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By Eleanor Rieffel and Wolfgang Polak

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Gov/archive/quant-ph. fxpal. com/Quantum Computing. The tensor product (⊗) of a n-dimensional and a k-dimensional vector is a nkdimensional vector. Similarly, if A and B are transformations on n-dimensional and k-dimensional vectors respectively, then A ⊗ B9 is a transformation on nkdimensional vectors. The exact mathematical details of tensor products are beyond the scope of this paper (see Hungerford [1974] for a comprehensive treatment). For our purposes the following algebraic rules are sufficient to calculate with tensor products.

1998. Quantum computing. Reports on Progress in Physics 61, 2, 117–173. gov/abs/quant-ph/9708022. TERHAL, B. M. AND SMOLIN, J. A. 1997. Single Quantum Querying of a Database. gov/abs/ quant-ph/9705041. VANDERSYPEN, L. M. , YANNONI, C. , SHERWOOD, M. , AND CHUANG, I. L. 1999. Realization of Effective Pure States for Bulk Quantum Computation. gov/abs/ quant-ph/9905041. , AND EKERT, A. K. 1996. Quantum Networks for Elementary Arithmetic Operations. Physical Review A. Preprint at Los Alamos Physics Preprint Archive, http://xxx.

In ALAN L. , Complexity Theory Retrospective, In Honor of Juris Hartmanis on the Occasion of His Sixtieth Birthday, (July 5, 1988), Vol. 2, 23– 51. , AND LIDAR, D. A. 1998. Generalized grover search algorithm for arbitrary initial amplitude distribution. gov/abs/quant-ph/9801066. , MARTINI, F. , AND POPESCU, S. 1998. Experimental realization of teleporting an unknown pure quantum state via dual classical and einstein-podolski-rosen channels. Physical Review Letters 80, 1121–1125. , AND ZEILINGER, A.

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