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 Y34: General Quantum Information: Quantum Simulation and AlgorithmsLive

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Sponsoring Units: DQI Chair: Davide Girolami, Los Alamos National Laboratory 
Friday, March 19, 2021 11:30AM  11:42AM Live 
Y34.00001: The Homotopy Operator and Conservation Laws in Fractional Quantum Mechanics Joel Been, Joshua Lewis, Lincoln D Carr Continuity equations are local conservation laws that describe the evolution of physically important quantities, such as mass, energy, and momentum, in terms of fluxes. For fractional evolution equations (FEEs), partial differential equations that are first order in time and have fractional derivatives in space, the fractional homotopy and correction operators allow the derivation of conservation laws. Conservation laws for FEEs are quasicontinuity equations of the form d_{t}ρ = d_{x}j + k where the source term, k, directly manifests the nonlocality of space fractional derivatives and shows that fractional derivatives force local conservation laws to become global. This is a direct result from the fractional homotopy and correction operators which give explicit form to the quasicontinuity equation for a given density. We applied these methods to describe probability and momentum transport for the space fractional Schrodinger equation which is important in quantum information processing because it describes the nonlocality of connected systems. These examples reveal artifacts of the generalization of quantum mechanics to fractional quantum mechanics. 
Friday, March 19, 2021 11:42AM  11:54AM Live 
Y34.00002: Generation of alltoall connections in a twodimensional qubit array with twobody interactions Tetsufumi Tanamoto Alltoall connections are required in general quantum annealing machines to solve various combinatorial optimization problems. The Lechner, Hauke, and Zoller (LHZ) method, which is used to realize the alltoall connections, requires manybody interactions in locally connected qubits. Because most of the qubit interactions are twobody interactions, Lechner also proposed the construction of each fourbody interaction by six controlledNOT (CNOT) gates between two qubits. However, it is difficult to construct many CNOT gates. Herein, we show more concrete sequences to produce fourbody and threebody interactions based on a twodimensional solidstate qubit system. We show that the number of operations needed to construct the manybody interactions can be reduced using appropriate pulse sequences. These findings will help reduce quantum computation costs for solving combinatorial problems. 
Friday, March 19, 2021 11:54AM  12:06PM Live 
Y34.00003: Digital Quantum Simulations of a NonStoquastic 2Qubit Hamiltonian Namitha Pradeep, Tameem Albash We study digital quantum simulations of a 2qubit system evolving according to a timedependent Hamiltonian. Depending on the choice of parameters, the Hamiltonian can be made stoquastic or nonstoquastic, which for our Hamiltonian can trigger a change from a symmetric to an antisymmetric ground state at the end of the interpolation. This change in the ground state as a function of the Hamiltonian parameters can be detected using a SWAP test with an ancilla qubit or by measuring the suppression of one of the computational basis states. We compare two techniques to simulate the evolution, namely Trotterization and `Continuous qDRIFT'. We plan on implementing these protocols on the Quantum Scientific Computing Open User Testbed (QSCOUT), a trappedion quantum information processor. 
Friday, March 19, 2021 12:06PM  12:18PM Live 
Y34.00004: Quantum Simulation of Hyperbolic Space with Circuit Quantum Electrodynamics: From Graphs to Geometry Igor Boettcher, Przemyslaw Bienias, Ron Belyansky, Alicia Kollar, Alexey V Gorshkov We show how quantum manybody systems on hyperbolic lattices with nearestneighbor hopping and local interactions can be mapped onto quantum field theories in continuous negatively curved space. The underlying lattices have recently been realized experimentally with superconducting resonators and therefore allow for a tabletop quantum simulation of quantum physics in curved background. Our mapping provides a computational tool to determine observables of the discrete system even for large lattices, where exact diagonalization fails. As an application and proof of principle we quantitatively reproduce the ground state energy, spectral gap, and correlation functions of the noninteracting lattice system by means of analytic formulas on the Poincare disk, and show how conformal symmetry emerges for large lattices. 
Friday, March 19, 2021 12:18PM  12:30PM Live 
Y34.00005: Hamiltonian simulation in the low energy subspace Burak Sahinoglu, Rolando Somma We study the problem of simulating the dynamics of spin systems when the initial state is supported on a subspace of low energy of a Hamiltonian $H$. This is a central problem in physics with vast applications in manybody systems and beyond, where the interesting physics takes place in the lowenergy sector. We analyze error bounds induced by product formulas that approximate the evolution operator and show that these bounds depend on an effective lowenergy norm of $H$. We find improvements over the best previous complexities of product formulas that apply to the general case, and these improvements are more significant for long evolution times that scale with the system size and/or small approximation errors. To obtain these improvements, we prove novel exponentiallydecaying upper bounds on the leakage to highenergy subspaces due to the product formula. Our results provide a path to a systematic study of Hamiltonian simulation at low energies, which will be required to push quantum simulation closer to reality. 
