Bulletin of the American Physical Society
APS March Meeting 2021
Volume 66, Number 1
Monday–Friday, March 15–19, 2021; Virtual; Time Zone: Central Daylight Time, USA
Session V34: Quantum Computing Algorithms IVLive

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Sponsoring Units: DQI Chair: Mekena Metcalf, Lawrence Berkeley National Laboratory 
Thursday, March 18, 2021 3:00PM  3:12PM Live 
V34.00001: Ab Initio Molecular Dynamics on Quantum Computers Dmitry Fedorov, Matthew Otten, Stephen Gray, Yuri Alexeev Simulation of quantum systems is one of the promising applications of quantum computers. In this work, we are exploring the possibility of simulation of the time evolution of molecular systems on quantum computers using the ab initio molecular dynamics (AIMD) approach. The nuclei are propagated classically on BornOppenheimer electronic potential energy surfaces, which are obtained from the solution of the electronic Schrödinger equation using the variational quantum eigensolver (VQE) method. The energy gradients are computed numerically using the HellmannFeynman theorem, finite differences, and a correlated sampling technique. Our method does not require additional calculations on a quantum computer. To achieve comparable accuracy, our gradient calculation method requires three to five orders of magnitude fewer measurements than the methods without correlated sampling. AIMD dynamics trajectories are simulated for the H_{2} molecule on IBM quantum devices. To the best of our knowledge, it is the first successful attempt to run AIMD on quantum devices. With the increasing quality of quantum hardware, our method can be used for studying larger molecules. 
Thursday, March 18, 2021 3:12PM  3:24PM Live 
V34.00002: Toward scalable simulations of lattice gauge theories on quantum computers Guglielmo Mazzola, Simon V Mathis, Giulia Mazzola, Ivano Tavernelli In this talk I will present a framework for simulating a discretized U(1) gauge theory with dynamical matter on a digital quantum computer, that is scalable towards an arbitrary number of spacial dimensions. 
Thursday, March 18, 2021 3:24PM  3:36PM Live 
V34.00003: Quantum algorithms for astrochemistry and atmospheric science: Calculating vibrational spectra. Nicolas Sawaya, Francesco Paesani, Daniel P. Tabor Though electronic structure is the most popular chemical application of the quantum information community, there are many substances for which it is the quantum vibrational (not electronic) behavior that is classically intractable. Here we outline the previously unaddressed ways in which solving the vibrational spectroscopy problem is mathematically distinct from the electronic problem. We discuss the calculation of highlying excited states, lowdepth methods for calculating transition amplitudes, and bosontoqubit mappings. We study SuzukiTrotter error for vibrational Hamiltonians relevant to astrochemistry, atmospheric science, and combustion. Most notably, we make resource comparisons with electronic structure, concluding with strong evidence that a vibrational problem instance will achieve quantum supremacy before an electronic one. 
Thursday, March 18, 2021 3:36PM  3:48PM Not Participating 
V34.00004: Simulating photosynthesis on an IBM quantum computer Ben Jaderberg, Alexander Eisfeld, Sarah Mostame Biological systems, such as green sulphur bacteria, have been found to have exceptional lightharvesting capabilities. A key component of this process occurs in the FennaMatthewsOlson (FMO) complex, where energy is transferred with nearperfect efficiency to the reaction site. Despite being a system open to its environment, it has been suggested that observed quantum effects play an important role in achieving such high efficiency. In this work, we look to simulate the intermolecular site dynamics of the FMO complex using a digital quantum computer. By modeling the vibrational phonon modes as harmonic oscillators, we verify our algorithm recovers site statistics of electronphonon systems with a strong agreement with simulations on classical devices. Subsequently, we apply our model to simulate the full FMO complex and compare our results to the most recent experimental observations. We find that achieving higher accuracy on such simulations is limited by the number and quality of available qubits and suggest ways this can be overcome in the near future. 
Thursday, March 18, 2021 3:48PM  4:00PM Live 
V34.00005: Band theory on a quantum computer Kyle Sherbert, Frank Cerasoli, Marco BuongiornoNardelli Band theory is a successful approach to studying the electronic structure of periodic systems under a singleelectron approximation. Typically, band theory considers a Hamiltonian in reciprocal space, with hopping parameters as functions of k, a vector in the Brillouin zone. We demonstrate a technique to perform band theory on a quantum computer. We also demonstrate an alternative which considers a Hamiltonian in real space, with constant hopping parameters and with k input directly into the quantum circuit. We show this alternative adds Θ(n) qubits, Θ(n^{2}) gate operations, and a factor of Θ(n) to algorithm complexity, where n is the maximum binary resolution of k. We validate our approach with results obtained from IBMQ cloud computers. Finally, we suggest how our approach may be adapted to consider correlations between multiple electrons. 
