An Analog Analogue of a Digital Quantum Computation

Details An Analog Analogue of a Digital Quantum Computation An Analog Analogue of a Digital Quantum Computation

1996-12-06

arxiv.org/abs/quant-ph/9612026v1

Physics

Quantum Physics

Latex, 6 pages

Scientific paper

We solve a problem, which while not fitting into the usual paradigm, can be viewed as a quantum computation. Suppose we are given a quantum system described by an N dimensional Hilbert space with a Hamiltonian of the form $E |w >< w|$ where $| w>$ is an unknown (normalized) state. We show how to discover $| w >$ by adding a Hamiltonian (independent of $| w >$) and evolving for a time proportional to $N^{1/2}/E$. We show that this time is optimally short. This process is an analog analogue to Grover's algorithm, a computation on a conventional (!) quantum computer which locates a marked item from an unsorted list of N items in a number of steps proportional to $N^{1/2}$.

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