Bulletin of the American Physical Society
APS March Meeting 2022
Volume 67, Number 3
Monday–Friday, March 14–18, 2022; Chicago
Session G38: Quantum Annealing and Optimization IIFocus Recordings Available

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Sponsoring Units: DQI Chair: Bibek Pokharel, USC Room: McCormick Place W195 
Tuesday, March 15, 2022 11:30AM  11:42AM 
G38.00001: A General Method for Solving Systems of Nonlinear Differential Equations on a Quantum Annealer with Application to Molecular Dynamics Igor Gayday, Dmitri Babikov, Alexander Teplukhin, Brian K Kendrick, Susan Mniszewski, Yu Zhang, Sergei Tretiak, Pavel A Dub One of the most fundamental problems that has no efficient solutions on classical computers is simulation of quantum systems. It has been long hypothesized that quantum computing devices are naturally more suitable for this task, but many aspects of practical implementations of such simulations remain unknown. One particularly important kind of these simulations is the simulation of molecular dynamics, i.e. prediction of time evolution for a system of interacting particles. In this work we show how a quantum annealer can be used to carry out such simulations by solving differential equations of motion, on the example of the hydrogen molecule. Although the considered system is simple, our method is well scalable and can be readily applied to more complicated systems as annealers with larger number of qubits become available. Importantly, the method is general and can be used to solve arbitrary systems of ordinary nonlinear differential equations, which can be helpful not only in the field of computational chemistry, but in many other fields as well. 
Tuesday, March 15, 2022 11:42AM  11:54AM 
G38.00002: Error Mitigation for Quantum Optimization Circuits by Leveraging Problem Symmetries Ashish KAKKAR, Alexey Galda, Jeffrey Larson, Ruslan Shaydulin

Tuesday, March 15, 2022 11:54AM  12:06PM 
G38.00003: Quantum Annealing for the FermiHubbard Model Ryan Levy, Zoe Gonzalez Izquierdo, Zhihui Wang, Eleanor G Rieffel, Filip A Wudarski Recently, a compact fermion to qubit encoding for the FermiHubbard model (FHM) on a square lattice was proposed [1]. The encoding uses at most terms of Pauli weight3 with an additional feature of low qubit to fermionic mode ratio. Studying a 2D square lattice, we propose a quantum annealing protocol using this compact encoding to access the FermiHubbard model ground state. We show with numerical simulation that for both interacting 2D spinless and spinful systems we are able to achieve low energy states for reasonable total annealing times. This setup provides a promising path for future analog quantum computing platforms to simulate FHMs. 
Tuesday, March 15, 2022 12:06PM  12:42PM 
G38.00004: Topological defects in a quantum annealer: KibbleZurek mechanism and beyond Invited Speaker: Adolfo Del Campo The number of topological defects created in a system driven through a quantum phase transition exhibits a powerlaw scaling with the driving time. This universal scaling law is the key prediction of the KibbleZurek mechanism (KZM), and testing it using a hardwarebased quantum simulator is a coveted goal of quantum information science. Here we provide such a test using quantum annealing. In addition, we probe physics beyond the KZM by identifying signatures of universality in the distribution and cumulants of the number of kinks and their decay, and again find agreement with the quantum simulator results. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system. To check whether an alternative, classical interpretation of these results is possible, we used the spinvector Monte Carlo model, a candidate classical description of the DWave device. We also introduce a new benchmark, the spinvector Langevin (SVL) model, in which Monte Carlo steps are replaced by timecontinuous stochastic Langevin dynamics. 
Tuesday, March 15, 2022 12:42PM  12:54PM Withdrawn 
G38.00005: Implementation of a Multiple Target Tracking Filter on an Adiabatic Quantum Annealer Tim M McCormick, Bryan R osborn, Ian Herbert, R. B Angle, Roy L Streit Recent work at Fraunhofer FKIE shows that Morefield's method for multiple target data association can in theory be solved on an adiabatic quantum annealer. Our calculations on a DWave device validate the theory and demonstrate the limitations of currently available adiabatic quantum annealers for solving the data association problem. The data association problem is formulated as a quadratic unconstrained binary optimization (QUBO) problem; consequently, much of the discussion is relevant to other applications which are, or can be, posed as QUBO problems. For a single scan, the underlying QUBO is equivalent to a disordered classical Ising model. Using forward and reverse annealing, we show that the lowenergy manifold of states of this equivalent Ising model can be identified as the high posterior likelihood, feasible MTDA assignments. This is validated by simulated annealing using Metropolis MCMC of the Ising model performed on a classical computer. 
