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 S34: Quantum Computing Algorithms IIILive
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Sponsoring Units: DQI Chair: Jhonathan Romero, Zapata Computing Inc |
Thursday, March 18, 2021 11:30AM - 11:42AM Live |
S34.00001: The Meta-Variational Quantum Eigensolver (Meta-VQE): Learning energy profiles of parameterized Hamiltonians for quantum simulation Alba Cervera-Lierta, Jakob S. Kottmann, Alan Aspuru-Guzik We present the meta-VQE, an algorithm capable to learn the ground state energy profile of a parametrized Hamiltonian. By training the meta-VQE with a few data points, it delivers an initial circuit parametrization that can be used to compute the ground state energy of any parametrization of the Hamiltonian within a certain trust region. We test this algorithm with an XXZ spin chain, an electronic H4 Hamiltonian and a single-transmon quantum simulation. In all cases, the meta-VQE is able to learn the shape of the energy functional and, in some cases, resulted in improved accuracy in comparison to individual VQE optimization. The meta-VQE algorithm introduces both a gain in efficiency for parametrized Hamiltonians, in terms of the number of optimizations, and a good starting point for the quantum circuit parameters for individual optimizations. The proposed algorithm can be readily mixed with other improvements in the field of variational algorithms to shorten the distance between the current state-of-the-art and applications with quantum advantage. |
Thursday, March 18, 2021 11:42AM - 11:54AM Live |
S34.00002: ctrl-VQE: Fast variational quantum eigensolver with gate-free state preparation Oinam Meitei, Bryan T Gard, George S Barron, David Pappas, Sophia Economou, Edwin Barnes, Nicholas J. Mayhall The variational quantum eigensolver (VQE) is currently the flagship algorithm for solving electronic structure problems on near-term quantum computers. The algorithm involves implementing a sequence of parameterized gates on quantum hardware to generate a target quantum state. Due to finite coherence times and frequent gate errors, the number of gates that can be implemented remains limited on current quantum devices, preventing accurate applications to systems with significant entanglement, such as strongly correlated molecules. In this work, we propose an alternative algorithm where the quantum circuit used for state preparation is removed entirely and replaced by a quantum control routine which variationally shapes a pulse to drive the initial Hartree-Fock state to the full CI target state. The objective function optimized is the expectation value of the qubit-mapped molecular Hamiltonian. However, by removing the quantum circuit, the coherence times required for state preparation can be drastically reduced by directly optimizing the pulses. We demonstrate the potential of this method numerically by directly optimizing pulse shapes which accurately model the dissociation curves of H2 and HeH+, and the ground state energy for LiH. |
Thursday, March 18, 2021 11:54AM - 12:06PM Live |
S34.00003: Mutual information-assisted Adaptive Variational Quantum Eigensolver Ansatz Construction Zi-Jian Zhang, Thi Ha Kyaw, Jakob S. Kottmann, Matthias Degroote, Alán Aspuru-Guzik Adaptive construction of ansatz circuits offers a promising route towards applicable variational quantum eigensolvers (VQE) on near-term quantum hardware. Those algorithms aim to build up optimal circuits for a certain problem. Ansatz circuits are adaptively constructed by selecting and adding entanglers from a predefined pool in those algorithms. In this work, we propose a way to construct entangler pools with reduced size for those algorithms by leveraging classical algorithms. Our method uses mutual information (MI) between the qubits in classically approximated ground state to rank and screen the entanglers. The density matrix renormalization group (DMRG) is employed for classical precomputation in this work. We corroborate our method numerically on small molecules. Our numerical experiments show that a reduced entangler pool with a small portion of the original entangler pool can achieve same numerical accuracy. We believe our method paves a new way for adaptive construction of VQE ansatz. |
Thursday, March 18, 2021 12:06PM - 12:18PM Live |
