Bulletin of the American Physical Society
APS March Meeting 2019
Volume 64, Number 2
Monday–Friday, March 4–8, 2019; Boston, Massachusetts
Session K42: Applications of Noisy Intermediate Scale Quantum Computers IVFocus

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Sponsoring Units: DQI Chair: Peter Johnson Room: BCEC 210A 
Wednesday, March 6, 2019 8:00AM  8:12AM 
K42.00001: Tensorial tools for quantum computing Yannick Meurice Tensorial methods have been playing an increasingly important role in the context of spin models and lattice gauge theory. In most examples, the variables of integration are compact and character expansion (for instance Fourier analysis for U(1) models) can be used to rewrite the partition function and average observables as discrete sums of contracted tensors. This reformulations have been used for RG coarsegraining but they are also very useful for quantum computing. Their buildin Trotter procedure allows us to write quantum circuit or propose analog simulations. We discuss recent applications and FAQs about the tensor reformulations such as boundary conditions, Grassmann variables, Ward identities, effects of truncations and gauge invariance. 
Wednesday, March 6, 2019 8:12AM  8:24AM 
K42.00002: How many qubits are needed for quantum computational supremacy? Alexander Dalzell, Aram Harrow, Dax Enshan Koh, Rolando La Placa Quantum computational supremacy arguments, which describe a way for a quantum computer to perform a task that cannot also be done by a classical computer, typically require a computational assumption related to the limitations of classical computation. One common assumption is that the polynomial hierarchy (PH) does not collapse, a stronger version of the statement that P =/= NP, which leads to the conclusion that any classical simulation of certain families of quantum circuits requires time scaling worse than any polynomial in the size of the circuits. However, the asymptotic nature of this conclusion prevents us from calculating exactly how many qubits these quantum circuits must have for their classical simulation to be intractable on modern supercomputers. We refine these quantum computational supremacy arguments and perform such a calculation by imposing finegrained versions of the noncollapse assumption. Based on these conjectures we conclude that IQP circuits with 180 qubits, QAOA circuits with 360 qubits and boson sampling circuits (i.e. linear optical networks) with 90 photons are large enough for producing samples from their output distributions to be intractable on current technology. 
Wednesday, March 6, 2019 8:24AM  8:36AM 
K42.00003: Verifying quantum supremacy by doubling the circuit depth Animesh Datta, Samuele Ferracin, Theodoros Kapourniotis Any fruitful use of the noisy intermediatescale quantum computing devices being developed relies crucially on our ability to verify the correctness of their outputs. This verification must be achievable within these noisy intermediatescale devices. We present a verification protocol in the circuit model where the “desired” computation is verified running several independent “trap” computations, each of which requires (i) no more qubits than the desired computation and (ii) a circuitdepth twice that of the desired computation. Our protocol exploits the fact that single qubit gates are often the best components in noisy intermediatescale quantum devices. We begin with the assumption that only the singlequbit gates are prefect, and then extend our protocol to account for all operations in intermediatescale quantum computing devices being noisy. Our protocol applies to sampling problems that underlie quantum supremacy. In particular we provide a verification scheme, with a doubling of the circuit depth, to bound the variation distance between ideal and noisy probability distributions resulting from random circuit sampling  a candidate for quantum supremacy. 
Wednesday, March 6, 2019 8:36AM  8:48AM 
K42.00004: Variational Quantum Factoring Eric Anschuetz, Jonathan Olson, Alan AspuruGuzik, Yudong Cao Integer factorization has been one of the cornerstone applications of the field of quantum com puting since the discovery of an efficient algorithm for factoring by Peter Shor. Unfortunately, factoring via Shor’s algorithm is well beyond the capabilities of today’s noisy intermediatescale quantum (NISQ) devices. In this work, we revisit the problem of factoring, developing an alternative to Shor’s algorithm, which employs established techniques to map the factoring problem to the ground state of an Ising Hamiltonian. The proposed variational quantum factoring (VQF) algorithm starts by simplifying equations over Boolean variables in a preprocessing step to reduce the number of qubits needed for the Hamiltonian. Then, it seeks an approximate ground state of the resulting Ising Hamiltonian by training variational circuits using the quantum approximate optimization algorithm (QAOA). We benchmark the VQF algorithm on various instances of factoring and present numerical results on its performance. 
