Controlled gates for multi-level quantum computation

Multi-level (ML) quantum logic can potentially reduce the number of inputs/outputs or quantum cells in a quantum circuit which is a limitation in current quantum technology. In this paper we propose theorems about ML-quantum and reversible logic circuits. New efficient implementations for some basic controlled ML-quantum logic gates, such as three-qudit controlled NOT, Cycle, and Self Shift gates are proposed. We also propose lemmas about r-level quantum arrays and the number of required gates for an arbitrary n-qudit ML gate. An equivalent definition of quantum cost (QC) of binary quantum gates for ML-quantum gates is introduced and QC of controlled quantum gates is calculated.

[1]  Mozammel H. A. Khan,et al.  Terary GFSOP Minimization Using Kronecker Decision Diagrams and Their Synthesis with Quantum Cascades , 2005, J. Multiple Valued Log. Soft Comput..

[2]  Majid Mohammadi,et al.  On figures of merit in reversible and quantum logic designs , 2009, Quantum Inf. Process..

[3]  T. Toffoli,et al.  Conservative logic , 2002, Collision-Based Computing.

[4]  Dianne P. O'Leary,et al.  Efficient circuits for exact-universal computationwith qudits , 2006, Quantum Inf. Comput..

[5]  Anas N. Al-Rabadi,et al.  Multiple-Valued Quantum Logic Synthesis , 2002 .

[6]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[7]  Majid Mohammadi,et al.  Heuristic methods to use don’t cares in automated design of reversible and quantum logic circuits , 2008, Quantum Inf. Process..

[8]  Rolf Landauer,et al.  Irreversibility and heat generation in the computing process , 1961, IBM J. Res. Dev..

[9]  Tommaso Toffoli,et al.  Reversible Computing , 1980, ICALP.

[10]  Md. Mujibur Rahman Khan.  Evolutionary algorithm based synthesis of multi-output ternary functions using quantum cascades , 2005 .

[11]  Gerhard W. Dueck,et al.  Synthesis of Quantum Multiple-Valued Circuits , 2006, J. Multiple Valued Log. Soft Comput..

[12]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[13]  Mozammel H. A. Khan,et al.  Genetic algorithm based synthesis of multi-output ternary functions using quantum cascade of generalized ternary gates , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[14]  Marek A. Perkowski,et al.  Efficient Implementation of Controlled Operations for Multivalued Quantum Logic , 2009, 2009 39th International Symposium on Multiple-Valued Logic.

[15]  Jr.,et al.  Multivalued logic gates for quantum computation , 2000, quant-ph/0002033.