Tuesday, March 15, 2022 12:54PM  1:06PM 
G38.00006: Fast, Scalable Calibration of a Quantum Annealer James I Basham, Steven M Disseler, Cyrus F Hirjibehedin, Bryce Fisher, Vladimir Bolkhovsky, John Cummings, Rabindra Das, David K Kim, Jeffrey M Knecht, Justin L Mallek, Bethany M Niedzielski, Ravi Rastogi, Danna Rosenburg, Kyle Serniak, DonnaRuth W Yost, Scott Zarr, Jeffrey A Grover, Joseph Gibson, Kenneth Zick, Sergey Novikov, Steven J Weber, William D Oliver, Jonilyn L Yoder Quantum annealers require a variety of calibration procedures, including calibration of crosstalk between flux bias lines, characterization of coupler strengths and qubit Ising parameters as a function of control flux, and optimization of readout. Flux crosstalk in particular can be data intensive as the number of individual measurements scales as O(N^{2}) with the number of control biases. 
Tuesday, March 15, 2022 1:06PM  1:18PM 
G38.00007: Design toolkit for quantum discrete optimization Nicolas P Sawaya, Stuart Hadfield We present a new representation for quantum algorithms that facilitates compilation, analysis, and solving of discrete optimization problems. Our methods and representations allow for automated design and compilation of subroutines relevant to a variety of quantum approaches including QAOA, quantum annealing, and quantum imaginary time evolution, in particular for problems with integer domains. Using our framework, we compare several distinct qubit encodings in five problem areas: routing, scheduling, graph coloring, portfolio rebalancing, and integer linear programming. We study resource counts for subroutines involving cost functions and constraintpreserving mixers, drawing practical conclusions regarding which encodings are most efficient for which problem classes in different parameter regimes. 
Tuesday, March 15, 2022 1:18PM  1:30PM 
G38.00008: A bridge between quantum and classical difficulty in portfolio optimization using the Quantum Approximate Optimization Algorithm Jack S Baker, Santosh Radha, William Cunningham The Quantum Approximate Optimization Algorithm (QAOA) has established itself as the most promising method for solving combinatorial optimization problems on nearterm gatebased quantum computers. As the quality of algorithms and hardware has continued to improve, the financial sector has taken notice due to the algorithm's ability to solve a myriad of concrete financial problems. This interest ranges from small hedge funds and quantshops all the way to multinational banks. Within these financial problems (and other related problems), it is not currently known how classical notions of problem difficulty translate into the quantum setting. I.e, are problems which are more difficult to solve via classical means also more difficult for the QAOA? Answering this question is clearly vital for the larger success of the QAOA and adoption in the mainstream financial sector. In this work, we show how to solve an important financial problem with the QAOA: discrete Markowitz portfolio optimization (MPO). We evaluate the success of the approach and address the parity between classical and quantum difficulty. To do so, we develop a new problem and applicationagnostic benchmark: the normalized and complementary Wasserstein distance (NCWD). Using the NCWD, we show that the average quality of portfolios yielded from the QAOA is a function of the number of viable (constraint satisfying) solutions of the classical problem; increasing the total number of viable portfolios deteriorates the average portfolio quality produced the QAOA. Although emerging in the finance setting, this is an important result for the QAOA in general as it is evidence that more difficult discrete problems in the (exhaustive search) classical setting are also more difficult in the quantum setting. We finish by demonstrating deployment of QAOAbased MPO on a trapped ion quantum computer and evaluate its success using the NCWD. 
Tuesday, March 15, 2022 1:30PM  1:42PM 
G38.00009: QFold: Quantum Walks and Deep Learning to Solve Protein Folding Roberto Campos, Pablo Antonio M Casares, Miguel Angel MartinDelgado We develop quantum computational tools to predict the 3D structure of proteins, one of the most important problems in current biochemical research. We explain how to combine recent deep learning advances with the wellknown technique of quantum walks applied to a Metropolis algorithm. The result, QFold, is a fully scalable hybrid quantum algorithm that, in contrast to previous quantum approaches, does not require a lattice model simplification and instead relies on the much more realistic assumption of parameterization in terms of torsion angles of the amino acids. We compare it with its classical analog for different annealing schedules and find a polynomial quantum advantage, and perform a minimal realization of the quantum Metropolis in IBMQ Casablanca quantum system. 
