Bulletin of the American Physical Society
2024 APS March Meeting
Monday–Friday, March 4–8, 2024; Minneapolis & Virtual
Session Z51: Parameterized Quantum CircuitsFocus

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Sponsoring Units: DQI Chair: Panagiotis Anastasiou, Virginia Tech Room: 200IJ 
Friday, March 8, 2024 11:30AM  12:06PM 
Z51.00001: Power and Limitations of Parameterized Quantum Circuits Invited Speaker: Xin Wang In recent years, the study of parameterized quantum circuits (PQCs) has gained significant attention in quantum machine learning and nearterm quantum information processing. These circuits are known for their potential to approximate complex functions and their ability to encode data efficiently. However, our understanding of the power and limitations of PQCs is still quite limited. In this talk, we will delve into the power and limits of parameterized quantum circuits in several essential tasks. We will analyze the expressivity and capability of PQCs in terms of approximating functions, learning quantum states, and encoding classical data. We will also discuss the potential of designing quantum algorithms by combining PQCs and existing algorithmic tools. Overall, this talk aims to shed light on the power of PQCs and their potential advantages in nearterm quantum applications. This talk is mainly based on arXiv:2205.07848, 2206.08273, 2310.07528. 
Friday, March 8, 2024 12:06PM  12:18PM 
Z51.00002: Iterative optimization of hard spin glass problems with high frequency AC drives (Part I) Jacob (Coby) Sagal, Brandon A Barton, Sean Feeney, George S Grattan, Pratik Patnaik, Vadim Oganesyan, Lincoln D Carr, Eliot Kapit Performance improvements of quantum algorithms such as quantum annealing, adiabatic quantum computing and the quantum approximate optimization algorithm over smart classical algorithms are often marginal, particularly when concerns such as the overhead of computing quantum expectation values for variational circuits, and the immense prefactor disadvantages quantum hardware exhibits compared to parallel silicon, are taken into account. In light of these challenges, we introduce a new quantum algorithm called ISTSAT (IterativeSymphonic TunnelingBoolean Satisfiability Problem) which circumvents computing gradients and parameter optimization. ISTSAT is a novel heuristic update to highdepth QAOA that simulates evolution under highfrequency drives tuned to the problem graph, and iteratively updates the applied Hamiltonian using bitstrings from previous shots. In this first talk, we introduce the ISTSAT algorithm and sketch its mechanism and workflow. 
Friday, March 8, 2024 12:18PM  12:30PM 
Z51.00003: Iterative optimization of hard spin glass problems with high frequency AC drives (Part II) Brandon A Barton, Sean Feeney, George S Grattan, Pratik Patnaik, Jacob Sagal, Vadim Oganesyan, Lincoln D Carr, Eliot Kapit In this talk, we benchmark the ISTSAT algorithm using sets of hard MAX3XORSAT instances, which are exponentially difficult for both exact and approximate optimization for all known classical and quantum methods. Using the Fujitsu Quantum Simulator–a classical HPC system–we estimate the average time to solution for ISTSAT through large scale numerical simulations of up to N = 30 qubit problems. We find that when ISTSAT is "seeded" using highdepth QAOA to set initial parameters, it demonstrates significant polynomial speedups over both QAOA (which performs relatively poorly for these problems) and the best reported classical algorithms. More sophisticated initial seeding algorithms can produce even larger gains. The mechanism for ISTSAT is fairly generic and we expect it should generalize to other quantum optimization problems which are bottlenecked by exponentially small gaps and firstorder transitions. 
Friday, March 8, 2024 12:30PM  12:42PM 
Z51.00004: Resource analysis of quantum algorithms for coarsegrained protein folding models Hanna Linn, Isak Brundin, Laura GarcíaÁlvarez, Göran Johansson Protein folding processes are a complex and vital aspect of molecular biology that quantum devices may help model. 
Friday, March 8, 2024 12:42PM  12:54PM 
Z51.00005: Variational Quantum Algorithm for Partial Singular Value Decomposition Shohei Miyakoshi, Takanori Sugimoto, Tomonori Shirakawa, Seiji Yunoki, Hiroshi Ueda Quantum entanglement is a key description of multiparticle correlations in various quantum systems and constitutes the fundamental basis for emerging technologies such as quantum computation and communication. Specifically, the entanglement spectrum, quantifying quantum entanglement, serves as a crucial criterion for identifying topological quantum phases and assessing quantum criticality around phase transitions. Utilizing quantum computing for Singular Value Decomposition (SVD) plays a pivotal role in understanding quantum entanglement in largescale quantum systems beyond the capability of classical computers. 
Friday, March 8, 2024 12:54PM  1:06PM 
Z51.00006: Reconfigurable Quantum Hutchinson with RealTime Evolution Yizhi Shen, Michael J Lindsey, Katherine Klymko, Eran Rabani, Daan Camps, Norm M Tubman, Roel Van Beeumen Recently, quantum algorithms leveraging dynamical evolution under the manybody Hamiltonian of interest have proven exceptionally effective in pinpointing individual eigenvalues near the edge of Hamiltonian spectrum, for example the ground state energy. This work delves into the potential of realtime evolution to evaluate the aggregate of eigenvalues across the entire spectrum. In particular, we introduce a simple nearterm algorithm designed to compute the trace of a wide class of operators, including functions of the target Hamiltonian. Using stochastic realtime evolution, we transform the task of trace estimations to straightforward statevector simulations on quantum computer. For numerical illustration, we highlight important applications, such as density of states and free energy calculations, relevant in physical, chemical, and materials sciences. 
