Implementation of the Four-Bit Deutsch-Jozsa Algorithm with Josephson Charge Qubits

We show that the Deutsch-Jozsa algorithm for up to four qubits can be realized with a setup of Josephson charge qubits. While existing proposals for the implementation of the algorithm (for up to three qubits) are based on certain classifications of the oracles, this approach becomes increasingly cumbersome for higher qubit numbers. Here we present a method to implement all balanced functions for the four-qubit algorithm by a fixed sequence of operations. The free parameters which define the implemented function are the rotation angles of 15 one-qubit operations.

[1]  David P. DiVincenzo,et al.  Quantum information and computation , 2000, Nature.

[2]  Siyuan Han,et al.  Coherent Temporal Oscillations of Macroscopic Quantum States in a Josephson Junction , 2002, Science.

[3]  Jens Siewert,et al.  Aspects of Qubit Dynamics in the Presence of Leakage , 2000 .

[4]  D. Deutsch,et al.  Rapid solution of problems by quantum computation , 1992, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[5]  A. Ekert,et al.  Universality in quantum computation , 1995, Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences.

[6]  P. Joyez,et al.  Manipulating the Quantum State of an Electrical Circuit , 2002, Science.

[7]  David Collins,et al.  NMR quantum computation with indirectly coupled gates , 2000 .

[8]  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.

[9]  K. Kim,et al.  Deutsch-Jozsa algorithm as a test of quantum computation , 1998, quant-ph/9807012.

[10]  R Fazio,et al.  Quantum algorithms for Josephson networks. , 2001, Physical review letters.

[11]  Vijay Patel,et al.  Quantum superposition of distinct macroscopic states , 2000, Nature.

[12]  Colin P. Williams,et al.  Universal quantum gates for single cooper pair box based quantum computing , 2001, Quantum Inf. Comput..

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

[14]  F K Wilhelm,et al.  Quantum superposition of macroscopic persistent-current states. , 2000, Science.

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

[16]  R. Cleve,et al.  Quantum algorithms revisited , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[17]  Y. Pashkin,et al.  Coherent control of macroscopic quantum states in a single-Cooper-pair box , 1999, Nature.