Abstract
Quantum logic decomposition refers to decomposing a given quantum gate to a set of physically implementable gates. An approach has been presented to decompose arbitrary diagonal quantum gates to a set of multiplexed-rotation gates around z axis. In this article, a special class of diagonal quantum gates, namely diagonal Hermitian quantum gates, is considered and a new perspective to the decomposition problem with respect to decomposing these gates is presented. It is first shown that these gates can be decomposed to a set that solely consists of multiple-controlled Z gates. Then a binary representation for the diagonal Hermitian gates is introduced. It is shown that the binary representations of multiple-controlled Z gates form a basis for the vector space that is produced by the binary representations of all diagonal Hermitian quantum gates. Moreover, the problem of decomposing a given diagonal Hermitian gate is mapped to the problem of writing its binary representation in the specific basis mentioned previously. Moreover, CZ gate is suggested to be the two-qubit gate in the decomposition library, instead of previously used CNOT gate. Experimental results show that the proposed approach can lead to circuits with lower costs in comparison with the previous ones.
- A. Barenco et al. 1995. Elementary gates for quantum computation. Phys. Rev. A 52, 3457--3467.Google ScholarCross Ref
- V. Bergholm, J. J. Vartiainen, M. Möttönen, and M. M. Salomaa. 2005. Quantum circuits with uniformly controlled one-qubit gates. Phys. Rev. A 71, 052330.Google ScholarCross Ref
- A. Broadbent and E. Kashefi. 2009. Parallelizing quantum circuits. Theoret. Comput. Sci. 410, 26 (June 2009), 2489--2510. Google ScholarDigital Library
- S. S. Bullock and I. L. Markov. 2003. An elementary two-qubit quantum computation in 23 elementary gates. Phys. Rev. A 68, 012318--012325.Google ScholarCross Ref
- S. S. Bullock and I. L. Markov. 2004. Asymptotically optimal circuits for arbitrary n-qubit diagonal computations. Quant. Inf. Computat. 4, 1, 27--47. Google ScholarDigital Library
- G. Cybenko. 2001. Reducing quantum computations to elementary unitary operations. Comput. Sci. Eng. 3, 2, 27--32. Google ScholarDigital Library
- T. Hogg, C. Mochon, W. Polak, and E. Rieffel. 1999. Tools for quantum algorithms. Int. J. Mod. Phys. C 10, 1, 1347--1361.Google ScholarCross Ref
- K. Iwama, Y. Kambayashi, and S. Yamashita. 2002. Transformation rules for designing CNOT-based quantum circuits. In Proceedings of Design Automation Conference. 419--424. Google ScholarDigital Library
- M. Möttönen, J. J. Vartiainen, V. Bergholm, and M. M. Salomaa. 2004. Quantum circuits for general multiqubit gates. Phys. Rev. Lett. 93, 13, 130502.Google ScholarCross Ref
- M. Nakhara and T. Ohmi. 2008. Quantum Computing: From Linear Algebra to Physical Reaizations (1st Ed.). Taylor and Francis.Google ScholarCross Ref
- M. A. Nielsen and I. L. Chuang. 2010. Quantum Computation and Quantum Information (10th anniversary Ed.). Cambridge University Press. Google ScholarDigital Library
- R. Raussendorf and H. J. Briegel. 2001. A one-way quantum computer. Phys. Rev. Lett. 86, 22 (May 2001), 5188--5191.Google ScholarCross Ref
- M. Saeedi, M. Arabzadeh, M. Saheb Zamani, and M. Sedighi. 2011. Block-based quantum-logic synthesis. Quant. Inf. Computat. 11, 3--4, 262--277. Google ScholarDigital Library
- V. V. Shende, S. S. Bullock, and I. L. Markov. 2006. Synthesis of quantum-logic circuits. IEEE Trans. Comput. Aided Des. 25, 6, 1000--1010. Google ScholarDigital Library
- V. V. Shende and I. L. Markov. 2009. On the CNOT-cost of Toffoli gates. Quant. Inf. Computat. 9, 5--6 (May 2009), 461--486. Google ScholarDigital Library
- V. V. Shende, I. L. Markov, and S. S. Bullock. 2004a. Minimal universal two-qubit quantum circuits. Phys. Rev. A 69 (2004), 062321.Google ScholarCross Ref
- V. V. Shende, I. L. Markov, and S. S. Bullock. 2004b. Smaller two-qubit circuits for quantum communication and computation. In Proceedings of Design, Automation and Test in Europe, 980--985. Google ScholarDigital Library
- G. Song and A. Klappenecker. 2003. Optimal realizations of controlled unitary gates. Quant. Inf. Computat. 3, 2, 139--155. Google ScholarDigital Library
- J. J. Vartiainen, M. Möttönen, and M. M. Salomaa. 2004. Efficient decomposition of quantum gates. Phys. Rev. Lett. 92, 177902.Google ScholarCross Ref
- F. Vatan and C. Williams. 2004. Optimal quantum circuits for general two-qubit gates. Phys. Rev. A 69, 032315.Google ScholarCross Ref
- G. Vidal and C. M. Dawson. 2004. A universal quantum circuit for two-qubit transformations with three CNOT gates. Phys. Rev. A 69, 010301.Google ScholarCross Ref
Index Terms
- Decomposition of Diagonal Hermitian Quantum Gates Using Multiple-Controlled Pauli Z Gates
Recommendations
Quantum-Logic Synthesis of Hermitian Gates
Regular PapersIn this article, the problem of synthesizing a general Hermitian quantum gate into a set of primary quantum gates is addressed. To this end, an extended version of the Jacobi approach for calculating the eigenvalues of Hermitian matrices in linear ...
Multi-qubit non-adiabatic holonomic controlled quantum gates in decoherence-free subspaces
Non-adiabatic holonomic quantum gate in decoherence-free subspaces is of greatly practical importance due to its built-in fault tolerance, coherence stabilization virtues, and short run-time. Here, we propose some compact schemes to implement two- and ...
Yang-Baxterizations, Universal Quantum Gates and Hamiltonians
The unitary braiding operators describing topological entanglements can be viewed as universal quantum gates for quantum computation. With the help of the Brylinski's theorem, the unitary solutions of the quantum Yang---Baxter equation can be also ...
Comments