Minimum construction of two-qubit quantum operations.

Optimal construction of quantum operations is a fundamental problem in the realization of quantum computation. We here introduce a newly discovered quantum gate, B, that can implement any arbitrary two-qubit quantum operation with minimal number of both two- and single-qubit gates. We show this by giving an analytic circuit that implements a generic nonlocal two-qubit operation from just two applications of the B gate. Realization of the B gate is illustrated with an example of charge-coupled superconducting qubits for which the B gate is seen to be generated in shorter time than the CNOT gate.

[1]  K. B. Whaley,et al.  Optimal quantum circuit synthesis from controlled-unitary gates , 2003, quant-ph/0308167.

[2]  Colin P. Williams,et al.  Optimal Quantum Circuits for General Two-Qubit Gates , 2003, quant-ph/0308006.

[3]  G. Vidal,et al.  Universal quantum circuit for two-qubit transformations with three controlled-NOT gates , 2003, quant-ph/0307177.

[4]  J. Siewert,et al.  Programmable networks for quantum algorithms. , 2003, Physical review letters.

[5]  K. B. Whaley,et al.  Geometric theory of nonlocal two-qubit operations , 2002, quant-ph/0209120.

[6]  N. Linden,et al.  Optimal entanglement generation from quantum operations , 2002, quant-ph/0205055.

[7]  J. Cirac,et al.  Nonlocal Hamiltonian simulation assisted by local operations and classical communication , 2002 .

[8]  A. Harrow,et al.  Practical scheme for quantum computation with any two-qubit entangling gate. , 2002, Physical review letters.

[9]  Mikhail N. Vyalyi,et al.  Classical and Quantum Computation , 2002, Graduate studies in mathematics.

[10]  B. Recht,et al.  Efficient discrete approximations of quantum gates , 2001, quant-ph/0111031.

[11]  Charles H. Bennett,et al.  Optimal Simulation of Two-Qubit Hamiltonians Using General Local Operations , 2001, quant-ph/0107035.

[12]  Y. Makhlin.  Nonlocal Properties of Two-Qubit Gates and Mixed States, and the Optimization of Quantum Computations , 2000, Quantum Inf. Process..

[13]  Kevin Barraclough,et al.  I and i , 2001, BMJ : British Medical Journal.

[14]  Y. Makhlin,et al.  Quantum-state engineering with Josephson-junction devices , 2000, cond-mat/0011269.

[15]  J. Cirac,et al.  Optimal creation of entanglement using a two-qubit gate , 2000, quant-ph/0011050.

[16]  R. Brockett,et al.  Time optimal control in spin systems , 2000, quant-ph/0006114.

[17]  A. Steane.  Efficient fault-tolerant quantum computing , 1998, Nature.

[18]  Y. Makhlin,et al.  Josephson-junction qubits with controlled couplings , 1998, Nature.

[19]  D. Gottesman.  Theory of fault-tolerant quantum computation , 1997, quant-ph/9702029.

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

[21]  F. Lowenthal,et al.  Uniform Finite Generation of SU(2) and SL(2, R) , 1972, Canadian Journal of Mathematics.