Friday, March 19, 2021 12:30PM  12:42PM Live 
Y34.00006: Analog of a quantum heat engine using a singlespin qubit Sergey Shevchenko, K. Ono, Takahiro Mori, S. Moriyama, Franco Nori

Friday, March 19, 2021 12:42PM  12:54PM Live 
Y34.00007: Qubit T Gate Magic State Stabilizer Rank Lucas Kocia, Mohan Sarovar

Friday, March 19, 2021 12:54PM  1:06PM Live 
Y34.00008: Quantum Phase Estimation with TimeFrequency Qudits in a Single Photon HsuanHao Lu, Hu Zixuan, Mohammed S. Alshaykh, Alexandria J. Moore, Yuchen Wang, Poolad Imany, Andrew M. Weiner, Sabre Kais In this work, we report an experimental realization of a quditbased PEA on a photonic platform, utilizing the high dimensionality in time and frequency degrees of freedom (DoFs) in a single photon. The controlledunitary gates can be realized in a deterministic fashion, as the control and target registers are now represented by two DoFs in a single photon. We also proposed a systematic scheme to decompose an arbitrary unitary matrix into smaller dlevel unitary matrices. Representing and connecting these dlevel unitary matrices with photonic qudit gates is our plan for future research. 
Friday, March 19, 2021 1:06PM  1:18PM Live 
Y34.00009: A MagnetismInspired Quantum Algorithm to Solve the Traveling Salesman Problem Luke EllertBeck, Michael Lawler, Samuel Gosin The Traveling Salesman Problem (TSP) is a standard example of an NPhard problem in combinatorial optimization. Although many researchers are looking for faster classical algorithms to solve TSP, it has yet to receive much attention from the quantum community. Our approach uses the Variational Quantum Eigensolver algorithm with tunable Heisenberg exchange gates in our variational ansatz instead of the standard gate set. This choice is motivated by the ability of Heisenberg exchange gates to generate superpositions of permutations. The goal of this research is to compare the performance of this quantum circuit with an analogous classical circuit to investigate whether the quantum circuit has an inherent advantage over its classical counterpart in this variational algorithm. We have implemented the Heisenberg exchange gates using SWAP^{n} gates on a circuit with cyclic, nearestneighbor connectivity in IBM's Qiskit library for a complete graph with 4 nodes, and we have evidence that, on average, the quantum algorithm descends into the optimal solution more quickly than the classical version for this simple case on the IBM QASM Simulator. 
Friday, March 19, 2021 1:18PM  1:30PM Live 
Y34.00010: A JointDetection Receiver for DeepSpace Communications Leveraging Intermediate Measurements on NISQ Hardware. Conor Delaney, Kaushik P Seshadreesan, Ian MacCormack, Alexey Galda, Saikat Guha, Prineha Narang Decoding laserlightmodulated classicalcommunication codewords on quantum devices presents a promising direction towards demonstrating quantum advantage in the near term. Here we implement the quantum circuit of a quantum joint detection receiver for a 3bit binary linear tree code based on the algorithm of belief propagation with quantum messages^{1}. Assuming ideal transduction from optical to trappedion domain, we provide the first experimental demonstration of the joint detection receiver circuit on the Honeywell LT1.0 trapped ion quantum computer. Our approach has the ability to conclusively surpass the quantum limit on the minimum average decoding error probability in the lowphoton limit. The implementation takes advantage of executing intermediate measurements on qubits and perform conditioning on outcomes without interrupting the quantum circuit, which makes trappedion quantum architectures ideal candidates for jointdetection receivers in the near future. Our work offers a clear path to demonstrating quantum advantage in quantumenhanced communications. 
Friday, March 19, 2021 1:30PM  1:42PM Live 
Y34.00011: Quantum statistics in Bohmian trajectory gravity Thomas Andersen The recent experimental proposals by Bose et al. and Marletto et al. (BMV) outline a way to test for the quantum nature of gravity by measuring gravitationally induced differential phase accumulation over the superposed paths of two ∼ 10−14kg masses. These authors outline the expected outcome of these experiments for semiclassical, quantum gravity and collapse models. It is found that both semiclassical and collapse models predict a lack of entanglement in the experimental results. This work predicts the outcome of the BMV experiment in Bohmian trajectory gravity  where classical gravity is assumed to couple to the particle configuration in each Bohmian path, as opposed to semiclassical gravity where gravity couples to the expectation value of the wave function, or of quantized gravity, where the gravitational field is itself in a quantum superposition. In the case of the BMV experiment, Bohmian trajectory gravity predicts that there will be quantum entanglement. This is surprising as the gravitational field is treated classically. A discussion of how Bohmian trajectory gravity can induce quantum entanglement for a non superposed gravitational field is put forward. 
