How to derive a quantum complexity lower bound

The modeling of computation using logic circuits occupies an important position in the fundamentals of complexity theory including quantum complexity theory. Consequently, research into methods for computing logic functions on quantum circuits as well as for minimizing and simplifying such circuits has become extremely important. In this paper we explicitly formulate the depth minimization problem for quantum logic circuits and show that this problem is closely related to a geometric approach to deriving a lower bound on the size of a quantum logic circuit. © 2007 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 90(10): 9–17, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20298

[1]  Umesh V. Vazirani,et al.  Quantum Complexity Theory , 1997, SIAM J. Comput..

[2]  Andrew Chi-Chih Yao,et al.  Quantum Circuit Complexity , 1993, FOCS.

[3]  Alexander A. Razborov,et al.  On the method of approximations , 1989, STOC '89.

[4]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[5]  Tetsuro Nishino,et al.  On the Complexity of Negation-Limited Boolean Networks , 1998, SIAM J. Comput..

[6]  Raymond Laflamme,et al.  An Introduction to Quantum Computing , 2007, Quantum Inf. Comput..

[7]  R. Solovay,et al.  Relativizations of the $\mathcal{P} = ?\mathcal{NP}$ Question , 1975 .

[8]  Paul E. Dunne,et al.  The Complexity of Boolean Networks , 1988 .

[9]  Yongwook Chung,et al.  A Practical Method of Constructing Quantum Combinational Logic Circuits , 1999 .

[10]  R. Cleve.  An Introduction to Quantum Complexity Theory , 1999, quant-ph/9906111.

[11]  D. Deutsch.  Quantum theory, the Church–Turing principle and the universal quantum computer , 1985, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[12]  Akira Maruoka,et al.  Potential of the approximation method , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[13]  Jan van Leeuwen,et al.  Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity , 1994 .

[14]  D. Deutsch.  Quantum computational networks , 1989, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.