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 X34: Quantum Computing Algorithms VLive
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Sponsoring Units: DQI Chair: Stuart Hadfield, NASA Ames Research Center |
Friday, March 19, 2021 8:00AM - 8:12AM Live |
X34.00001: Near-Optimal Ground State Preparation Yu Tong, Lin Lin Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We assume that an initial state with non-trivial overlap with the ground state can be efficiently prepared. With this assumption we propose a hybrid quantum-classical algorithm to estimate the ground energy, where the dependence of the number of queries to the initial state on the desired precision is exponentially improved compared to current state-of-the-art algorithms. When further assuming the existence of a spectral gap, we design an algorithm that prepares the ground state, whose runtime has a logarithmic dependence on the inverse error. We also prove that our algorithms reach the complexity lower bounds by applying it to the unstructured search problem and the quantum approximate counting problem. |
Friday, March 19, 2021 8:12AM - 8:24AM Live |
X34.00002: Measurement-based algorithms for quantum simulation of many-body fermionic systems Woo-Ram Lee, Zhangjie Qin, Robert Raussendorf, Eran Sela, Vito W Scarola Measurement-based quantum computation (MBQC) is a model of universal quantum computation driven by local measurements on an initial entangled resource state. MBQC is potentially advantageous over a conventional circuit-based algorithm when an entangled qubit state is accurately prepared and efficient single-qubit measurements are available. Along these lines, the application of MBQC to quantum simulation of physical systems is highly desirable but has yet to be explored in depth. In this talk, I will discuss the implementation of mappings between spins and many-body fermionic systems in the context of MBQC. I will also discuss development of MBQC algorithms capturing the time evolution of certain fermionic Hamiltonians. We will propose a design for single-qubit measurement patterns that implement MBQC quantum simulation algorithms while taking into account computational efficiency. |
Friday, March 19, 2021 8:24AM - 8:36AM Live |
X34.00003: Variational Hamiltonian Diagonalization for Dynamical Quantum Simulation Benjamin Commeau, Marco Cerezo, Zoe Holmes, Lukasz Cincio, Patrick Coles, Andrew Sornborger Dynamical quantum simulation may be one of the first applications to see quantum advantage. However, the circuit depth of standard Trotterization methods can rapidly exceed the coherence time of noisy quantum computers. In this work, we aim to make variational dynamical simulation practical and near-term. We propose an algorithm called Variational Hamiltonian Diagonalization (VHD), which approximately transforms a given Hamiltonian into a diagonal form that can be easily exponentiated. VHD allows for fast forwarding, i.e., simulation beyond the coherence time with a fixed-depth quantum circuit. It removes Trotterization error and allows simulation of the entire Hilbert space. We prove an operational meaning for the VHD cost function in terms of the average simulation fidelity. Moreover, we prove that the VHD cost function does not exhibit a barren plateau. Our proof relies on locality of the Hamiltonian, and hence we connect locality to trainability. Our numerical simulations verify that VHD can be used for fast-forwarding dynamics. https://arxiv.org/abs/2009.02559 |
Friday, March 19, 2021 8:36AM - 8:48AM Live |
X34.00004: Quantum-Classical Simulation of Dynamical Mean-Field Theory Using Coupled-Cluster Methods Trevor Keen, Bo Peng, Karol Kowalski, Pavel Lougovski, Steven S. Johnston We propose a new method of calculating Green’s functions on a quantum computer in the time domain for condensed matter applications using coupled cluster methods. This approach removes the quantum complexity of state preparation and eliminates the need to make any assumptions about the ground state of the system. As a test case, and to assess the scalability of the method, we applied our approach to the single-impurity Anderson model (SIAM) employed in dynamical mean-field theory. As a specific example, we present results for running the procedure for a two-site SIAM on a quantum simulator. |
Friday, March 19, 2021 8:48AM - 9:00AM Live |
X34.00005: Coherent Protocols for Distinguishing Noisy Quantum Channels Jeffery Yu, Zane Rossi, Sho Sugiura, Isaac Chuang A simple instance of quantum hypothesis testing involves identifying from which of two distributions a single-qubit rotation is drawn. As a twist on this well-known problem, suppose multiple rotations can be cascaded together coherently, rather than requiring that the result of each rotation be measured independently. Assuming independent measurements, an optimal strategy is entirely defined by the Helstrom bound for distinguishing states. Given the possible coherent protocol, what is the optimal error-minimizing procedure for solving this inference problem? Distinguishing channels as opposed to states offers opportunities for coherent protocols to improve over independent measurements. We show that if the coherent protocol is used, then for narrow distributions the number of queries required to achieve a particular inference confidence is reduced compared to simple Helstrom measurements. The constructive protocol employs quantum signal processing, performing polynomial transforms on the underlying distributions in a way that applies flexibly to many channel inference scenarios. This work expands the concept of quantum advantage to the statistical inference problem of quantum channel property testing. |
Friday, March 19, 2021 9:00AM - 9:12AM Live |
