of these problems and open questions. 
Wednesday, March 17, 2021 3:36PM  3:48PM Live 
P34.00002: Quantum Algorithm for Simulating Hamiltonian Dynamics with an Offdiagonal Series Expansion Itay Hen, Amir Kalev We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the timeevolution operator in its offdiagonal terms. The expansion decouples the dynamics due to the diagonal component of the Hamiltonian from the dynamics generated by its offdiagonal part, which we encode using the linear combination of unitaries technique. Our method has an optimal dependence on the desired precision and, as we illustrate, generally requires considerably fewer resources than the current stateoftheart. We provide an analysis of resource costs for several sample models. 
Wednesday, March 17, 2021 3:48PM  4:00PM Live 
P34.00003: Shortcuts to Adiabaticity in Digitized Adiabatic Quantum Computing Narendra Hegade, Koushik Paul, Yongcheng Ding, Mikel Sanz, Francisco AlbarránArriagada, Enrique Solano, Xi Chen Shortcuts to adiabaticity are wellknown methods for controlling the quantum dynamics beyond the adiabatic criteria, where counterdiabatic (CD) driving provides a promising means to speed up quantum manybody systems. In this work, we show the applicability of CD driving to enhance the digitized adiabatic quantum computing paradigm in terms of fidelity and total simulation time. We study the state evolution of an Ising spin chain using the digitized version of the standard CD driving and its variants derived from the variational approach. We apply this technique in the preparation of Bell and GreenbergerHorneZeilinger states with high fidelity using a very shallow quantum circuit. We implement this proposal in the IBM quantum computer, proving its usefulness for the speed up of adiabatic quantum computing in noisy intermediatescale quantum devices. 
Wednesday, March 17, 2021 4:00PM  4:12PM Live 
P34.00004: Quantum linear system solver based on continuous and discrete adiabatic quantum computing Dong An, Lin Lin We demonstrate that with an optimally tuned scheduling function, adiabatic quantum computing (AQC) can solve a quantum linear system problem with O(κ*poly(log(κN/ε))) complexity, where κ is the condition number, N is the dimension of the linear system, and ε is the desired level of errors. This achieves an exponential speedup over classical iterative linear system solvers such as conjugate gradient method in terms of the dimension N, and the scalings in terms of all parameters are near optimal. Furthermore, we carefully discuss how to discretize our AQCbased algorithm. Amazingly, it turns out that the simplest first order Trotterization can preserve the O(κ*poly(log(κN/ε))) complexity without incurring any overhead, thus promising to be implemented on nearterm quantum devices. Such an unexpected exponential convergence of the first order Trotterization can be proved via discrete version of adiabatic theorem, and also motivates further research on general applications of AQC other than solving quantum linear system problem. 
Wednesday, March 17, 2021 4:12PM  4:24PM 
P34.00005: Efficient stepmerged quantum imaginary time evolution algorithm for quantum chemistry Niladri Gomes, Feng Zhang, Noah Berthusen, CaiZhuang Wang, KaiMing Ho, Peter Orth, Yongxin Yao We develop a resource efficient stepmerged quantum imaginary time evolution approach (smQITE) to solve for the ground state of a Hamiltonian on quantum computers. This heuristic method features a fixed shallow quantum circuit depth along the state evolution path. We use this algorithm to determine binding energy curves of a set of molecules, including H_{2}, H_{4}, H_{6}, LiH, HF, H_{2}O and BeH_{2}, and find highly accurate results. The required quantum resources of smQITE calculations can be further reduced by adopting the circuit form of the variational quantum eigensolver (VQE) technique, such as the unitary coupled cluster ansatz. We demonstrate that smQITE achieves a similar computational accuracy as VQE at the same fixedcircuit ansatz, without requiring a generally complicated highdimensional nonconvex optimization. Finally, smQITE calculations are carried out on Rigetti quantum processing units, demonstrating that the approach is readily applicable on current NISQ devices. 
Wednesday, March 17, 2021 4:24PM  4:36PM Live 
P34.00006: Quantum Computation of Eigenvalues within Target Intervals Phillip Jensen, Lasse B. Kristensen, Jakob S. Kottmann, Alan AspuruGuzik There is widespread interest in calculating the energy spectrum of a Hamiltonian, for example to analyze optical spectra and energy deposition by ions in materials. In this study, we propose a quantum algorithm that samples the set of energies within a target energyinterval without requiring good approximations of the target energyeigenstates. We discuss the implementation of direct and iterative amplification protocols and give resource and runtime estimates. We illustrate initial applications by amplifying excited states on molecular Hydrogen. 
