Bulletin of the American Physical Society
2024 APS March Meeting
Monday–Friday, March 4–8, 2024; Minneapolis & Virtual
Session B52: Quantum Algorithms and ComplexityFocus

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Sponsoring Units: DQI Chair: Kevin Smith, Yale University Room: 201AB 
Monday, March 4, 2024 11:30AM  11:42AM 
B52.00001: Quantum simulation of paritytime symmetric systems with diagonal operators Maryam Abbasi, Anthony Schlimgen, Kade HeadMarsden Quantum simulation of quantum systems stands as a pivotal application in the field of quantum computation. However, the accurate representation of real quantum systems poses a challenge, given that most are open systems undergoing nonunitary processes. To capture the dynamics of nonhermitian systems, we must employ innovative simulation methods. In this presentation, I will talk about the implementation of singular value decomposition of the evolution operator for a ParityTime symmetric system. This method requires dilation of the Hilbert space of the desired quantum system with only one extra qubit. I will demonstrate the scalability of this technique by applying it to twolevel and threelevel nonHermitian systems on a real quantum processor. 
Monday, March 4, 2024 11:42AM  11:54AM 
B52.00002: Theoretical constraints on simulating nonMarkovian topological quantum walks in synthetic dimensions Valentin F Boettcher, Félix Pellerin, Philippe StJean, William A Coish Topologically protected quantities are robust to symmetrypreserving perturbations that don’t close an energy gap. However, every realistic system is coupled to an environment that may break those symmetries and thus break the topological protection. A significant recent effort has been focussed on the nonHermitian description of open systems in this context [1]. When considering Hermitian systembath models, where the bath is included in the model, new behavior can become apparent. This is the case in the nonMarkovian topological quantum walks, introduced in Ref. [2]. In this model, a walker can evolve on an SSHchain with quantum baths attached to every other site. The mean displacement of the walker before leaving the bath is quantized and equal to the topological invariant of the SSH model for subohmic baths. For superohmic baths, however, this quantization breaks down. We will discuss theoretical constraints on reproducing this effect experimentally with a finite bath and how to implement the resulting model in synthetic dimensions [3]. 
Monday, March 4, 2024 11:54AM  12:06PM 
B52.00003: Simulation of open quantum systems with giant atoms Guangze Chen, Anton Frisk Kockum Open quantum manybody systems are both of fundamental interest and have practical applications. In many cases, numerically solving such systems with classical methods is infeasible; instead, quantum simulation is required. Yet, conventional quantum simulation methods either require a large amount of ancilla qubits or operate within limited parameter spaces. To overcome these challenges, we put forward a novel protocol for simulating open quantum manybody systems with giant atoms. Unlike conventional pointlike small atoms, giant atoms couple to the environment at multiple points, yielding interference effects that grant remarkable tunability in the interactions between the atoms and the environment. Utilizing this high tunability, we demonstrate efficient simulation of a variety of open quantum systems with two giant atoms coupled to a waveguide. We further show the capability of this setup to simulate models not intrinsically present in the system by tuning the qubit frequencies at different time steps. Our results can be extended to a larger number of giant atoms, and pave the way towards versatile simulation of open quantum manybody systems. 
Monday, March 4, 2024 12:06PM  12:18PM 
B52.00004: Gibbs sampling via cluster expansions Norhan M Eassa, Mahmoud M Moustafa, Arnab Banerjee, Jeffrey Cohn Gibbs states (i.e., thermal states) can be used for several applications such as quantum simulation, quantum machine learning, quantum optimization, and the study of open quantum systems. Moreover, semidefinite programming, combinatorial optimization problems, and training quantum Boltzmann machines can all be addressed by sampling from wellprepared Gibbs states. With that, however, comes the fact that preparing and sampling from Gibbs states on a quantum computer are notoriously difficult tasks. Such tasks can require large overhead in resources and/or calibration even in the simplest of cases, as well as the fact that the implementation might be limited to only a specific set of systems. We propose a method based on sampling from a quasidistribution consisting of tensor products of mixed states on local clusters, i.e., expanding the full Gibbs state into a sum of products of local "Gibbscumulant" type states easier to implement and sample from on quantum hardware. We present results for measuring both the dynamical structure factor and the specific heat of different Gibbs states of spin systems. 
Monday, March 4, 2024 12:18PM  12:30PM 
B52.00005: Nearlyoptimal simulation of quantum field theory Michael Kreshchuk, Christian W Bauer, Christopher F Kane, Neel Modi, Siddharth Hariprakash, Niladri Gomes I will present recent results on state preparation and time evolution in quantum field theories, based on utilizing quantum simulation algorithms with nearlyoptimal scaling in problem parameters. I will also discuss ways to overcome the major bottleneck of such methods — the efficient implementation of block encoding — with the aid of the recently developed Quantum Eigenvalue Transformation for Unitary Matrices. 