Wednesday, March 6, 2019 8:48AM  9:00AM 
K42.00005: Variational quantum eigensolver of interacting bosons with NISQ devices Andy C. Y. Li, Alexandru Macridin, Panagiotis Spentzouris Interacting boson systems are of broad interest in different fields of physics. Their simulation on classical computers is in general very challenging. The recent advances in variationalquantumeigensolver (VQE) algorithms offer new scalable ways to investigate these systems with noisy intermediate scale quantum (NISQ) devices. In this work, we present a proofofprinciple experiment of a boson VQE algorithm implemented on Rigetti's 8Qdevice. Our experiment determines the lowenergy eigenspectrum of the Rabi model  a simple boson model with interactions mediated by an atom. Our results illustrate that scalable quantum simulations of interacting boson systems using NISQ devices have a promising future. 
Wednesday, March 6, 2019 9:00AM  9:12AM 
K42.00006: A Quantum Algorithm for SymmetryExploitation in Exact Diagonalization of Quantum ManyBody Systems Albert Schmitz, Sonika Johri Grover’s search algorithm can be extended to a minimization procedure on a quantum computer. Here, we find a new application for this procedure – the symmetrybased size reduction of matrices corresponding to quantum manybody Hamiltonians before they are diagonalized. This is currently a memory/computational bottleneck on classical computers. In this case, the minimization problem cannot tolerate an approximate minimum ruling out variational quantum algorithms, and adiabatic minimization is unsuitable since there is no notion of a finite energy gap protecting the ground state during the evolution from the starting to the final state. Instead, Grover’s minimization procedure provides a reliable means to obtain a quadratic speedup over classical algorithms. We discuss both the theory and full circuit implementation of Grover minimization as applied to this problem. We find that the oracle for this problem only scales as polylog in the size of the search space, in contrast to many oracles in proposed applications for Grover’s algorithm which scale polynomially. Further, we design an error mitigation scheme that significantly reduces the effects of noise on the computation, making it a plausible candidate for the Noisy Intermediate Scale Quantum era. 
Wednesday, March 6, 2019 9:12AM  9:24AM 
K42.00007: Variational Quantum Optics Agustín Di Paolo, Panagiotis Barkoutsos, Ivano Tavernelli, Alexandre Blais Quantum processors of intermediate scale have been used to simulate quantum chemistry by means of the variational quantum algorithm (VQA). VQAs has been shown to be robust against noise and can handle limited connectivity by using hardwareefficient statepreparation protocols. This makes VQAs a promising tool for nearterm application of quantum coprocessors in the hybrid quantumclassical computation paradigm. In this talk, we extend the applicability of variational quantum algorithms to bosonic Hamiltonians with applications to quantum optics. 
Wednesday, March 6, 2019 9:24AM  9:36AM 
K42.00008: Study networkrelated optimization problems using quantum alternating optimization ansatz Zhihui Wang, Mustafa Adnane, Eleanor Rieffel, Bryan O'Gorman, Stuart Hadfield, Riccardo Mengoni, Davide Venturelli Networkrelated connectivity optimization problems are underlying a wide range of applications and are of high computational complexity. We consider studying network optimization problems using quantum heuristics. In particular, we consider Quantum Alternating Operator Ansatz, an extension of the Quantum Approximate Optimization Algorithms, in which a costfunction based unitary and a noncommuting mixing unitary are applied alternately. We present mappings for a few network optimization problems, including variants of finding the optimal spanningtree or spanninggraph of a graph. We give special focus on the design of mixers based on the constraints in the problem such that the system evolution remains in a subspace of the full Hilbert space where all constraints are satisfied. In the spanningtree problem, one such constraint is that a mixer applied to a spanning tree needs also be a spanning tree. This involves checking the connectivity of a subgraph, which is a global condition common for most networkrelated problems. We show how this feature can be efficiently represented in the mixer in a quantum coherent way, based on manipulation of a descendantmatrix and an adjacent matrix. We further develop a mixer for the spanninggraphs based on the spanningtree mixer. 
Wednesday, March 6, 2019 9:36AM  9:48AM 
K42.00009: Adiabatic Quantum Chemistry Simulations with Superconducting Qubits Nikolaj Moll, Gian Salis, Marc Ganzhorn, Daniel Egger, Stefan Filipp, Marco Roth, Sebastian Schmidt The simulation of a quantum system with a classical computer without any approximations is intractable even for moderate systems sizes. It has been recognized early that using a controllable quantum system as a simulator could solve this for increasing system sizes. We propose a scalable quantum simulator based on driven superconducting qubits where the interactions are generated parametrically by polychromatic magnetic flux modulation of a tunable bus element. In this system, the XX and YYtype interactions as well as transverse fields are independently tunable over a large parameter range. We experimentally demonstrate an adiabatic simulation using two superconducting qubits and one tunable bus element. The time required to reach the ground state of the Hamiltonian lies in the few microseconds range and therefore is well within the capability of currently available superconducting circuits. 