Thursday, March 18, 2021 4:00PM  4:12PM Live 
V34.00006: Graph Optimization Perspective for LowDepth TrotterSuzuki Decomposition Albert Schmitz, Nicolas Sawaya, Sonika Johri, Anne Matsuura Hamiltonian simulation represents an important module in many quantum algorithms such as quantum machine learning, quantum linear algebra, and design of materials and chemistry. The most prominent methods for realizing the timeevolution unitary is the TrotterSuzuki approximation. However, there are many possible decompositions for the infinitesimal timeevolution operator as the order in which each term of the Hamiltonian is implemented is arbitrary. We discuss a novel perspective for generating a lowdepth TrotterSuzuki decomposition assuming the Clifford+RZ gate set by adapting ideas from quantum error correction. We map a given TrotterSuzuki decomposition to a constrained path on a graph which we deem the Pauli Frame Graph (PFG). Each node of the PFG represents the set of Hamiltonian terms currently available to be applied, Clifford operations represent a move between nodes, and the graph distance of the path represents the gate cost of implementation. Finding the optimal decomposition is then equivalent to solving a problem similar to the traveling salesman. Though this is an NPhard problem, we use this perspective to demonstrate the simplest heuristic, greedy search, and compare the resulting twoqubit gate count and circuit depth to more standard methods. 
Thursday, March 18, 2021 4:12PM  4:24PM Live 
V34.00007: Operator Ordering Ambiguity in Trotterized Unitary Coupled Cluster Theory and How to Take Advantage of It Harper Grimsley, Sophia Economou, Edwin Barnes, Nicholas J. Mayhall The unitary coupled cluster (UCC) ansatz is an attractive choice for representing chemical wavefunctions on a quantum computer. In practice, a Trotter decomposition of the ansatz is necessary for convenient preparation on hardware. Finiteorder Trotter decomposition of the same UCC ansatz, however, gives different Trotterized ansatz structures depending on the ordering of the individual operators in the Trotter product. We demonstrate that even after variationally optimizing these different parametrized ansatzë, one obtains dramatically different ground state energies, many of them superior to that of the unTrotterized UCC energy. We consider our Adaptive, DerivativeAssembled, PseudoTrotterized Variational Quantum Eigensolver (ADAPTVQE) through the lens of building a quasioptimal, welldefined, Trotterized UCClike ansatz, reflecting on why ADAPT is so much more parameterefficient than UCC. 
Thursday, March 18, 2021 4:24PM  4:36PM Live 
V34.00008: Quantum Chaos and Trotterisation Thresholds in Digital Quantum Simulations Cahit Kargi, Fabio Henriques, Lukas Sieberer, Tobias Olsacher, Philipp Hauke, Markus Heyl, Juan Pablo Dehollain, Peter Zoller, Nathan Langford Digital quantum simulation is one of the most promising paths for achieving useful realworld applications for industryscale quantum processors. Yet even assuming continued rapid progress in device engineering, extensive resource optimisation will remain crucial to exploiting the full computational power of a device. In digital quantum simulations, Trotter step size has a profound impact on required qubit and gate numbers for each application. But contrary to standard rigorous bounds, recent theory results predict a performance threshold connecting simulation fidelity, system localisation and quantum chaos. Here, we numerically analyse several experimentally accessible digital simulation models, supporting and extending these predictions. In each case, we show that a range of numerical signatures share the same sharp threshold, at a step size that is largely independent of system size. We study in detail the relationship between the Trotterisation threshold and the onset of digitisationinduced quantum chaos. We show that chaotic dynamics can be conclusively observed down to modest system sizes, and that the same sharp threshold may even be observed in smaller systems which do not exhibit conclusive evidence of chaos. 
Thursday, March 18, 2021 4:36PM  4:48PM Live 
V34.00009: Randomizing multiproduct formulas for improved Hamiltonian simulation Paul K Faehrmann, Mark Steudtner, Richard Kueng, Mária Kieferová, Jens Eisert Digital quantum simulation suggests a path forward for the efficient simulation of problems in condensedmatter physics, quantum chemistry and materials science. While the majority of quantum simulation algorithms are deterministic, a recent surge of ideas has shown that randomization can greatly benefit algorithmic performance. In this work, we introduce a scheme for quantum simulation that unites the advantages of randomized compiling and higherorder linearcombinationofunitaries (LCU) algorithms. In doing so, we propose a framework of randomized sampling that could prove useful for quantum simulation on nearterm devices and present two new LCU algorithms tailored to this framework. Our framework greatly reduces the circuit depth by circumventing the need for oblivious amplitude amplification required by standard LCU methods, rendering it especially useful for mediumterm quantum computing. Our algorithms achieve a simulation error that shrinks exponentially with the circuit depth. To corroborate their functioning, we prove rigorous performance bounds and discuss examples at hand of noninteracting models. 
