Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session A09: Algorithms and Architecture for Quantum Information I 
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Sponsoring Units: DQI Chair: Yunseong Nam, IONQ Room: 106 
Monday, March 2, 2020 8:00AM  8:12AM 
A09.00001: Finding NavierStokes fluid flows through quantum computung Frank Gaitan We present a quantum algorithm that solves an arbitrary set of coupled nonlinear partial differential equations and show how it can be used to solve the governing equations for a NavierStokes fluid. To test the algorithm we examine the problem of inviscid, compressible flow through a convergentdivergent nozzle. We numerically simulate application of the algorithm to find the steadystate flow when a shockwave is and is not present in the divergent part of the nozzle. In each case excellent agreement is found between the output of the quantum simulation and the exact analytical solution, with the simulation successfully capturing the shockwave when present. We compare the computational cost of the quantum algorithm to that of deterministic and random classical algorithms; discuss future applications as well as the potential longterm significance of quantum computing for the fluid dynamics community. 
Monday, March 2, 2020 8:12AM  8:24AM 
A09.00002: Quantum eigenvalue estimation via time series analysis Rolando Somma We present an efficient method for estimating the eigenvalues of a Hamiltonian H from the expectation values of the evolution operator for various times. For a given quantum state ρ, our method outputs a list of eigenvalue estimates and approximate probabilities. Each probability depends on the support of ρ in those eigenstates of H associated with eigenvalues within an arbitrarily small range. The complexity of our method is polynomial in the inverse of a given precision parameter. Unlike the wellknown quantum phase estimation algorithm that uses the quantum Fourier transform, our method does not require large ancillary systems, large sequences of controlled operations, or preserving coherence between experiments, and is therefore more attractive for nearterm applications. The output of our method can be used to compute spectral properties of H and other expectation values efficiently. 
Monday, March 2, 2020 8:24AM  8:36AM 
A09.00003: A robust algorithm for finding phase factors in quantum signal processing Yulong Dong, Lin Lin, Xiang Meng, Birgitta K Whaley Quantum Signal Processing (QSP) provides a general way to implement matrix functions on quantum computers. The algorithm can be efficiently used to solve quantum linear systems, to perform Hamiltonian simulation, and to prepare Gibbs ensembles, among other applications. QSP can exactly encode a degreed polynomial transformation of a matrix using d+1 phase factors. However, the current strategies for solving for the phase factors of a given function can be numerically unstable. We present an efficient method to find the phase factors for a general real function, and demonstrate the performance for solving linear systems and eigenvalue problems. 
Monday, March 2, 2020 8:36AM  8:48AM 
A09.00004: Finding symmetrybroken ground states with variational quantum algorithms Nicolas Vogt, Sebastian Zanker, JanMichael Reiner, Thomas Eckl, Anika Marusczyk, Michael Marthaler One of the most promising applications for nearterm intermediate scale quantum computers (NISQ) is the preparation of the true ground state of strongly correlated electron systems. Besides the groundstate energy the properties of interest of the ground state are its broken symmetries and the corresponding phases of the system. 
Monday, March 2, 2020 8:48AM  9:00AM 
A09.00005: Strategies for digital quantum simulation of bosons Nicolas Sawaya, Tim Menke, Thi Ha Kyaw, Sonika Johri, Alan AspuruGuzik, Gian Giacomo Guerreschi Many prominent bosonic simulation problems are thought to be intractable on a classical computer, including the BoseHubbard model, quantum photonics, and molecular vibronics. The behavior of such systems would be efficiently studied on a quantum computer. Before such a simulation is performed, one must choose how to encode the bosonic degrees of freedom into a set of qubits. We present a general methodology for encoding truncated bosons into arrays of qubits, and consider several encoding types. We study the quantum operations and qubit counts for local and composite operators. Importantly, we also consider the utility of interconverting between mappings in the middle of a simulation. These methods lower the quantum resource requirements compared to previous encoding strategies, which may allow for larger problems to be simulated on nearterm quantum devices. 