Wednesday, March 17, 2021 4:36PM  4:48PM Live 
P34.00007: The importance of the spectral gap in estimating groundstate energies Abhinav Deshpande, Alexey V Gorshkov, Bill Fefferman The Local Hamiltonian problem, which is concerned with estimating the groundstate energy of a local Hamiltonian, is a central object in the field of Hamiltonian complexity and is complete for the class QMA. A major challenge in the field is to understand the complexity of the problem in more physically natural parameter regimes. Despite its importance in quantum manybody physics, the role played by the spectral gap in the complexity of the Local Hamiltonian is less wellunderstood. In this work, we make progress on this question by considering the precise regime, in which one estimates the groundstate energy to within inverseexponential precision. In this setting, there is a surprising result that the complexity of Local Hamiltonian is magnified from QMA to PSPACE. We clarify the reason behind this boost in complexity. Specifically, we show that the full complexity of the high precision case only comes about when the spectral gap is exponentially small. As a consequence, we uncover important implications for the representability and circuit complexity of ground states of local Hamiltonians, the theory of uniqueness of quantum witnesses, and techniques for the amplification of quantum witnesses in the presence of postselection. 
Wednesday, March 17, 2021 4:48PM  5:00PM Live 
P34.00008: Enhancing the Quantum Linear Systems Algorithm using Richardson Extrapolation Almudena Carrera Vazquez, Ralf Hiptmair, Stefan Woerner We present a quantum algorithm to solve systems of linear equations of the form Αx=b, where Α is a tridiagonal Toeplitz matrix and b results from discretizing an analytic function, with a circuit complexity of polylog(κ, 1/ε, N), where N denotes the number of equations, ε the accuracy, and κ the condition number. 
Wednesday, March 17, 2021 5:00PM  5:12PM Live 
P34.00009: Lanczos recursion on a quantum computer for the Green's function Thomas Baker The technique of quantum counting is used to obtain coefficients from a Lanczos recursion from a single groundstate wavefunction on the quantum computer. This is used to compute the continued fraction representation of an interacting Green's function, useful for condensed matter, particle physics, and other areas. The wavefunction does not need to be reprepared at each iteration. The quantum algorithm represents an exponential reduction in memory required over classical methods. 
Wednesday, March 17, 2021 5:12PM  5:24PM Live 
P34.00010: The ground state phases of the disordered BoseHubbard model with attractive interactions Olli Mansikkamäki, Matti Silveri In this work we describe the ground state phases of the disordered BoseHubbard model with attractive interactions. The model can be experimentally realised with a chain of capacitively coupled superconducting transmon devices. For a fixed number of photons, the model exhibits three distinct ground state phases. With strong enough disorder, all the photons are localised onto the site with the lowest onsite energy. With weaker disorder and with low hopping frequency J relative to the strength of the interactions U, the ground state is a symmetric superposition of localised states, or a Wstate. At the other end of the J / U axis, the ground state is superfluid. 
Wednesday, March 17, 2021 5:24PM  5:36PM Live 
P34.00011: Adiabatic evolution to a Fermi Liquid on nearterm quantum computers Gaurav Gyawali, Michael Lawler Landau's Fermi Liquid theory is central to our understanding of many modern condensed matter systems, yet the adiabatic dynamics leading to the formation of Fermi Liquid state remains vastly unexplored. We thus propose studies that can be done on nearterm quantum computers to enhance our understanding of Fermi Liquid theory. We were able to generate strongly correlated ground states by performing an adiabatic evolution on the ground states of a noninteracting, few qubit FermiHubbard model. We use this method to determine whether a given Hamiltonian will have a ground state described by the Fermi Liquid theory. Additionally, we develop tools to study the evolution and understand how the quasiparticle picture develops. 
Wednesday, March 17, 2021 5:36PM  5:48PM Live 
P34.00012: Phase cancellation diagonalization method: A general approach to nonorthogonal basis sets for quantum devices Katherine Klymko, Carlos Mejuto Zaera, Filip Andrzej Wudarski, Miroslav Urbanek, Stephen J. Cotton, Wibe A De Jong, Norm Tubman Here we examine a family of algorithms that use real time Hamiltonian dynamics for quantum subspace diagonalization. The algorithm we focus on generates a series of time evolved states, resulting in a generalized eigenvalue equation that can be solved for ground and excited eigenstates. This method requires a surprisingly small number of basis states generated by real time evolution to compute chemically accurate results, making it particularly attractive for the NISQ era. We examine the theoretical underpinnings of the method, which involves the cancellation of phases with time evolution, and also systematically examine the role of noise in solving the generalized eigenvalue equation. We demonstrate our approach numerically over a range of systems, both in classical simulations (for LiH and Cr2) and on quantum hardware (for the transverse field Ising model). 
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