## Ilon Joseph | 19-FS-072

### Project Overview

The goals of this project were to develop quantum algorithms that address the mission needs of Lawrence Livermore National Laboratory and to determine the feasibility of performing the first quantum calculations of these algorithms using Livermore's Quantum Design and Integration Testbed (QuDIT), a multidisciplinary research environment where scientists develop novel algorithms for a range of research applications. Our project's objective was to develop practical approaches to algorithms that are capable of simulating the complex behavior of dynamical systems given the realistic constraints and limited capabilities of emerging quantum hardware platforms.

We developed a number of new conceptual approaches, including (1) a new approach to Hamiltonian simulation of nonlinear classical dynamics; (2) a hardware-efficient algorithm for Hamiltonian simulation of three-wave interactions; and (3) a hardware-efficient generalization of Grover's search algorithm to qudit platforms, which are multi-level superconducting qubits. Initial implementations of specific algorithms were developed for the QuDIT platform by designing optimal microwave control pulses that cause the quantum hardware to emulate the unitary transformations that comprise a quantum program. The performance of the hardware in the presence of noise was estimated by using the Lindblad master equation to simulate the dynamics of an open quantum system that experiences decay and dephasing processes.

The outcome of this project was a set of preliminary modeling results that proved that these algorithms could be implemented on the QuDIT platform without being overwhelmed by noise and decoherence processes. This project provided the foundation for the first cross-cutting collaboration between experts in quantum information science (QIS), high-energy-density (HED) science, and fusion energy science—a collaboration that would not have occurred through other means.

### Mission Impact

The successful outcome of this project has the potential for significant future impact on the Laboratory's mission research challenge in energy and resource security and its core competencies in HED science and high-performance computing, simulation, and data science. Because of the potential for significant impact in many areas of science, engineering, and national security, QIS research—including sensors, computers, and algorithms—now falls under a new quantum science and technology mission research challenge at the Laboratory. In addition, passage of the National Quantum Initiative Act in 2018 highlights the importance of QIS research to the Department of Energy and the nation.

### Publications, Presentations, and Patents

Castelli, A. R., et al. 2020. "Experimental realization of a nonlinear 3-wave mixing gate for quantum simulation." American Physical Society March Meeting,* *Colorado, CO, March 2020. LLNL-PRES-805647

Geyko, V., et al. 2020a. "Using Grover's search algorithm to test a three-level quantum system." American Physical Society March Meeting, Colorado, CO, March 2020. LLNL-CONF-805838

——— 2020b. "Implementation of Grover's search algorithm for a three-level system on Rigetti quantum hardware." LLNL–Rigetti Meeting, February 2020. LLNL-PRES-805369

Joseph, I., et al. 2020a. "Using Grover's search algorithm to test a three-level quantum system." American Physical Society March Meeting,* *Colorado, CO, March 2020. LLNL-PRES-805938

——— 2020b. "Quantum Leap for Fusion Energy Sciences." U.S. DOE Quantum Information Science Principal Investigator's Meeting, March 2020. LLNL-PRES-807166

——— 2020c. "Exploration of Quantum Computing for Fusion Energy Science Applications." International Sherwood Fusion Theory Conference, April 2020. LLNL-ABS-806061

——— 2020d. "Koopman-von Neumann Approach to Quantum Simulation of Nonlinear Classical Dynamics." *Phys. Rev. Research* 2, 043102. LLNL-JRNL-807423

Porter, M. D., et al. 2020. "Using Chaotic Quantum Maps as a Test of Current Quantum Computing Hardware Fidelity." International Sherwood Fusion Theory Conference, April 2020. LLNL-ABS-806062

Shi, Y., et al. 2020a. "Quantum Computation of Three-Wave Interactions with Engineered Cubic Couplings." arxiv:2004.06885. LLNL-JRNL-808551

——— 2020b. "Quantum simulation of nonlinear three-wave interactions with engineered cubic couplings." American Physical Society March Meeting, Denver, CO, March 2020. LLNL-PRES-805512