By Eleanor Rieffel and Wolfgang Polak
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Additional info for An Introduction to Quantum Computing for Non-Physicists
It also discusses the thermodynamics of computations, which is closely tied with reversible computing and information theory. Colin Williams and Scott Clearwater’s book Explorations in Quantum Computing [Williams and Clearwater 1998] comes with software, in the form of Mathematica 332 E. Rieffel and W. Polak notebooks, that simulates some quantum algorithms such as Shor’s algorithm. The second half of the October 1997 issue of the SIAM Journal of Computing contains six seminal articles on quantum computing, including four we have already cited [Bennett et al.
Even though ACM Computing Surveys, Vol. 32, No. 3, September 2000. Introduction to Quantum Computing Grover’s algorithm has been shown to be optimal, there is hope that faster algorithms can be found by exploiting properties of the problem structure. We have described one such approach taken by Hogg. There are a few other known quantum algorithms that we did not discuss. Jones and Mosca  describe the implementation on a 2-bit quantum computer of a constant time algorithm [Deutsch and Jozsa 1992] that can distinguish whether a function is balanced or constant.
329 1 C|ψ = |φ = √ (|000 − |111 ), 2 i Quantum parallelism gives a superposition of different errors each associated with their respective error index i. 2. Measure the |i component of the result. This yields some (random) value i0 and projects the state to ACM Computing Surveys, Vol. 32, No. 3, September 2000. and the error E= 3 4 X ⊗ I ⊗ I + I ⊗ X ⊗ I. 5 5 The resulting error state is − 330 E. Rieffel and W. Polak 4 3 X ⊗I⊗I+ I⊗X ⊗I 5 5 1 × √ (|000 − |111 ) 2 1 4 = X ⊗ I ⊗ I √ (|000 − |111 ) 5 2 3 1 + I ⊗ X ⊗ I √ (|000 − |111 ) 5 2 4 = √ X ⊗ I ⊗ I (|000 − |111 ) 5 2 3 + √ I ⊗ X ⊗ I (|000 − |111 ) 5 2 4 = √ (|100 − |011 ) 5 2 3 + √ (|010 − |101 ).