Monday, March 4, 2024 12:30PM  1:06PM 
B52.00006: Linear Combination of Hamiltonian Simulation for Nonunitary Dynamics Invited Speaker: Dong An We propose a simple method for simulating a general class of nonunitary dynamics as a linear combination of Hamiltonian simulation (LCHS) problems. LCHS does not rely on converting the problem into a dilated linear system problem or on the spectral mapping theorem. The latter is the mathematical foundation of many quantum algorithms for solving a wide variety of tasks involving nonunitary processes, such as the quantum singular value transformation. The LCHS method can achieve optimal cost in terms of state preparation, and an improved LCHS method further achieves nearoptimal dependence on all parameters in terms of matrix queries. We also demonstrate an application for open quantum dynamics simulation using the complex absorbing potential method. 
Monday, March 4, 2024 1:06PM  1:18PM 
B52.00007: Abstract Withdrawn

Monday, March 4, 2024 1:18PM  1:30PM 
B52.00008: Toward a Unified Picture of FermiontoQubit Transforms Brent A Harrison, Andrew M Projansky, Jason T Necaise, Joseph Gibson, James D Whitfield Several mappings of fermions to qubits analogous to JordanWigner have been proposed, including the BravyiKitaev transformation, as well as the Ternary Tree and Parity mappings. Using graph and grouptheoretic methods, we present progress toward a unified framework for all such mappings. In particular, we describe the set of such mappings whose qubit representations of creation and annihilation operators are single Pauli strings. We endow this set with a group structure, divide it into equivalence classes based on operator locality properties, and show that these classes can be labeled by certain orbits of the symplectic group over $mathbb{F}_2$. For encodings with nonentangled basis states, we find a labeling in terms of nonsingular directed graphs. We present considerations for optimization over this space of equivalence classes, with applications to nearterm quantum simulation. 
Monday, March 4, 2024 1:30PM  1:42PM 
B52.00009: Effective quantum volume, fidelity and computational cost of noisy quantum processing experiments Salvatore Mandra, Kostyantyn Kechedzhi, Sergei V Isakov, Benjamin Villalonga, Sergio Boixo, Vadim Smelyanskiy Today’s experimental noisy quantum processors can compete with and surpass all known algorithms on stateoftheart supercomputers for the computational benchmark task of Random Circuit Sampling. Additionally, a circuitbased quantum simulation of quantum information scrambling, which measures a local observable, has already outperformed standard full wave function simulation algorithms, such as, exact Schrodinger evolution and Matrix Product States (MPS). Nevertheless, this experiment has not yet surpassed tensor network contraction for computing the value of the observable. 
Monday, March 4, 2024 1:42PM  1:54PM 
B52.00010: Entanglement spectrum statistics in matchgate circuits with supplemental resources Andrew M Projansky, Joshuah T Heath, James D Whitfield We study the entanglement spectrum generated by matchgate circuits with various additional resources. We show that, for matchgate circuits acting on product states, WignerDyson entanglement statistics emerges in the thermodynamic limit by virtue of a single SWAP gate. This is analogous to the Clifford case, in which only a single Tgate is needed to achieve universal entanglement spectrum statistics under similar system size scaling [1]. Additionally, we examine the entanglement complexity [2] of matchgate circuits with varied initial states, showing a jump in complexity when input states are composed of entangled products of three or more qubits. Our work clarifies the relationship between simulatability, entanglement entropy, and the complexity of entanglement in several different simulable gate sets. 
Monday, March 4, 2024 1:54PM  2:06PM 
B52.00011: Classical limits of quantum algorithms Peter K Schuhmacher Faulttolerant quantum computing promises to solve some computational tasks that turn out to be hard on classical computing machines. There are algorithms like Grover's algorithm that have proven speedup against any classical algorithm. Unfortunately, truly faulttolerant quantum computers have not been realized yet. The potential to achieve quantum advantage with quantum algorithms that run on today's noisy intermediate scale quantum (NISQ) devices remains an open question to date. Here, we propose a systematic strategy to benchmark given NISQalgorithms for their potential of quantum advantage by comparing these algorithms to their own classical limits. 
Monday, March 4, 2024 2:06PM  2:18PM 
B52.00012: What physical model does a Trotterized time evolution on a noisy quantum computer effectively simulate? Keith R Fratus, Kirsten Bark, Nicolas F Vogt, Juha Leppäkangas, Sebastian Zanker, Michael Marthaler, JanMichael Reiner We consider the extent to which a noisy quantum computer is able to simulate the time evolution of a quantum spin system in a faithful manner. Given a reasonable set of assumptions regarding the manner in which noise acts on such a device, we argue for a circuitlevel description of noise in terms of individual decoherence events following otherwise noisefree gates. With such a model, we further show how the effects of noise can be reinterpreted as a modification to the dynamics of the original system being simulated. We find that this modification corresponds to the introduction of static Lindblad terms, which act in addition to the original unitary dynamics. The form of these terms depends not only on the underlying noise processes occurring on the device, but also on the original unitary dynamics, as well as the manner in which these dynamics are simulated on the device, i.e., the choice of quantum algorithm. Our results are confirmed through numerical analysis. In addition to understanding the extent to which the result of a digital quantum simulation may differ from the intended calculation, our results may aide in tailoring quantum circuits to achieve the simulation of a given noisy spin system, as well as provide additional insight into Lindblad dynamics more broadly. 
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