Analog analogue of a digital quantum computation
- Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts02139 (United States)
- Department of Mathematics, Northeastern University, Boston, Massachusetts02115 (United States)
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 with a Hamiltonian of the form E{vert_bar}w{r_angle}{l_angle}w{vert_bar} where {vert_bar}w{r_angle} is an unknown (normalized) state. The problem is to produce {vert_bar}w{r_angle} by adding a Hamiltonian (independent of {vert_bar}w{r_angle}) and evolving the system. If {vert_bar}w{r_angle} is chosen uniformly at random we can (with high probability) produce {vert_bar}w{r_angle} in a time proportional to N{sup 1/2}/E. If {vert_bar}w{r_angle} is instead chosen from a fixed, known orthonormal basis we can also produce {vert_bar}w{r_angle} in a time proportional to N{sup 1/2}/E and we show that this time is optimally short. This restricted problem is an analog analogue to Grover{close_quote}s algorithm, a computation on a conventional (!) quantum computer that locates a marked item from an unsorted list of N items in a number of steps proportional to N{sup 1/2}. {copyright} {ital 1998} {ital The American Physical Society}
- OSTI ID:
- 625859
- Journal Information:
- Physical Review A, Journal Name: Physical Review A Journal Issue: 4 Vol. 57; ISSN 1050-2947; ISSN PLRAAN
- Country of Publication:
- United States
- Language:
- English
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