Bulletin of the American Physical Society
APS March Meeting 2020
Volume 65, Number 1
Monday–Friday, March 2–6, 2020; Denver, Colorado
Session F07: NISQ: Variational Quantum Eigensolvers |
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Sponsoring Units: DQI Chair: Sarah Sheldon, IBM Thomas J. Watson Research Center Room: 102 |
Tuesday, March 3, 2020 8:00AM - 8:12AM |
F07.00001: Variational Quantum Fidelity Estimation Marco Cerezo de la Roca, Alexander Poremba, Lukasz Cincio, Patrick Coles We present an efficient, near-term algorithm for estimating the well-known fidelity, which quantifies the closeness of quantum states. Our algorithm is an important tool for verifying and characterizing states on a quantum computer. This work is timely given the industrial rise of quantum computing. Prior to our work, there was no efficient algorithm to estimate the fidelity that could be refined to arbitrary tightness. We solve this outstanding problem by introducing novel bounds on the fidelity that can be estimated with hybrid quantum-classical computation. We show that our approach can detect quantum phase transitions and cannot be classical simulated efficiently. |
Tuesday, March 3, 2020 8:12AM - 8:24AM |
F07.00002: Variational Quantum Algorithm for Markovian Open Quantum Systems Nobuyuki Yoshioka, Yuya O. Nakagawa, Kosuke Mitarai, Keisuke Fujii We propose a quantum-classical hybrid variational algorithm to simulate the non-equilibrium stationary states of Markovian open quantum systems, named the dissipative-system Variational Quantum Eigensolver (dVQE) [1]. In order to employ the variational optimization technique for a unitary quantum circuit, we first map a density matrix into a wavefunction with the doubled number of qubits, and then design the unitary quantum circuit so that the physical requirements for a mixed state are fulfilled. This allows us to define a cost function that consists of the time evolution generator of the Markovian quantum master equation. After the optimization, physical observables are evaluated by a quantum circuit with the original number of qubits. Our dVQE scheme is demonstrated by both numerical simulation on a classical computer and actual quantum simulation that makes use of the device provided in Rigetti Quantum Cloud Service. |
Tuesday, March 3, 2020 8:24AM - 8:36AM |
F07.00003: Variational Generation of Thermofield Double States and Critical Ground States with a Quantum Computer Anne Matsuura, Sonika Johri, Daiwei Zhu, Norbert M Linke, kevin landsman, Nhung Nguyen, Cinthia Alderete, Timothy Hsieh, Christopher Roy Monroe Finite-temperature phases of many-body quantum systems are fundamental to phenomena ranging from condensed-matter physics to cosmology, yet they are generally difficult to simulate. Using an ion trap quantum computer and protocols motivated by the Quantum Approximate Optimization Algorithm (QAOA), we generate nontrivial thermal quantum states of the transversefield Ising model (TFIM) by preparing thermofield double states at a variety of temperatures. We also prepare the critical state of the TFIM at zero temperature using quantum-classical hybrid optimization. The entanglement structure of thermofield double and critical states plays a key role in the study of black holes, and our work simulates such nontrivial structures on a quantum computer. Moreover, we find that the variational quantum circuits exhibit noise thresholds above which the lowest depth QAOA circuits provide the best results. |
Tuesday, March 3, 2020 8:36AM - 8:48AM |
F07.00004: Exactly-solvable models as benchmarks for VQE Ken Robbins, Peter Love Perhaps the most promising application of Noisy Intermediate Scale Quantum (NISQ) computers is the Variational Quantum Eigensolver (VQE). Due to their namesake noise, NISQ computers performing VQE will need benchmarks to interpret their results. Exactly solvable models such as the Lipkin-Meshkov-Glick (LMG) model, a simple nuclear model of N fermions, can provide such benchmarks. We give circuits that produce low-N LMG eigenstates on a quantum computer with gate and qubit costs suited to the NISQ era. Further, we discuss how we might generalize the circuits for simulations of a higher number of particles. |
Tuesday, March 3, 2020 8:48AM - 9:00AM |
F07.00005: Variational Quantum Linear Solver: A Hybrid Algorithm for Linear Systems Carlos Bravo-Prieto, Ryan M LaRose, Marco Cerezo, Yigit Subasi, Lukasz Cincio, Patrick Coles Solving linear systems of equations is central to many engineering and scientific fields. Several quantum algorithms have been proposed for linear systems, where the goal is to prepare |x> such that A|x> ∝ |b>. While these algorithms are promising, the time horizon for their implementation is long due to the required quantum circuit depth. In this work, we propose a variational hybrid quantum-classical algorithm for solving linear systems, with the aim of reducing the circuit depth and doing much of the computation classically. We propose a cost function based on the overlap between |b> and A|x>, and we derive an operational meaning for this cost in terms of the solution precision. We also introduce a quantum circuit to estimate this cost, while showing that this cost cannot be efficiently estimated classically. Using Rigetti’s quantum computer, we successfully implement our algorithm up to a problem size of 32 × 32. Furthermore, we numerically find that the complexity of our algorithm scales efficiently in both 1/ and κ, with κ the condition number of A. Our algorithm provides a heuristic for quantum linear systems that could make this application more near term. |
