Robust quantum searching with spontaneously decaying qubits

Abstract

We present a modification of the standard single-item quantum search procedure that acquires robustness from spontaneous decay of the qubits. This damps the usual oscillation of populations, driving the system to a steady state with a strongly enhanced population of the solution. Numerical evaluation of the steady state was performed for up to 36 qubits. The huge size of the state space in our analysis is dealt with by exploiting a symmetry in the master equation that reduces the scaling of computer resources from exponential to polynomial. Based on these results we estimate that an error-free solution can be retrieved from the steady state after O(log log N) repetitions, with near-unit probability. This brings the overall scaling to O(sqrt{N} log log N), only slightly worse than for the ideal quantum case.

4 pages, 4 figures v2: modified title, abstract, and introduction; some extra refs v3: considerable revision, extended data range to 36 qubits, added an appendix with the re-expressed master equation. Now 6 pages. v4: few final tweaks

References in corpus (3)

• A quantitative model for the effective decoherence of a quantum computer with imperfect unitary operations
• Dissipative decoherence in the Grover algorithm
• Time and frequency domain solutions in an optical analogue of Grover's search algorithm

Cited by in corpus (7)

• Preservation of Positivity by Dynamical Coarse-Graining
• Critically damped quantum search
• Geometric Algebra and Information Geometry for Quantum Computational Software
• Decrease of Fisher information and the information geometry of evolution equations for quantum mechanical probability amplitudes
• Effect of qubit losses on Grover's quantum search algorithm
• Simulation of Grover's quantum search algorithm in a Ising nuclear spin chain quantum computer with first and second nearest neighbour couplings
• The speed of Markovian relaxation towards the ground state