Work

Geometric quantum control and the random Schrödinger equation

Year: 2025

Type: article

Abstract: Understanding and mitigating noise in quantum systems is a fundamental challenge in achieving scalable and fault-tolerant quantum computation. Error modeling for quantum systems can be formulated in many ways, some of which are very fundamental, but hard to analyze (evolution by general dynamical map) and others perhaps too simplistic to represent physical reality. In this paper, we present an intermediate approach, introducing the random Schrödinger equation, with a noise term given by a time-varying random Hermitian matrix as a means to model noisy quantum systems. We derive bounds on the error of the synthesized unitary in terms of bounds on the norm of the noise, and show that for certain noise processes these bounds are tight. We then show that in certain situations, minimizing the error is equivalent to finding a geodesic on SU ( n ) with respect to a Riemannian metric encoding the coupling between the control pulse and the noise process, thus connecting our work to the complexity geometry pioneered by Michael Nielsen.

Source: Physical Review Research

DOI: 10.1103/y8nw-n1wb

Authors: Rufus Lawrence, Aleš Wodecki, Johannes Aspman, Llorenç Balada Gaggioli, Jakub Mareček

Institution: Czech Technical University in Prague

Language: English

Topic: Quantum Computing Algorithms and Architecture

Subfield: Artificial Intelligence

Field: Computer Science

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,625

Funders: European Commission, Grantová Agentura České Republiky, HORIZON EUROPE Framework Programme, HORIZON EUROPE Marie Sklodowska-Curie Actions