Tuesday, March 15, 2022 1:42PM  1:54PM 
G38.00010: Quantum annealing applied to ionic diffusion in solids Ryo Maezono, Keishu Utimula, Tom Ichibha, Genki I Prayogo, Kousuke Nakano, Kenta Hongo We have developed a framework for using quantum annealing computation to evaluate a key quantity in ionic diffusion in solids, the correlation factor. Existing methods can only calculate the correlation factor analytically in the case of physically unrealistic models, making it difficult to relate microstructural information about diffusion path networks obtainable by current ab initio techniques to macroscopic quantities such as diffusion coefficients. We have mapped the problem into a quantum spin system described by the Ising Hamiltonian. We have calculated the correlation factor in a simple case with a known exact result by a variety of computational methods, including simulated quantum annealing on the spin models, the classical random walk, the matrix description, and quantum annealing on DWave with hybrid solver . This comparison shows that all the evaluations give consistent results with each other, but that many of the conventional approaches require infeasible computational costs. By applying our framework in combination with ab initio technique, it is possible to understand how diffusion coefficients are controlled by temperatures, pressures, atomic substitutions, and other factors. 
Tuesday, March 15, 2022 1:54PM  2:06PM 
G38.00011: quadratic unconstrained binary optimization of the fuel loading pattern in nuclear reactors ahmed s marzouki The loading pattern problem in nuclear reactors is a hard optimization problem with non convex and non linear objective function, this makes the optimization task for classical algorithms challenging . Over the last years , quantum annealing has shown promising results in solving large scale industrial optimization problems , this motivates the investigation of this method to the loading pattern problem . To be able to run an optimization problem on a quantum annealer , one should put it in a quadratic unconstrained binary optimization (QUBO) form . This is non trivial task due to the non linearity of the objective function . I have discussed how one may surmount this problem and and develop a QUBO for the LP problem and then run the QUBO on the DWave quantum simulator . The obtained results are satisfactory encouraging further exploration of the method to more complex settings in the loading pattern problem hoping to achieve better optimal configurations than those obtained via classical methods which can result in a big savings for nuclear power plants . 
Tuesday, March 15, 2022 2:06PM  2:18PM 
G38.00012: Financial risk analysis using Quantum Computing Pallasena Viswanathan Sriluckshmy, Mario Ponce, Vicente Pina Canelles, Hermanni Heimonen, Adrian Auer, Bruno Taketani, Ines de Vega, Martin Leib Unpredictability and Risk management are some of the key issues that are plaguing the financial world today. We explore the use of quantum computing in prediction and risk assessment using a toymodel of a network of financial institutions. To this end the prediction of the behaviour of the toy model is mapped on to an optimization problem that we attempt to solve with the Quantum Approximate Optimisation Algorithm (QAOA). QAOA is a powerful algorithm for gate based quantum computers that can be used to solve combinatorial optimisation problems. We considerably improve on prior encodings of the problem with the help of Walsh functions. Such an encoding also significantly reduces the circuit depth and the qubit resources required when compared to prior works. We preform extensive numerical experiments evaluating the properties of the toy model in a wide range of parameters. Thus our work provides a viable, scalable and efficient solution to avert the failures and manage risks in reasonable time frame. 
Tuesday, March 15, 2022 2:18PM  2:30PM 
G38.00013: Reinforcement Learning strategies for Quantum Optimization Algorithms Jordi Riu Vicente, Artur GarciaSaez We present a strategy based on classical control of Quantum devices using Reinforcement Learning. Our strategy is applied to Quantum algorithms designed for classical optimization problems such as the QAOA and Quantum Annealing. Our method provides optimal control of the Quantum device following a reformulation the Quantum algorithm as an environment where an autonomous classical agent interacts and performs actions to achieve higher rewards. This formulation allows a hybrid classicalQuantum device to train itself from previous executions using both modelbased and modelfree Reinforcement Learning to control the degrees of freedom of the Quantum Algorithm. Our approach makes a selective use of Quantum measurements to complete the observations of the Quantum state available to the agent. We run tests of this approach on several classical optimization problems, obtaining optimal results for problem instances with N > 20 decision variables. We show how this formulation can be used in variational algorithms to transfer the knowledge from shorter training episodes to reach larger circuit depths and deliver better results. 
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