Monday, March 2, 2020 9:00AM  9:12AM 
A09.00006: A Method of Determining ExcitedStates for Quantum Computation Pejman Jouzdani, Stefan A Bringuier, Mark kostuk The calculation of molecular groundstate and excitedstate energies, or more generally the energy spectra of chemical and material systems, is an application of great interest in a gatebased quantum computational model. In this contribution, we propose a phenomenological approach to the calculation of lowlying excitedstates of a given problem Hamiltonian. Specifically, a method is presented in which the groundstate subspace is projected out of a Hamiltonian representation. As a result of this projection, an effective Hamiltonian is constructed where its groundstate coincides with an excitedstate of the original problem. Thus, lowlying excitedstate energies can be calculated using existing hybrid quantumclassical techniques and variational algorithm(s) for determining groundstate. The method is shown to be fully valid for the H2 molecule. In addition, conditions for the method’s success are discussed in terms of classes of Hamiltonians. A discussion on the broad impact of this method in the era of NISQ devices will also be presented. 
Monday, March 2, 2020 9:12AM  9:24AM 
A09.00007: Quantum simulation by qubitization without Toffoli gates Mark Steudtner, Stephanie Wehner Qubitization is a modern approach to estimate Hamiltonian eigenvalues without simulating its time evolution. While in this way approximation errors are avoided, its resource and gate requirements are more extensive: qubitization requires additional qubits to store information about the Hamiltonian, and Toffoli gates to probe them throughout the routine. Recently, it was shown that storing the Hamitlonian in a unary representation can alleviate the need for such gates in one of the qubitization subroutines. Building on that principle, we develop an entirely new decomposition of the entire algorithm: without Toffoli gates, we can encode the Hamiltonian into qubits within logarithmic depth. 
Monday, March 2, 2020 9:24AM  9:36AM 
A09.00008: Emulation of fractional quantum Hall states with existing quantum hardware Armin Rahmani, Pouyan Ghaemi, Zhang Jiang, Pedram Roushan, Kevin J Sung Emulating strongly correlated phases of matter with existing or nearterm quantum hardware is of considerable interest. Here we present quantum circuits to generate both the ground and quasiparticle states corresponding to the Laughlin's $\nu=1/3$ fractional quantum Hall state in the secondquantized representation. Our circuit depth is linear in the number of qubits. We identify experimentally accessible correlation functions as signatures of this state and discuss the quantum hardware implementation. 
Monday, March 2, 2020 9:36AM  9:48AM 
A09.00009: Computing partition functions in the one clean qubit model Anirban Narayan Chowdhury, Rolando Somma, Yigit Subasi In this talk we will present a method to approximate partition functions of quantum systems using mixedstate quantum computation. For nonnegative Hamiltonians, our method runs on average in time almost linear in (M/(ε_{rel}Z))^{2}, where M is the dimension of the quantum system, Z is the partition function, and ε_{rel} is the relative precision. It is based on approximations of the exponential operator as linear combinations of certain operations related to blockencoding of Hamiltonians or Hamiltonian evolutions. The trace of each operation is estimated using a standard algorithm in the one clean qubit model. For large values of Z, our method may run faster than exact classical methods, whose complexities are polynomial in M. Using this method we will demonstrate that a version of the partition function estimation problem within additive error is complete for the socalled DQC1 complexity class, suggesting that our method provides an exponential speedup. 
Monday, March 2, 2020 9:48AM  10:00AM 
A09.00010: Reaction dynamics on a quantum computer Andrew Tranter, Peter Love

Monday, March 2, 2020 10:00AM  10:12AM 
A09.00011: A sizeextensive scheme for variational quantum ansatzes without Trotter approximation Yaroslav Herasymenko, Thomas O'Brien One of the most promising applications for quantum computers is simulating the lowenergy states of complex quantum systems. In the nearterm, this can be done with variational ansatzes. Such ansatzes should follow physical principles to ensure high performance, one of the key principles being sizeextensivity. Unfortunately, digitizing such ansatzes into standard operations generally requires the use of the inexact Trotter expansion, which constrains the expected accuracy of the ansatz. 
