Quantum chaos and quantum computing

Dima L. Shepelyansky

Dima L. Shepelyansky

The standard generic quantum computer model is studied analytically and numerically and the border for emergence of quantum chaos, induced by imperfections and residual inter-qubit couplings, is determined. This phenomenon appears in an isolated quantum computer without any external decoherence. The onset of quantum chaos leads to quantum computer hardware melting, strong quantum entropy growth and destruction of computer operability. The time scales for development of quantum chaos and ergodicity are determined. In spite the fact that this phenomenon is rather dangerous for quantum computing it is shown that the quantum chaos border for inter-qubit coupling is exponentially larger than the energy level spacing between quantum computer eigenstates and drops only linearly with the number of qubits n . As a result the ideal multi-qubit structure of the computer remains rather robust against imperfections. This opens a broad parameter region for a possible realization of quantum computer. The obtained results are related to the recent studies of quantum chaos in such many-body systems as nuclei, complex atoms and molecules, finite Fermi systems and quantum spin glass shards which are also reviewed in the paper.

Laurin E. Fischer, Matea Leahy, Andrew Eddins +16 more

Dima L. Shepelyansky

The standard generic quantum computer model is studied analytically and numerically and the border for emergence of quantum chaos, induced by imperfections and residual inter-qubit couplings, is determined. This phenomenon appears in an isolated quantum computer without any external decoherence. The onset of quantum chaos leads to quantum computer hardware melting, strong quantum entropy growth and destruction of computer operability. The time scales for development of quantum chaos and ergodicity are determined. In spite the fact that this phenomenon is rather dangerous for quantum computing it is shown that the quantum chaos border for inter-qubit coupling is exponentially larger than the energy level spacing between quantum computer eigenstates and drops only linearly with the number of qubits n. As a result the ideal multi-qubit structure of the computer remains rather robust against imperfections. This opens a broad parameter region for a possible realization of quantum computer. The obtained results are related to the recent studies of quantum chaos in such many-body systems as nuclei, complex atoms and molecules, finite Fermi systems and quantum spin glass shards which are also reviewed in the paper.

Ilki Kim, G. Mahler

Jincheng Zhang

This paper explores the potential of quantum chaos control for advanced quantum computation and information processing. We propose a system leveraging the inherent properties of quantum chaos, specifically the extreme sensitivity to initial conditions, to achieve precise control and manipulation of quantum systems. The core mechanism involves inducing and managing quantum chaos within a system of qubits by carefully tuning their parameters. This approach aims to exploit the chaotic dynamics for quantum computation, offering a novel pathway beyond traditional quantum control methods. The theoretical framework presented outlines the design considerations and potential applications of this technique, focusing on harnessing the unique characteristics of chaotic quantum systems. This work establishes a foundation for future research into utilizing quantum chaos as a powerful tool in the development of more robust and versatile quantum computing architectures.