Estimation of the Local Density of States on a Quantum Computer

Abstract

We report an efficient quantum algorithm for estimating the local density of states (LDOS) on a quantum computer. The LDOS describes the redistribution of energy levels of a quantum system under the influence of a perturbation. Sometimes known as the ``strength function'' from nuclear spectroscopy experiments, the shape of the LDOS is directly related to the survivial probability of unperturbed eigenstates, and has recently been related to the fidelity decay (or ``Loschmidt echo'') under imperfect motion-reversal. For quantum systems that can be simulated efficiently on a quantum computer, the LDOS estimation algorithm enables an exponential speed-up over direct classical computation.

4 pages (revtex) including 1 figure

References in corpus (5)

• Golden rule decay versus Lyapunov decay of the quantum Loschmidt echo
• Fidelity Decay as an Efficient Indicator of Quantum Chaos
• Experimental Implementation of the Quantum Baker's Map
• Quantum irreversibility, perturbation independent decay, and the parametric theory of the local density of states
• Eigenstates of Operating Quantum Computer: Hypersensitivity to Static Imperfections

Cited by in corpus (10)

• Entanglement and the Power of One Qubit
• On the role of entanglement and correlations in mixed-state quantum computation
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• Quasi-probability representations of quantum theory with applications to quantum information science
• Quantum Computing with black-box Subroutines
• Quantum Discord and Quantum Computing - An Appraisal
• Classical simulation of short-time quantum dynamics
• Probing quantum chaos in multipartite systems
• Studies on the Role of Entanglement in Mixed-state Quantum Computation
• One, Two, and $n$ Qubit Decoherence