Emergence of Quantum Chaos in Quantum Computer Core and How to Manage It

Abstract

We study the standard generic quantum computer model, which describes a realistic isolated quantum computer with fluctuations in individual qubit energies and residual short-range inter-qubit couplings. It is shown that in the limit where the fluctuations and couplings are small compared to one-qubit energy spacing the spectrum has a band structure and a renormalized Hamiltonian is obtained which describes the eigenstate properties inside one band. The studies are concentrated on the central band of the computer (``core'') with the highest density of states. We show that above a critical inter-qubit coupling strength, quantum chaos sets in, leading to quantum ergodicity of the computer eigenstates. In this regime the ideal qubit structure disappears, the eigenstates become complex and the operability of the computer is quickly destroyed. We confirm that the quantum chaos border decreases only linearly with the number of qubits n, although the spacing between multi-qubit states drops exponentially with n. The investigation of time-evolution in the quantum computer shows that in the quantum chaos regime, an ideal (noninteracting) state quickly disappears and exponentially many states become mixed after a short chaotic time scale for which the dependence on system parameters is determined. Below the quantum chaos border an ideal state can survive for long times and be used for computation. The results show that a broad parameter region does exist where the efficient operation of a quantum computer is possible.