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Analog analogue of a digital quantum computation

Dec, 1996
6 pages
Published in:
  • Phys.Rev.A 57 (1998) 4, 2403
  • Published: Apr 1, 1998
e-Print:
DOI:
Report number:
  • MIT-CTP-2593,
  • MIT-CTP-2593
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Abstract: (APS)
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∣w〉〈w∣E|w〉〈w| where ∣w〉|w〉 is an unknown (normalized) state. The problem is to produce ∣w〉|w〉 by adding a Hamiltonian (independent of ∣w〉)|w〉) and evolving the system. If ∣w〉|w〉 is chosen uniformly at random we can (with high probability) produce ∣w〉|w〉 in a time proportional to N1/2/E{N}^{1/2}/E. If ∣w〉|w〉 is instead chosen from a fixed, known orthonormal basis we can also produce ∣w〉|w〉 in a time proportional to N1/2/E{N}^{1/2}/E and we show that this time is optimally short. This restricted problem is an analog analogue to Grover's algorithm, a computation on a conventional (!) quantum computer that locates a marked item from an unsorted list of NN items in a number of steps proportional to N1/2{N}^{1/2}.
Note:
  • Latex, 6 pages