Friday, March 19, 2021 1:42PM  1:54PM Live 
Y34.00012: Custom fermionic codes for quantum simulation Riley Chien, James D Whitfield Simulating a fermionic system on a quantum computer requires encoding the anticommuting fermionic variables into the operators acting on the qubit Hilbert space. The most familiar transformation which achieves this, the JordanWigner transformation, encodes fermionic operators into nonlocal qubit operators. As nonlocal operators lead to a slower quantum simulation, recent works have proposed ways of encoding fermionic systems locally. We present a general construction for designing codes to suit the problem and resources at hand. We also show that locality may be too strict of a condition and the size of operators can be reduced by encoding the system quasilocally. We give examples relevant to lattice models of condensed matter and systems relevant to quantum gravity such as SYK models. We finally mention how hardwareinformed codes can be designed using the framework presented. 
Friday, March 19, 2021 1:54PM  2:06PM Live 
Y34.00013: Simulation of the Fractional Schrödinger Equation in Materials with Sub and SuperDiffusive Transport Joshua Lewis, Joel Been, Lincoln D Carr Fractional derivatives (FDs) allow us to effectively describe transport in bumpy, wrinkled, or jagged materials in nature. In quantum systems that have these rough characteristics, such as in materials with sub and superdiffusive transport, it is described by the fractional Schrödinger equation (FSE); as such, simulating the FSE is important to understanding quantum phenomena in complex geometries. We constructed an algorithm that solves the FSE in space using an integer derivative series approximation to the FD and evolves it in time using Volterralike integral equations of first kind. Using this algorithm, we were able to simulate the FSE in materials that exhibit a nonlocal or fractional geometry. We were also able to quantitatively describe, in general, what the effects are that the fractional geometry has on the solution to the FSE. This applies to quantum information processing with connected systems because complex networks and complexity science can be related to the same source of space and time nonlocality as found in the FSE. Using this simulation of the FSE, we want to construct materials from ground up with prescribed transport properties where we may control the movement of charge and spin through materials in quantum computing. 
Friday, March 19, 2021 2:06PM  2:18PM Live 
Y34.00014: Driven dynamics of a quantum dot electron coupled to a spin 3/2 nuclear bath Arian Vezvaee, Girish Sharma, Sophia Economou, Edwin Barnes Periodic driving of an electron confined in a selfassembled quantum dot can produce dynamic nuclear polarization in the surrounding nuclear spin bath through hyperfine interactions. This dynamic nuclear polarization can in turn be detected through feedback effects on the electron spin. While materials such as InGaAs contain nuclei with spin greater than 1/2, most existing theoretical frameworks assume spin 1/2 nuclei and employ perturbation theory to simplify calculations. In this talk, we present a fully quantum, nonperturbative approach that works for any nuclear spin. Using this framework, we calculate effects that are unique to higher nuclear spin such as quadrupolar interactions. We show that higher total spin can have a significant impact on the generation of dynamic nuclear polarization and how it influences the electron spin evolution in these systems. 
Friday, March 19, 2021 2:18PM  2:30PM On Demand 
Y34.00015: Quantum algorithm for Petz recovery channels and pretty good measurements Andras Gilyen, Seth Lloyd, Iman Marvian, Yihui Quek, Mark Wilde The Petz recovery channel plays an important role in quantum information science as an operation that approximately reverses the effect of a quantum channel. The pretty good measurement is a special case of the Petz recovery channel, and it allows for nearoptimal state discrimination. A hurdle to the experimental realization of these vaunted theoretical tools is the lack of a systematic and efficient method to implement them. This paper sets out to rectify this lack: using the recently developed tools of quantum singular value transformation and oblivious amplitude amplification, we provide a quantum algorithm to implement the Petz recovery channel when given the ability to perform the channel that one wishes to reverse. Moreover, we prove that our quantum algorithm's usage of the channel implementation cannot be improved by more than a quadratic factor. Our quantum algorithm also provides a procedure to perform pretty good measurements when given multiple copies of the states that one is trying to distinguish. 
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