S34.00004: Variational Quantum Algorithm for Coarse Grained Atomistic Modelling Lewis Anderson, Martin Kiffner, Jason Crain, Dieter Jaksch Variational quantum algorithms (VQAs) have seen significant application to ab initio simulation of quantum chemistry systems. In this work, we propose a novel VQA to calculate the ground state of interacting molecules in condensed phase systems based on the classical method of electronic coarse graining. The electronic coarse grained approach uses coupled quantum Drude oscillators to represent interacting molecular moieties. It can model two- and many-body polarisation and dispersion interactions to all orders without a priori knowledge about the dominant interaction scales. We present simulated results of using this VQA to find ground states for small systems of interacting Drude oscillators that include effective three-body interaction terms. This work opens up the possibility of using quantum computers for quantum chemistry calculations at time and length scales beyond those captured by ab initio methods. |
Thursday, March 18, 2021 12:18PM - 12:30PM Live |
S34.00005: Contextual Subspace Variational Quantum Eigensolver William Kirby, Andrew Tranter, Peter J Love We describe contextual subspace variational quantum eigensolver (CS-VQE), an approximation method based on standard VQE that can be adjusted to use any number of qubits to approximately simulate a given Hamiltonian. The qubits used on the quantum computer simulate the contextual part of the Hamiltonian, while the remaining, noncontextual part is simulated classically, at the cost of incurring an overall error. The more qubits used on the quantum computer, the smaller the overall error will be, providing a method that can be tailored to match available hardware. |
Thursday, March 18, 2021 12:30PM - 12:42PM Live |
S34.00006: Benchmarking Adaptive Variational Quantum Eigensolvers Daniel Claudino, Jerimiah Wright, Alexander J McCaskey, Travis S Humble The variational quantum eigensolver (VQE) is one of the cornerstones of simulations of quantum systems in noisy intermediate-scale quantum devices. Formulations based on established many-body methods tend to map onto unattainable circuit depths, often alleviated by somewhat arbitrary approximations, while amenable implementations typically lose the intuitive connection to their many-body formalism. Novel adaptive variants of VQE are worthy prospect avenues, with potentially shallower circuits, yet at the expense of more measurements. In this work we provide a comprehensive benchmark of the adaptive derivative-assembled pseudo-Trotter (ADAPT) VQE algorithm for the H2, NaH, and KH molecules, assessing the aptness of the prepared state and its corresponding energy compared to exact diagonalization, which are accompanied by the respective measurement and circuit depth estimates. There is much to be understood about these algorithms and these noiseless simulations pave the way to a better understanding of how they work and constitute the reference figures for future studies in noisy settings and hardware deployment. |
Thursday, March 18, 2021 12:42PM - 12:54PM Live |
S34.00007: An Exactly-Solvable Model as a Benchmark for VQE Ken Robbins, Peter J Love The Noisy Intermediate-Scale Quantum (NISQ) era of computation provides new opportunities for calculations with the Variational Quantum Eigensolver (VQE) algorithm but these machines will require benchmarking. The Lipkin-Meshkov-Glick (LMG) model provides an exact standard for which to compare the results of VQE. By exploiting the algebraic structure of the LMG Hamiltonian we use the Bethe ansatz to design a state-preparation quantum circuit to generate ansatz states for the LMG. The proposed circuit is qudit-based and scales to simulate higher numbers of particles. |
Thursday, March 18, 2021 12:54PM - 1:06PM Live |
S34.00008: An optimal quantum sampling regression algorithm for variational eigensolving in the low qubit number regime Pedro Rivero, Ian Cloet, Zack E Sullivan The VQE algorithm, with all its merits, has turned out to be quite expensive to run given the way we currently access quantum processors (i.e. over the cloud). In order to alleviate this issue, in this paper we introduce an alternative hybrid quantum-classical algorithm, and analyze some of its use cases based on time complexity in the low qubit number regime. In exchange for some extra classical resources, this novel strategy is proved to be optimal in terms of the number of samples it requires from the quantum processor. We develop a simple —yet general— analytical model to evaluate when this algorithm is more efficient than VQE, and, from the same theoretical considerations, establish a threshold above which quantum advantage can occur. Finally, we then make use of this novel method to simulate a simplified model of NJL: an effective quantum field theory based on the BCS theory of superconductivity. Our goal with this work is to reproduce the spontaneous symmetry breaking mechanism characteristic of these models, which in turn is responsible for the generation of dressed mass in a number of quantum many-body systems. |