Thursday, March 18, 2021 4:48PM  5:00PM Live 
V34.00010: Quantum simulation via randomized product formulas: Low gate complexity with accuracy guarantees ChiFang Chen, HsinYuan Huang, Richard Kueng, Joel Tropp Quantum simulation has wide applications in quantum chemistry and physics. Recently, scientists have begun exploring the use of randomized methods for accelerating quantum simulation. Among them, a simple and powerful technique, called qDRIFT, is known to generate random product formulas for which the average quantum channel approximates the ideal evolution. This work provides a comprehensive analysis of a single realization of the random product formula produced by qDRIFT. The main results prove that a typical realization of the randomized product formula approximates the ideal unitary evolution up to a small diamondnorm error. The gate complexity is independent of the number of terms in the Hamiltonian, but it depends on the system size and the sum of the interaction strengths in the Hamiltonian. Remarkably, the same random evolution starting from an arbitrary, but fixed, input state yields a much shorter circuit suitable for that input state. If the observable is also fixed, the same random evolution provides an even shorter product formula. The proofs depend on concentration inequalities for vector and matrix martingales. Numerical experiments verify the theoretical predictions. 
Thursday, March 18, 2021 5:00PM  5:12PM Live 
V34.00011: Nonlocal approximation toward implementation of quantum imaginarytime evolution method on NISQ devices Hirofumi Nishi, Taichi Kosugi, Yuichiro Matsushita In quantum manybody problems, the imaginarytime evolution method is a well known approach to obtain the ground state on classical computers. A recent proposed imaginarytime evolution (QITE) method on quantum computers is expected to solve problems faster than classical computers [1], however, its implementation on noisy intermediatescale quantum (NISQ) devices is difficult due to the depth of the circuits. We propose two methods to overcome this problem [2]: the first is a nonlocal approximation method removing the locality condition imposed when transforming the imaginarytime evolution operator into a unitary operator in the QITE method; the second is a compression method of the quantum circuit for imaginarytime steps. We show that the introducing the nonlocal approximation and compression methods can significantly reduce the accumulation of errors attributed to deep circuit depth, paving the way for the implementation of the QITE method on NISQ devices. 
Thursday, March 18, 2021 5:12PM  5:24PM Live 
V34.00012: Creating and manipulating a Laughlintype ν=1/3 fractional quantum Hall state on a quantum computer with linear depth circuits Armin Rahmani, Kevin J Sung, Harald Putterman, Pedram Roushan, Pouyan Ghaemi, Zhang Jiang Here we present an efficient quantum algorithm to generate an equivalent manybody state to Laughlin's ν=1/3 fractional quantum Hall state on a digitized quantum computer. Our algorithm only uses quantum gates acting on neighboring qubits in a quasionedimensional setting, and its circuit depth is linear in the number of qubits, i.e., the number of Landau orbitals in the second quantized picture. We identify correlation functions that serve as signatures of the Laughlin state and discuss how to obtain them on a quantum computer. We also discuss a generalization of the algorithm for creating quasiparticles in the Laughlin state. This paves the way for several important studies, including quantum simulation of nonequilibrium dynamics and braiding of quasiparticles in quantum Hall states. 
Thursday, March 18, 2021 5:24PM  5:36PM Live 
V34.00013: Collective Neutrino Oscillations on a Quantum Computer Kubra Yeter Aydeniz, Shikha Bangar, George Siopsis, Raphael Pooser In this study, we use the quantum Lanczos (QLanczos) algorithm to calculate the eigenvalues and eigenstates of a collective neutrino system as a function of the radial dependence of the coupling strength of neutrino interactions on IBM Q quantum hardware. To this end, we use neutrino interactions Hamiltonian expressed in terms of manybody Hamiltonian in [1] with limitation to twoflavor/mass states of neutrinos, exclusion of the antineutrino interactions, and neutrino background matter interactions. We demonstrate that the system Hamiltonian in mass basis can be separated into smaller blocks which can be represented using less number of qubits in a quantum circuit. This is an important result as this shows that a larger number of collective neutrino systems can be represented with less quantum resources. We also demonstrate the collective neutrino oscillations in flavor basis using a singlestep Trotterization method on quantum hardware. 
Thursday, March 18, 2021 5:36PM  5:48PM Live 
V34.00014: Toward Quantum Simulations of Z_{2} Gauge Theory in 1+1Dimensions Without State Preparation Erik Gustafson, Henry Lamm Preparing stronglycoupled states on quantum computers requires large resources. In this work, we show how classical sampling coupled with projection operators can be used to compute Minkowski matrix elements on a quantum computer without explicitly preparing these stronglycoupled states on the quantum computer. We demonstrate this for the 2+1d Z_{2} lattice gauge theory. 
Thursday, March 18, 2021 5:48PM  6:00PM Live 
V34.00015: Simulating phi4 scalar field on quantum computers Andy C. Y. Li, Alexandru Macridin, Stephen Mrenna, Panagiotis Spentzouris Digital quantum simulation of lattice quantum field theory models could significantly enhance our ability to investigate those models, in particular, with strong interaction or under nonequilibrium conditions. We present a quantum algorithm to prepare the ground state of a lattice scalarfield model with a quartic interaction. This gives an insight into the anharmonic effect on a relativistic field and serves as a stepping stone toward simulating more complex models. Our algorithm combines a local variational approach with an adiabatic state transfer to allows efficient state preparation with high fidelity. We show that this algorithm can be flexibly employed under various conditions and is scalable to large lattices. 
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