Dynamical stabilization of Grover's algorithm with embedded quantum codes

Stabilizing quantum algorithms against external perturbations and preserving quantum coherence are main challenges in the area of quantum information processing. In this contribution main ideas underlying a new class of recently proposed embedded error-correcting quantum codes are discussed. These detected-jump correcting quantum codes are capable of stabilizing distinguishable qubits against spontaneous decay provided these decay processes originate from couplings to statistically independent reservoirs. Exploiting the classical information about which qubit has been affected by the environment these embedded quantum codes minimize the number of required control measurements and recovery operations as well as redundancy. Their stabilizing properties are exemplified by applying them to Grover's quantum search algorithm.

[1]  Lov K. Grover.  Quantum Mechanics Helps in Searching for a Needle in a Haystack , 1997, quant-ph/9706033.

[2]  A. Delgado,et al.  Error avoiding quantum codes and dynamical stabilization of Grover's algorithm , 2000, quant-ph/0003141.

[3]  P. Zanardi,et al.  Noiseless Quantum Codes , 1997, quant-ph/9705044.

[4]  Zoller,et al.  Inversion of quantum jumps in quantum optical systems under continuous observation. , 1996, Physical review letters.

[5]  Steane,et al.  Error Correcting Codes in Quantum Theory. , 1996, Physical review letters.

[6]  Gilles Brassard,et al.  Tight bounds on quantum searching , 1996, quant-ph/9605034.

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

[8]  Laflamme,et al.  Perfect Quantum Error Correcting Code. , 1996, Physical review letters.

[9]  P. Knight,et al.  Quantum error correction in the presence of spontaneous emission. , 1996, quant-ph/9603022.

[10]  K. B. Whaley,et al.  Robustness of Decoherence-Free Subspaces for Quantum Computation , 1999 .

[11]  Christof Zalka.  GROVER'S QUANTUM SEARCHING ALGORITHM IS OPTIMAL , 1997, quant-ph/9711070.

[12]  E. Knill,et al.  Theory of quantum error-correcting codes , 1997 .

[13]  Shor,et al.  Scheme for reducing decoherence in quantum computer memory. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[14]  G. Guo,et al.  Reducing decoherence in quantum-computer memory with all quantum bits coupling to the same environment , 1996, quant-ph/9612003.

[15]  Daniel A. Lidar,et al.  Decoherence-Free Subspaces for Quantum Computation , 1998, quant-ph/9807004.

[16]  Kempe,et al.  Universal fault-tolerant quantum computation on decoherence-free subspaces , 2000, Physical review letters.

[17]  I. Averbukh,et al.  Fractional revivals: Universality in the long-term evolution of quantum wave packets beyond the correspondence principle dynamics , 1989 .

[18]  Dominic J. A. Welsh,et al.  Codes and cryptography , 1988 .

[19]  Juan Pablo Paz,et al.  QUANTUM COMPUTATION WITH PHASE DRIFT ERRORS , 1997 .

[20]  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.

[21]  N. Gershenfeld,et al.  Experimental Implementation of Fast Quantum Searching , 1998 .

[22]  B. E. Kane.  A silicon-based nuclear spin quantum computer , 1998, Nature.

[23]  Daniel R. Simon,et al.  On the power of quantum computation , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[24]  U. Weiss.  Quantum Dissipative Systems , 1993 .

[25]  Guang-Can Guo,et al.  Preserving Coherence in Quantum Computation by Pairing Quantum Bits , 1997 .

[26]  H. Carmichael.  An open systems approach to quantum optics , 1993 .

[27]  C. DeWitt-Morette,et al.  Techniques and Applications of Path Integration , 1981 .

[28]  Gottesman.  Class of quantum error-correcting codes saturating the quantum Hamming bound. , 1996, Physical review. A, Atomic, molecular, and optical physics.

[29]  Daniel A. Lidar,et al.  CONCATENATING DECOHERENCE-FREE SUBSPACES WITH QUANTUM ERROR CORRECTING CODES , 1998, quant-ph/9809081.