Thursday, March 18, 2021 1:06PM - 1:18PM Live |
S34.00009: Implementation of Measurement Reduction for the Variational Quantum Eigensolver Alexis Ralli, Peter J Love, Peter Coveney, Andrew Tranter One limitation of the variational quantum eigensolver algorithm is the large number of state preparation and measurement steps required to estimate different terms in the Hamiltonian of interest. Here we investigate two different implementations of the unitary partitioning measurement reduction strategy achieved by (1) a sequence of rotations and (2) a linear combination of unitaries (LCU). Simulations show this reduction can significantly benefit calculations by reducing the standard error of the mean. To our knowledge, this work also demonstrates the first experimental execution of LCU on quantum hardware. |
Thursday, March 18, 2021 1:18PM - 1:30PM Live |
S34.00010: Variational Quantum Algorithm for Quantum Sensor Evaluation Jacob Beckey, Akira Sone, Marco Cerezo de la Roca, Patrick Coles The Quantum Fisher information (QFI) quantifies the ultimate precision of estimating a parameter from a quantum state via the quantum Cramér-Rao bound. Thus, the estimation of the QFI is needed in order to assess the quality of a quantum system as a quantum sensor. However, estimation of the QFI for a mixed quantum state is, in general, a computationally demanding task. In this presentation, we present two recent works addressing this issue. First, we discuss a generalized notion of QFI called the Truncated Quantum Fisher Information (TQFI). This quantity lower bounds the standard QFI and, under certain conditions, is efficiently computable on a quantum computer. Next, we discuss our new variational quantum algorithm called Variational Quantum Fisher Information Estimation (VQFIE) which estimates the lower and upper bounds on the QFI and thus outputs a range in which the actual QFI lies. We show that the algorithm can also be used to variationally prepare the state that maximizes the QFI, for the application of quantum sensing. We simulate the algorithm for a magnetometry setup and demonstrate good performance over a range of scenarios. Finally, we compare our contributions to recent literature and discuss the benefits of our methods. |
Thursday, March 18, 2021 1:30PM - 1:42PM Live |
S34.00011: Scattering in the Ising Model with the Quantum Lanczos Algorithm Kubra Yeter Aydeniz, George Siopsis, Raphael Pooser Time evolution and scattering simulation in phenomenological models are of great interest for testing and validating the potential for near-term quantum computers to simulate quantum field theories. Here, we simulate one-particle propagation and two-particle scattering in the one-dimensional transverse Ising model for 3 and 4 spatial sites with periodic boundary conditions on a quantum computer. We use the quantum Lanczos algorithm to obtain all energy levels and corresponding eigenstates of the system. We simplify the quantum computation by taking advantage of the symmetries of the system. These results enable us to compute one- and two-particle transition amplitudes, particle numbers for spatial sites, and the transverse magnetization as functions of time. The quantum circuits were executed on IBM 5-qubit superconducting hardware. The experimental results with readout error mitigation are in very good agreement with the values obtained using exact diagonalization. |
Thursday, March 18, 2021 1:42PM - 1:54PM Live |