Tuesday, March 3, 2020 9:00AM - 9:12AM |
F07.00006: Variational Preparation of Quantum Hall States on a Lattice Eric Jones, Eliot Kapit Simulation of many-body quantum systems is one of the most promising applications of near-term quantum computers. The fractional quantum Hall states display fascinating many-body physics such as topological order and strong correlations and so are interesting candidates for quantum simulation experiments. We classically diagonalize for the low-energy spectrum of the Kapit-Mueller Hamiltonian for hardcore bosons on a lattice. The Laughlin state is an exact ground state of this long-range Hamiltonian for appropriate magnetic flux densities. In addition, we study the low-lying spectrum of a shorter-range proxy Hamiltonian and tune its hopping and interaction parameters in order to optimize the associated topological degeneracy and many-body gap. We then demonstrate a scheme for variational preparation of the Laughlin state on the lattice through a Trotterization of adiabatic state preparation with defect-pinned particles as the reference state. Such calculations suggest a way forward in the simulation of fractional quantum Hall states on quantum hardware. |
Tuesday, March 3, 2020 9:12AM - 9:24AM |
F07.00007: Variational quantum simulation of the Fermi-Hubbard model Alexandre Choquette, Agustin Di Paolo, Panagiotis Barkoutsos, David Senechal, Ivano Tavernelli, Alexandre Blais Noisy intermediate-scale quantum devices have the potential to be useful for quantum simulation of materials. A prominent approach for near-term quantum simulation is based on variational quantum algorithms (VQAs). In this talk, we propose a VQA to prepare the groundstate of the Fermi-Hubbard model. In particular, we investigate various state-preparation circuits and benchmark their performance in presence of realistic noise. We find that Hamiltonian-inspired variational forms perform better than a hardware-efficient approach. This work constitutes a first step towards the simulation of strongly correlated fermionic systems. |
Tuesday, March 3, 2020 9:24AM - 9:36AM |
F07.00008: A Non-Orthogonal Variational Quantum Eigensolver William Huggins, Joonho Lee, Unpil Baek, Bryan O'Gorman, Birgitta K Whaley We present an extension to the variational quantum eigensolver that approximates the ground state of a system by solving a generalized eigenvalue problem in a subspace spanned by a collection of parametrized quantum states. This allows for systematic improvement of a logical wavefunction ansatz without significant increase in circuit complexity. To minimize the circuit complexity, we propose a strategy for efficiently measuring the Hamiltonian and overlap matrix elements between states parametrized by circuits that commute with the total particle number operator. We propose a classical Monte Carlo scheme to estimate the uncertainty in the ground state energy caused by a finite number of measurements of matrix elements and to adaptively schedule the required measurements. We apply these ideas to two strongly correlated systems, a square configuration of H4 and the π-system of Hexatriene (C6H8). |
Tuesday, March 3, 2020 9:36AM - 9:48AM |
F07.00009: Barren Plateau Issues for Variational Quantum-Classical Algorithms Marco Cerezo, Akira Sone, Lukasz Cincio, Patrick Coles Variational quantum-classical algorithms (VQCAs) optimize the parameters of a quantum neural network, V, to minimize a cost function, C. Many researchers believe that VQCAs will enable the first practical applications of noisy quantum computers. However, VQCAs are heuristic methods with unproven scaling. Here, we rigorously prove two results related to the trainability of VQCAs. Our first result states that choosing C to be a global function of V leads to an exponentially vanishing gradient (i.e., a barren plateau) even when V is shallow. This implies that many VQCAs proposed in the literature must revise their proposed cost functions. Our second results states that, under the same conditions, choosing C to be a local function of V leads to a non-vanishing gradient, i.e., with the gradient vanishing no worse than polynomially. This suggests that VQCAs have the potential to be trainable, if one chooses an appropriate cost function. We support these analytical results with numerics for large problem sizes. |
Tuesday, March 3, 2020 9:48AM - 10:00AM |
F07.00010: Approaching scalable VQE of interacting bosons with NISQ devices Andy C. Y. Li, Alexandru Macridin, Panagiotis Spentzouris Scaling up variational quantum eigensolver (VQE) algorithms to practical applications utilizing quantum advantage with noisy intermediate-scale quantum (NISQ) devices is challenging. The expansive cost-function evaluation and demanding optimization quickly exhaust the precious quantum resource available on NISQ devices. In this work, we discuss the appropriate VQE strategy suitable for multi-site interacting boson systems, for example, the Holstein model and the Rabi lattice model. We investigate the cost-function setup and the optimization tactics to utilize the limited quantum resource efficiently. Our strategy illustrates that the scalable VQE algorithms of interacting bosons have a promising future. |
Tuesday, March 3, 2020 10:00AM - 10:12AM |