X34.00006: Quantum optimal control on many-body states in a Jaynes-Cummings lattice Prabin Parajuli, Lin Tian The quantum optimal control technique is a powerful tool for efficiently implementing high-fidelity quantum operations and generating desirable quantum states. Here we use this technique to study the robust generation of quantum many-body states in a Jaynes Cummings (JC) lattice near quantum critical regions. The chopped random basis (CRAB) algorithm is employed to optimize the time dependence of the light-matter coupling constant and the photon hopping rate of the JC lattice, where these parameters are expanded into a Fourier basis with optimizable Fourier coefficients and frequencies. Our numerical simulation demonstrates that this approach can significantly improve the fidelity of the prepared many-body ground states in comparison with the adiabatic evolution approach. We also analyze the energy gap along the optimized evolution trajectory and the lower bound of the evolution time in relation to the quantum speed limit. |
Friday, March 19, 2021 9:12AM - 9:24AM Live |
X34.00007: Robust Preparation of Many-body Ground States in Jaynes-Cummings Lattices Kang Cai, Prabin Parajuli, Guilu Long, Chee Wei Wong, Lin Tian Strongly-correlated polaritons in Jaynes-Cummings (JC) lattices can exhibit quantum phase transitions between the Mott-insulating and the superfluid phases at integer fillings. However, it is often challenging to prepare such many-body states with high accuracy. Here we present an approach for the robust preparation of many-body ground states in a finite-sized JC lattice. Using the ground states in the deep Mott-insulating or deep superfluid regimes as initial state, which can be generated accurately via engineered pulse sequences, and employing optimized nonlinear ramping, we demonstrate that many-body ground states in the intermediate regimes of a JC lattice can also be generated with high fidelity. For each given ramping trajectory, we derive an optimal ramping index with a Landau-Zener-type of estimation on finite-sized systems. Our numerical simulation shows that with the optimal ramping index on an appropriate trajectory, the fidelity of the generated states can remain close to unity in almost the entire parameter space. This method is general and can be applied to many other systems. |
Friday, March 19, 2021 9:24AM - 9:36AM Live |
X34.00008: Bayesian inference with engineered likelihood functions for robust amplitude estimation Guoming Wang, Dax Enshan Koh, Peter D. Johnson, Yudong Cao The number of measurements demanded by hybrid quantum-classical algorithms is prohibitively high for many problems of practical value. Quantum algorithms that reduce this cost (e.g. quantum amplitude and phase estimation) require error rates that are too low for near-term implementation. Here we propose methods that take advantage of the available quantum coherence to maximally enhance the power of sampling on noisy quantum devices, reducing measurement number and runtime compared to VQE. Our scheme derives inspiration from quantum metrology, phase estimation, and the "alpha-VQE" proposal, arriving at a general formulation that is robust to error and does not need ancilla qubits. The central object of this method is what we call the "engineered likelihood function" (ELF), used for carrying out Bayesian inference. In this talk we show how the ELF formalism enhances the information gain rate in sampling as the physical hardware transitions from the regime of noisy intermediate-scale quantum computers into that of quantum error corrected ones. This technique speeds up a central component of many quantum algorithms, with applications including chemistry, materials, finance, and beyond. Similar to VQE, we expect small-scale implementations to be realizable on today's quantum devices. |
Friday, March 19, 2021 9:36AM - 9:48AM Live |
X34.00009: Constant Depth Exact Time Evolution of Spin Systems based on Cartan Decomposition Efekan Kökcü, Thomas Steckman, James Freericks, Eugen Dumitrescu, Alexander F Kemper Spin models are ubiquitous in physics, arising directly in materials physics, or as representatives of electronic systems. Simulating spin systems via classical computers is not effective for large systems, which makes Hamiltonian simulation by quantum computers a promising option due to its success on executing certain algorithms exponentially faster than classical computers. However current generation quantum computers have excessive noise due to gate implementation and loss of coherence; thus avoiding additional error from approximations such as Trotter is ideal. Here we present an algorithm that enables exact time evolution for ordered and disordered spin models for a given time t with a fixed depth circuit. The algorithm is based on Cartan Decomposition of the algebra generated by the Hamiltonian. Although in general the circuit depth scales exponentially with the number of qubits, for a certain class models of interest to the community — e.g. XY model, transverse field Ising model, and the Kitaev spin chain — the circuit depth scales polynomially. |
Friday, March 19, 2021 9:48AM - 10:00AM Live |
X34.00010: Digital Heater: Engineering Thermal Distributions on Quantum Computers Mekena Metcalf, Emma Stone, Katherine Klymko, Alexander F Kemper, Mohan Sarovar, Wibe A De Jong Dynamically generating thermal states of quantum systems is difficult, and requires modeling a macroscopic environment or obtaining detailed knowledge of the system energy spectra. Modeling the macroscopic environment on a quantum simulator may be achieved by coupling ancillary qubits such that each of the transitions in the system spectrum is covered. This approach requires an exponential number of ancillary degrees of freedom which is impractical. We develop a quantum algorithm that uses spectral combing with ancillary qubits that are on average in a thermal state. Our algorithm simulates a large bath while only requiring linear complexity by periodically modulating the ancilla energy over a time period. We evaluate the algorithm by determining error in magnetization of the finite-temperature transverse Ising model. |
