By Gilles Brassard, Tal Mor (auth.), Colin P. Williams (eds.)
This ebook comprises chosen papers offered on the First NASA foreign convention on Quantum Computing and Quantum Communications, QCQC'98, held in Palm Springs, California, united states in February 1998.
As the list of the 1st large-scale assembly completely dedicated to quantum computing and communications, this ebook is a special survey of the cutting-edge within the region. The forty three rigorously reviewed papers are equipped in topical sections on entanglement and quantum algorithms, quantum cryptography, quantum copying and quantum info conception, quantum blunders correction and fault-tolerant quantum computing, and embodiments of quantum pcs.
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Extra info for Quantum Computing and Quantum Communications: First NASA International Conference, QCQC’98 Palm Springs, California, USA February 17–20, 1998 Selected Papers
B. The components of the 2B × 2B qubit number operator are defined by (13) (ˆ na )µν ≡ bµa δµν . In terms of (13), the operators for mass and momentum are B ˆ◦ = m Q n ˆa (14) eai n ˆa. (15) a=1 and B ˆ i = mc Q a=1 In terms of (13) the invariant quantities are simply expressed as the following matrix elements B ρ= m ψ|n ˆa | ψ (16) mceai ψ | n ˆa | ψ . (17) a=1 B ρvi = a=1 The matrix elements (9) and (10) must remain constant after each time step iteration ˆ α | ψ(t) . ˆ α | ψ(t + τ ) = ψ(t) | Q (18) ψ(t + τ ) | Q ˆ | ψ(t) , this implies that Since | ψ(t + τ ) = U ˆ αU ˆ =Q ˆ α, ˆ †Q U (19) ˆ, Q ˆ α ] = 0.
J. Bernstein, and P. Bertani, ”Experimental realization of any discrete unitary operator”, Physical Review Letters, 73, p. 58, 1994. 14. E. gov/archive/quant-ph/9508006, 1995. 15. A. Barenco, A. Ekert, K-A Suominen, and P. Torma,”Approximate quantum Fourier transform and decoherence,” Physical Review A, 54, p. 139, 1996. 16. C. Van Loan, Computational Frameworks for the Fast Fourier Transform. SIAM Publications, Philadelphia, 1992. 17. J. Fino and R. Alghazi,”A unified treatment of discrete unitary transforms,” SIAM J.
The matrix element (9) defines the mass density as ρ = ψ | Q B ˆ ψ , where (Q◦ )αβ = m a=1 baα δαβ , and the matrix element (10) defines the ˆ i | ψ , where (Q ˆ i )αβ = mc B baα eai δab . momentum density as ρvi = ψ | Q a=1 Equating (46) with (9) and equating (47) with (10) gives us a way to check the projection operator (45). This is done as follows B | ωa |2 ω|m ˆ |ω =m (48) a=1 2B B | ψα |2 bαa =m (49) a=1 α=1 2B B | ψα |2 = bαa , m α=1 (50) a=1 where we used the square of (45) on the second line of the derivation.