Holographic deep thermalization for secure and efficient quantum random state generation (2411.03587v3)

Abstract: Randomness is a cornerstone of science, underpinning fields such as statistics, information theory, dynamical systems, and thermodynamics. In quantum science, quantum randomness, especially random pure states, plays a pivotal role in fundamental questions like black hole physics and quantum complexity, as well as in practical applications such as quantum device benchmarking and quantum advantage certification. The conventional approach for generating genuine random states, called `deep thermalization', faces significant challenges, including scalability issues due to the need for a large ancilla system and susceptibility to attacks, as demonstrated in this work. We introduce holographic deep thermalization, a secure and hardware-efficient quantum random state generator. By adopting a sequential application of a scrambling-measure-reset process, it continuously trades space with time, and substantially reduces the required ancilla size to as small as a system-size independent constant; At the same time, it guarantees security by removing quantum correlation between the data system and attackers. Thanks to the resource reduction, our circuit-based implementation on IBM Quantum devices achieves genuine $5$-qubit random state generation utilizing only a total of $8$ qubits.