Monday, March 2, 2020 10:12AM  10:24AM 
A09.00012: Finding the ground state of the Hubbard model by variational methods on a quantum computer with gate errors JanMichael Reiner, Frank Wilhelm, Gerd Schön, Michael Marthaler A key goal of digital quantum computing is the simulation of fermionic systems such as molecules or the Hubbard model. Unfortunately, for present and nearfuture quantum computers the use of quantum error correction schemes is still out of reach. Hence, the finite error rate limits the use of quantum computers to algorithms with a low number of gates. The variational Hamiltonian ansatz (VHA) has been shown to produce the ground state in good approximation in a manageable number of steps. Here we study explicitly the effect of gate errors on its performance. The VHA is inspired by the adiabatic quantum evolution under the influence of a timedependent Hamiltonian, where the  ideally short  fixed Trotter time steps are replaced by variational parameters. The method profits substantially from quantum variational error suppression, e.g., unitary quasistatic errors are mitigated within the algorithm. We test the performance of the VHA when applied to the Hubbard model in the presence of unitary control errors on quantum computers with realistic gate fidelities. 
Monday, March 2, 2020 10:24AM  10:36AM 
A09.00013: Quantum algorithm for spectral projection by measuring an ancilla iteratively TzuChieh Wei, Yanzhu Chen We propose a quantum algorithm for projecting a quantum system to eigenstates of any Hermitian operator, provided one can access the associated controlunitary evolution for the ancilla and the system. The procedure is iterative by preparing a fresh ancilla state, applying the controlled unitary, and then measuring the ancilla. There are some freedoms in the ancilla state parameter and the control unitary. We give examples to illustrate that the alogrithm works. Simulations of the procedure also show that the distribution of the projected eigenstates obeys the Born rule. This algorithm can be used as a subroutine in the quantum annealing procedure by measurement to drive the system to the ground state, and we also simulate this for a quantum spin chain. 
Monday, March 2, 2020 10:36AM  10:48AM 
A09.00014: Quantum Simulation of Quantum Z2 Gauge Theory demonstrated in a GPU Simulator Yu Shi We outline a quantum simulation scheme of quantum Z2 gauge theory using quantum adiabatic algorithm implemented in terms of quantum circuit, and then demonstrate it in the classical simulator QuEST using a CUDA enabled GPU server. In particular, we obtained useful results in (3+1)dimensional and (2+1)dimensional theories. It is identified that the quantum phase transition is topological in both dimensions, and is firstorder in (3+1) dimensions but secondorder in (2+1) dimensions. Highperformance classical simulation of quantum simulation, which may be dubbed pseudoquantum simulation, is not only a platform of developing quantum software, but also represents a new practical mode of computation. 
Monday, March 2, 2020 10:48AM  11:00AM 
A09.00015: Term Grouping Techniques for VQE and Quantum Dynamics Circuits Kaiwen Gui, Pranav Gokhale, Teague Tomesh, Yongshan Ding, Olivia Angiuli, Martin Suchara, Margaret Martonosi, Fred Chong Digital quantum simulations are among the most promising nearterm applications of quantum computation. Variational Quantum Eigensolver and time evolution of quantum dynamics are two examples of such algorithms. However, the amount of required quantum resources typically do not scale favorably as the desired accuracy of the calculations increases. Both VQE and quantum dynamics circuits are represented by tensor products of Pauli matrices that are obtained from the second quantization form using transformation methods such as JordanWigner or BravyiKitaev. We demonstrate various grouping techniques that optimize the order of these tensor products, with the goal of optimizing the total quantum resource cost. For VQE circuits, we minimize the number of required measurement operations. For quantum dynamics circuits, we minimize the circuit depth and maximize its fidelity. 
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