Wednesday, March 6, 2019 9:48AM  10:24AM 
K42.00010: Faster classical sampling from distributions defined by quantum circuits Invited Speaker: Igor Markov As quantum computers become more capable, the question of when they surpass stateoftheart classical computation for a welldefined computational task is attracting much attention. The leading candidate task for this milestone entails sampling from the output distribution defined by a random quantum circuit. We develop algorithms and software for massivelyparallel simulation. In particular, we propose two new ways to trade circuit fidelity for computational speedups, so as to match the fidelity of a given quantum computer  a task previously thought impossible. We report massive speedups for the sampling task over prior software from Microsoft, IBM, Alibaba and Google, as well as supercomputer and GPUbased simulations. By using publicly available Google Cloud Computing, we price such simulations and enable comparisons by total cost across hardware platforms. We simulate approximate sampling from the output of a circuit with 7x8 qubits and depth 1+40+1 by producing one million bitstring probabilities with fidelity 0.5%, at an estimated cost of $35184. Simulating circuits of depth to 1+48+1 would cost one million dollars. 
Wednesday, March 6, 2019 10:24AM  10:36AM 
K42.00011: Subspacesearch variational quantum eigensolver for excited states Ken M Nakanishi, Kosuke Mitarai, Keisuke Fujii The variational quantum eigensolver (VQE), a variational algorithm to obtain an approximated ground state of a given Hamiltonian, is an appealing application of nearterm quantum computers. To extend the framework to excited states, we here propose an algorithm, the subspacesearch variational quantum eigensolver (SSVQE). This algorithm searches a low energy subspace by supplying orthogonal input states to the variational ansatz and relies on the unitarity of transformations to ensure the orthogonality of output states. The kth excited state is obtained as the highest energy state in the low energy subspace. The proposed algorithm does not employ any ancilla qubits. The disuse of the ancilla qubits in our algorithm is a great improvement from the existing proposals for excited states, which have utilized the swap test, making our proposal a truly nearterm quantum algorithm. We further generalize the SSVQE to obtain all excited states up to the kth by only single optimization procedure. From numerical simulations, we verify the proposed algorithms. This work greatly extends the applicable domain of the VQE to excited states and their related properties like a transition amplitude without sacrificing any feasibility of it. 
Wednesday, March 6, 2019 10:36AM  10:48AM 
K42.00012: Holistic Error Mitigation Frameworks For NearTerm Computations Eugen Dumitrescu, Raphael Pooser, Alexander McCaskey, Titus Morris, Pavel Lougovski It is necessary to mitigate physical errors in order for NISQ computations to compute quantities with reasonable accuracy. Therefore NISQ programming stacks must include a robust error mitigation infrastructure supplementing principal quantum programs at compile time and operating at a high level of abstraction. We introduce an error mitigation framework consisting of routines built into a software stack aiming to return corrected data from programs run on NISQ devices. As a demonstration, we implement a variety of protocols which increase the accuracy of variational quantum eigensolverstyle hybrid algorithms running on multiple NISQ devices. 
Wednesday, March 6, 2019 10:48AM  11:00AM 
K42.00013: Quantum Kitchen Sinks: An algorithm for machine learning on nearterm quantum computers Christopher Wilson, Johannes Otterbach, Nikolas Tezak, Robert S Smith, Peter Karalekas, Anthony Polloreno, Sohaib Alam, Gavin Crooks, Marcus Da Silva Noisy intermediatescale quantum (NISQ) computing devices are an exciting platform for the exploration of the power of nearterm quantum applications. We describe a nearterm quantum application for machine learning tasks by building upon the classical algorithm known as random kitchen sinks. Our technique, called quantum kitchen sinks, uses quantum circuits to nonlinearly transform classical inputs into features that can then be used in a number of machine learning algorithms. We demonstrate the power and flexibility of this proposal by using it to solve binary classification problems for synthetic datasets as well as handwritten digits from the MNIST database. Simulations show, in particular, that small quantum circuits provide significant performance lift over standard linear classical algorithms, reducing classification error rates from 50% to <0.1%, and from 4.1% to 1.4% in these two examples, respectively. We show comparable performance for these examples in experiments with superconducting qubits. 
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