F07.00011: Efficient Variational Generation of Thermofield Double States on a Superconducting Quantum Processor: Theory (Part 1) Shavindra Premaratne, Sonika Johri, Xiang Chris Zou, Ramiro Sagastizabal, Michiel Adriaan Rol, Berend Klaver, Miguel Moreira, Carmina Almudever, Leonardo DiCarlo, Anne Matsuura Thermofield double (TFD) states are entangled pure states between two systems which yield a thermal state when one of the systems is traced out [1]. TFD state generation on larger qubit systems is relevant for studying the finite-temperature phase diagram of condensed matter systems. We implement a quantum-classical hybrid variational optimization algorithm to efficiently generate TFD states of the tranverse-field Ising chain. Unlike Variational Quantum Eigensolvers with a cost function that is known a priori, the success of our optimization hinges on choosing the best cost function which can generate the desired TFD state. Here, we discuss the benefits and drawbacks of various cost functions that can be used for the optimization, and show how our constructed cost function yields excellent agreement across the full temperature range. |
Tuesday, March 3, 2020 10:12AM - 10:24AM |
F07.00012: Efficient Variational Generation of Thermofield Double States on a Superconducting Quantum Processor: Experiment (Part 2) Ramiro Sagastizabal, Michiel Adriaan Rol, Berend Klaver, Miguel Moreira, Shavindra Premaratne, Sonika Johri, Xiang Chris Zou, Carmina Almudever, Anne Matsuura, Leonardo DiCarlo Recent progress on Near Intermediate Small Quantum devices has allowed the field of quantum simulation to experimentally investigate many interesting systems such as spin lattices, Fermi-Hubbard models and electronic orbitals of molecules. Most of this work focuses on preparing low-energy eigenstates of a known target Hamiltonian. Here, we experimentally investigate finite-temperature effects on a transverse-field Ising chain using four qubits of a seven-transmon quantum processor. Specifically, we variationally approximate thermofield double (TFD) states through minimization of the constructed cost function described in Part 1. We extract various correlation functions over a range of simulated temperatures, showing good agreement to those of an exact TFD. |
Tuesday, March 3, 2020 10:24AM - 10:36AM |
F07.00013: Efficient Symmetry-Preserving State Preparation Circuits for the Variational Quantum Eigensolver Algorithm Linghua Zhu, Bryan T. Gard, George S. Barron, Nicholas J. Mayhall, Sophia E. Economou, Edwin Barnes The variational quantum eigensolver (VQE) is one of the most promising approaches for performing chemistry simulations using noisy intermediate-scale quantum (NISQ) processors. The efficiency of this algorithm depends crucially on the ability to prepare multi-qubit trial states on the quantum processor that either include, or at least closely approximate, the actual energy eigenstates of the problem being simulated while avoiding states that have little overlap with them. Symmetries play a central role in determining the best trial states. Here, we present efficient state preparation circuits that respect particle number, total spin, spin projection, and time-reversal symmetries. These circuits contain the minimal number of variational parameters needed to fully span the appropriate symmetry subspace dictated by the chemistry problem while avoiding all irrelevant sectors of Hilbert space. We show how to construct these circuits for arbitrary numbers of orbitals, electrons, and spin quantum numbers, and we provide explicit decompositions and gate counts in terms of standard gate sets in each case. |
Tuesday, March 3, 2020 10:36AM - 10:48AM |
F07.00014: Noncontextuality as classicality in variational quantum eigensolvers William Kirby, Peter Love In this talk we show how to use contextuality, an indicator of non-classicality in quantum systems, to evaluate the variational quantum eigensolver (VQE), a promising tool for near-term quantum simulation. We present an efficiently computable test to determine whether or not the Hamiltonian in a VQE procedure is contextual. We then show that we may construct a simple, global unitary mapping that diagonalizes a noncontextual Hamiltonian. The diagonal Hamiltonian resulting from this mapping is efficiently classically calculable, which proves that the noncontextual Hamiltonian problem is NP-complete. We also give a quasi-quantized model for variational quantum eigensolvers whose Hamiltonians are noncontextual. This provides a second sense in which noncontextual Hamiltonians are essentially classical. These results support the notion of noncontextuality as classicality in quantum systems. |
Tuesday, March 3, 2020 10:48AM - 11:00AM |
F07.00015: Shot Frugal Optimization for Variational Quantum-Classical Hybrid Algorithms Andrew Arrasmith, Jonas M Kubler, Lukasz Cincio, Patrick J Coles Variational hybrid quantum-classical algorithms (VHQCAs) seem likely to be the first useful algorithms in the era of near-term quantum computing. There is however a justified concern that the number of measurements needed for these algorithms to converge might become prohibitive when scaling up to non-trivial problem sizes. We address this issue by adapting results from classical optimization to the problem of shot-frugal optimization of VHQCAs. Specifically, we present new techniques and compare them with standard methods to demonstrate the potential for improvement both with noiseless and noisy quantum devices. |
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