Friday, March 19, 2021 10:00AM - 10:12AM Live |
X34.00011: Computing Free Energy with Fluctuation Relations on Quantum Computers Lindsay Bassman, Katherine Klymko, Norm Tubman, Wibe A De Jong One of the most promising applications for quantum computers is the dynamic simulation of quantum materials. Current hardware, however, sets stringent limitations on how long such simulations can run before decoherence begins to corrupt results. The Jarzynski equality, a fluctuation theorem that allows for the computation of equilibrium free energy differences from a set of short, non-equilibrium dynamics simulations, can make use of such short-time simulations on quantum computers. Here, we present a quantum algorithm based on the Jarzynski equality for computing free energies of quantum materials. We demonstrate our algorithm using the transverse field Ising model on both a quantum simulator and real quantum hardware. As the free energy is a central thermodynamic property that allows one to compute virtually any equilibrium property of a physical system, the ability to perform this algorithm for larger quantum systems in the future has implications for a wide range of applications including construction of phase diagrams, prediction of transport properties, and computer-aided drug design. |
Friday, March 19, 2021 10:12AM - 10:24AM Live |
X34.00012: Resource Estimate for Quantum Many-Body Ground State Preparation on a Quantum Computer Jessica Lemieux, Guillaume Duclos-Cianci, David Senechal, David Poulin Quantum devices promise efficient simulation of quantum many-body systems. Of particular interest are properties at low temperature where, to a good approximation, the system is in its ground state. Thus, a quantum simulation requires a quantum circuit that maps a fiducial state to the ground state of interest. This problem is generally QMA-complete, so the existence of a general-purpose efficient procedure is believed to be impossible. Nonetheless, heuristic methods could be sufficiently fast for intermediate-size problems. |
Friday, March 19, 2021 10:24AM - 10:36AM Live |
X34.00013: Two Approaches to Quantum Simulation of Classical Dynamics Ilon Joseph, Alessandro Castelli, Vasily Geyko, Frank R Graziani, Stephen Bernard Libby, Max Porter, Yaniv J Rosen, Yuan Shi, Jonathan L DuBois There are two approaches to quantum simulation of nonlinear classical dynamics: (i) quantize the classical Hamiltonian and (ii) use the Koopman-von Neumann approach to reformulate the conservation of probability, the Liouville equation, as an equivalent Schrodinger equation with a unitary evolution operator. The latter approach tracks the exact evolution of probability on phase space but requires simulating a system of twice the dimensionality. The former approach tracks the dynamics of the classical probability distribution until the Heisenberg time, at which point the quantum dynamics departs from that of the classical system. Simulating dissipative processes can be accomplished by embedding the N-dimensional system within a larger Hilbert space of size N2, which is similar in cost to doubling the phase space dimension. For either approach, using a quantum computer to simulate these systems is exponentially more efficient than simulating the Eulerian discretization of the Liouville equation when the Hamiltonian is sparse. Using quantum walks to generate desired initial conditions and using amplitude estimation to measure observables is up to quadratically more efficient than time-dependent Monte Carlo techniques. |
Friday, March 19, 2021 10:36AM - 10:48AM Live |
X34.00014: Quantum Divide and Compute and its Application zain Saleem We introduce a "Quantum Divide and Compute" technique that allows dividing a quantum circuit in smaller sub circuits that can run on devices with a limited number of qubits. The naïve Quantum Divide and Compute algorithm does not ensure that recombined output distribution is well defined as a probability distribution. We introduce Maximum Likelihood Fragment Tomography (MLFT) to ensure that all reconstructed probability distributions are strictly non-negative and normalized. We also provide numerical evidence and theoretical arguments that circuit cutting can estimate the output of a clustered circuit with a higher fidelity than full circuit execution for certain types of circuits. We illustrate the application of these techniques on quantum approximate optimization circuits. |
Friday, March 19, 2021 10:48AM - 11:00AM Live |
X34.00015: State-to-state fermionic mapping to quantum processors using a combinatoric representation Mekena Metcalf, Diana Chamaki, Nathan Wiebe, Ojas D Parehk, Wibe A De Jong Emulating chemical and material systems with quantum computers is a tractable path for obtaining low energy observables for systems that are strongly correlated or require accurate treatment of large active spaces. Current techniques for mapping fermions to spin-1/2 systems center around mapping orbital operators to spin operators. In this representation, despite current techniques to remove qubits using symmetries, the size of the Hilbert space accessed on the quantum processor includes irrelevant states for the properties a quantum computationalist may be interested in. By considering the many-body fermion problem with a combinatoric representation, we demonstrate how fermionic states can be bijectively mapped to a compressed quantum Hilbert space with an analytic function. Our technique yields a significant reduction in the number of qubits required to represent the Hamiltonian subspace. We develop algorithms for near-term and fault-tolerant devices while demonstrating the effectiveness of our technique by implementing the Variational Quantum Eigensolver for molecular Hamiltonians on a compressed basis. |
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