Parametrized Hamiltonian simulation using quantum optimal control

Abstract

Analog quantum simulation offers a hardware-specific approach to studying quantum dynamics, but mapping a model Hamiltonian onto the available device parameters requires matching the hardware dynamics. We introduce a paradigm for quantum Hamiltonian simulation that leverages digital decomposition techniques and optimal control to perform analog simulation. We validate this approach by constructing the optimal analog controls for a superconducting transmon device to emulate the dynamics of an extended Bose-Hubbard model. We demonstrate the role of control time, digital error, and pulse complexity, and we explore the accuracy and robustness of these controls. We conclude by discussing the opportunity for implementing this paradigm in near-term quantum devices.

String order melting of spin-1 particle chains in superconducting transmons using optimal control

“…( 15) and iteratively optimize the time-dependent device controls to minimize the infidelity between the evolved system dynamics and a target unitary operator. These methods and implementations follow what has been discussed in previous work [11,48] and we review the details for completeness and convenience.…”

“…( 4) with the transverse field strength parameter given as b = ∆bn x , where ∆b is the interval of b on which we wish to explore quench dynamics and n x is an integer that determines the total magnitude of b. This reparametrization allows us to decompose the global time evolution of the quantum quench into a product of local evolutions via Trotterization [11]. In this work, the time evolution operator can be defined as…”

“…There are several unique approaches to quantum simulation; from purely digital approaches on universal quantum computers to purely analog approaches using tailor-made quantum devices. Recent work suggests that there are also a number of intermediate paradigms capable of realizing quantum simulation [2][3][4][5][6][7][8][9][10][11].…”

“…Quantum simulation based on quantum optimal control (QOC) permits one to take advantage of the natural device dynamics and Hilbert space while also enabling the use of digital decomposition methods [11]. In principle, this permits efficient use of coherent resources within quantum hardware.…”

Snowmass White Paper: Quantum Computing Systems and Software for High-energy Physics Research

“…Analog realizations of gauge invariant encodings, such loop-string-hadron encoding in cold atom systems [47], have also appeared. Lastly, with some modest abstraction one popular near term approach has been to leverage the natural device physics in order to augment the conventional digital gate-sets with analog processes [48]. For example, select bosonic vibrational modes can be used to simulate U (1) gauge variables in a resource efficient manner [49], e.g., using trapped ion systems [50].…”