Friday, March 8, 2024 1:06PM  1:18PM 
Z51.00007: Variational secure cloud quantum computing Yuta Shingu, Yuki Takeuchi, Suguru Endo, Shiro Kawabata, Shohei Watabe, Tetsuro Nikuni, Hideaki Hakoshima, Yuichiro Matsuzaki

Friday, March 8, 2024 1:18PM  1:30PM 
Z51.00008: On the approximability of randomhypergraph MAX3XORSAT problems with quantum algorithms Eliot Kapit, Brandon A Barton, Sean Feeney, George S Grattan, Pratik Patnaik, Jacob (Coby) Sagal, Lincoln D Carr, Vadim Oganesyan Using the prototypically hard MAX3XORSAT problem class, we explore the practical mechanisms for exact and approximate hardness, for both classical and quantum algorithms. We conclude that while both tasks are classically difficult for essentially the same reason, in the quantum case the mechanisms are distinct. We qualitatively identify why traditional methods (e.g. high depth QAOA) are not reliably good approximation algorithms. We propose a new method, called spectral folding, that does not suffer from these issues, and study it analytically and numerically. We show that, for random hypergraphs including extremal planted solution instances (where the ground state satisfies a much higher fraction of constraints than in truly random problems), if we define the energy to be $E = N_{unsat}N_{sat}$, then spectral folding will return states with energy $E leq A E_{GS}$ in polynomial time, where conservatively, $A simeq 0.6$. We benchmark variations of spectral folding for random approximationhard (planted partial solution) instances in simulation; our results support this prediction. We do not claim that this guarantee holds for all possible hypergraphs. These results suggest that quantum computers are more powerful for approximate optimization than had been previously assumed. 
Friday, March 8, 2024 1:30PM  1:42PM 
Z51.00009: Recursive Quantum Eigenvalue/Singularvalue Transformation Kaoru Mizuta, Keisuke Fujii Quantum eigenvalue transformation (QET) and quantum singular value transformation (QSVT), are versatile quantum algorithms that allow us to apply broad matrix functions to quantum states, covering quantum algorithms such as Hamiltonian simulation. However, finding a parameter set for preferable matrix functions is generally difficult: there is no analytical result other than trivial cases and we often suffer also from numerical instability. We propose recursive QET or QSVT (rQET or rQSVT), in which we can execute complicated matrix functions by recursively organizing blockencoding by lowdegree QET or QSVT. Owing to the simplicity of recursive relations, it works only with a few parameters with exactly determining the parameters, while its iteration results in complicated matrix functions. In particular, Newton iteration allows us to analytically construct a parameter set of the matrix sign function, which can be applied for eigenstate filtering for example. The analyticallyobtained parameter set composed of only different values is sufficient for executing QET of the matrix sign function with an arbitrarily small error . Our protocol will serve as an alternative protocol for constructing QET or QSVT for some useful matrix functions without numerical instability. 
Friday, March 8, 2024 1:42PM  1:54PM 
Z51.00010: Efficient Convex Unitary Decompositions for Quantum Simulation Joseph Peetz, Scott E Smart, Prineha Narang Current quantum approaches to simulating quantum systems are still practically challenging on NISQera devices, because they often require extensive gate sequences and/or many ancilla qubits. We propose a hybrid quantumclassical approach to problems in quantum simulation, which we demonstrate for both standard Hamiltonian simulation and open quantum systems. Our approach generates a novel decomposition of unitary operators, which can be efficiently implemented on a quantum computer. The resulting scheme allows for resource tradeoffs between circuit depth and sample complexity, enabling nearterm applications. 
Friday, March 8, 2024 1:54PM  2:06PM 
Z51.00011: Digital quantum simulations of the SSH model on a parameterized quantum circuit Qing Xie, Seki Kazuhiro, Tomonori Shirakawa, Yunoki Seiji Quantum computing holds immense potential to revolutionize many fields, including cryptography, material science, drug discovery, and artificial intelligence. Currently, we are in the NISQ era, where quantum devices up to a few hundred noisy qubits are available. We carry out digital quantum simulations of the noninteracting SSH model on a parameterized quantum circuit. The circuit is composed of two parts: the first part is used to prepare the initial bonding state from the product state 00....0>. The second part consists of Mlayer composite quantum gates that process the quantum state. The rotation angles of the singlequbit gates are treated as variational parameters which are optimized using classical algorithms. We then study the evolutions of the groundstate energy, entanglement entropy, and mutual information on the circuit for two scenarios where the initial and final states either belong to the same or different topological phases. In the first case, we find that the groundstate energy converges exponentially fast with increasing circuit depth M. The entanglement entropy approaches saturation values after very few layers and the mutual information is nonzero only for a few close neighbor sites. However, in the second case where the initial and final state have different topologies, to prepare the ground state exactly, the minimal circuit depth is a quarter of the system size, consistent with the LiebRonbinson bound for propagating the information. Additionally, the maxima of the entanglement entropy grows with the system size and mutual information propagates throughout the entire system. 
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