The Quantum Esscher Transform | Yixian Qiu, Kelvin Koor, Patrick Rebentrost | TQC 2024

Описание: The Quantum Esscher Transform | Yixian Qiu, Kelvin Koor, Patrick Rebentrost

The Esscher Transform is a tool of broad utility in various domains of applied probability. It provides the solution to a constrained minimum relative entropy optimization problem. In this work, we study the generalization of the Esscher Transform to the quantum setting. We examine a relative entropy minimization problem for a quantum density operator, potentially of wide relevance in quantum information theory. The resulting solution form motivates us to define the quantum Esscher Transform, which subsumes the classical Esscher Transform as a special case. Envisioning potential applications of the quantum Esscher Transform, we also discuss its implementation on fault-tolerant quantum computers. Our algorithm is based on the modern techniques of block-encoding and quantum singular value transformation (QSVT). We show that given block-encoded inputs, our algorithm outputs a subnormalized block-encoding of the quantum Esscher transform within accuracy $\epsilon$ in $\tilde O(\kappa d \log^2 1/\epsilon)$ queries to the inputs, where $\kappa$ is the condition number of the input density operator and $d$ is the number of constraints.

TQC 2024 | 9-13 September 2024 at OIST, Japan
http://tqc-conference.org

19th Conference on the Theory of Quantum Computation, Communication and Cryptography.

TQC is a leading annual international conference for students and researchers working in the theoretical aspects of quantum information science. The scientific objective is to bring together the theoretical quantum information science community to present and discuss the latest advances in the field.


Organisation:
OIST: Okinawa Institute for Science and Technology
Squids: Schools for Quantum Information Development



Sponsors:
JPMorganChase
Google Quantum AI
Horizon Quantum Computing
Quantinuum
Japan National Tourism Organization