Quantum Chaos Border for Quantum Computing

B. Georgeot, D. L. Shepelyansky

Published 1999-09-23, updated 2000-01-17Version 3

We study a generic model of quantum computer, composed of many qubits coupled by short-range interaction. Above a critical interqubit coupling strength, quantum chaos sets in, leading to quantum ergodicity of the computer eigenstates. In this regime the noninteracting qubit structure disappears, the eigenstates become complex and the operability of the computer is destroyed. Despite the fact that the spacing between multi-qubit states drops exponentially with the number of qubits $n$, we show that the quantum chaos border decreases only linearly with $n$. This opens a broad parameter region where the efficient operation of a quantum computer remains possible.