S34.00012: Generic constructin of quantum circuits for nonunitary operations: linear-response functions of molecules Yu-ichiro Matsushita, Taichi Kosugi The logic gates on a quantum circuit are restricted to unitary ones. This restriction makes it difficult to develop quantum algorithms for various practical problems. For example, quantum chemistry often requires us to calculate the quantities given via nonunitary operators. In this study, we propose a scheme for the construction of a quantum circuit for an arbitrary nonunitary operator given as a linear combination of unitary operators. Depending on the outcome of a measurement on the ancillary qubits, the input state on which the nonunitary operator has acted will be obtained probabilistically. This appoarch enables us to calculate the one-particle Green's functions[1] and linear-response functions.[2] |
Thursday, March 18, 2021 1:54PM - 2:06PM Live |
S34.00013: State preparation for molecular Hamiltonians with the quantum alternating operator ansatz (QAOA) Norm Tubman, Tad Hogg, Stephen J. Cotton, Stuart Hadfield This work explores the use of the quantum alternating operator ansatz (QAOA) as a algorithm for state preparation for chemical systems. In our approach, the QAOA procedure is modified from its typical application in combinatorial optimization in two important ways: the initial state is chosen to be the Hartree-Fock (HF) approximation to the ground state rather than the commonly used uniform superposition and, in consistent fashion, the QAOA mixer is chosen to be the HF Hamiltonian. The algorithm is evaluated for CH2 and H2O in simple basis sets of 8 orbitals on classical hardware using traditional sparse matrix-based quantum dynamics approaches. A simple linear schedule for the usual QAOA parameters and a moderate number of iterations is shown to lead to final states with high overlap with the true ground state. This work thereby illustrates how existing quantum algorithms for combinatorial optimization can be adapted for application to chemical problems. It is anticipated that this QAOA protocol will readily extend to larger molecular systems. |
Thursday, March 18, 2021 2:06PM - 2:18PM Live |
S34.00014: Scalable Variational Ansatz for Quantum Many-Body Dynamics on Noisy Quantum Devices Niladri Gomes, Yongxin Yao, Feng Zhang, Cai-Zhuang Wang, Thomas Iadecola, Peter Orth Quantum algorithms designed to simulate many-body quantum dynamics and their implementation on present-day noisy intermediate-scale quantum (NISQ) hardware should prioritize resource efficiency. Simulating time-dependent quantum Hamiltonians by explicit construction of the evolution operator requires a circuit depth scaling with the number of time steps, making it prohibitive for NISQ devices. Variational hybrid quantum-classical approaches, although approximate, make repeated use of short circuits and are thus more attractive for use in NISQ settings. However, finding a scalable variational ansatz capable of representing the dynamics in both adiabatic and non-adiabatic limits is a non-trivial problem. In our work, we use a variational time-evolution algorithm to simulate time-dependent spin models. Our ansatz scales polynomially with system size and provides qualitative agreement with exact numerics in adiabatic and non-adiabatic regimes with possible implementation in NISQ devices. |
Thursday, March 18, 2021 2:18PM - 2:30PM Live |
S34.00015: Error-mitigated tensor network-based ansatz for a noisy quantum computer Unpil Baek, William Huggins, Birgitta K Whaley Quantum computers can approximately prepare the ground states of many physical systems without using an exponential amount of resources. A hybrid quantum-classical algorithm, such as the variational quantum eigensolver (VQE), is a promising candidate for simulating electronic structures on a near-term device. Simulating complex systems with VQE, however, poses serious challenges because of limited qubit coherence times and non-negligible error rates within near-term devices. To tackle this challenge, we integrate the geometric structure of Deep Multiscale Entanglement Renormalization Ansatz (DMERA) circuits with the low-cost error mitigation, using fermionic parity symmetry verification, to simulate ground states of the Fermi-Hubbard model and the jellium model. Requiring only a gate depth logarithmic in the total system size and a number of qubits independent of the system size, this protocol enables us to study larger systems than are possible for approaches with different ansatzes. Results for the Fermi-Hubbard model and the jellium model indicate that the DMERA protocol, combined with the error mitigation, effectively leverages the ability of near-term devices to simulate complex lattice models. |
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