Bang–Bang Operations from a Geometric Perspective

AbstractStrong, fast pulses, called “bang–bang” controls can be used to eliminate the effects of system-environment interactions. This method for preventing errors in quantum information processors is treated here in a geometric setting which leads to an intuitive perspective. Using this geometric description, we clarify the notion of group symmetrization as an averaging technique, provide a geometric picture for evaluating errors due to imperfect bang–bang controls and give conditions for the compatibility of BB operations with other controlling operations. This will provide additional support for the usefulness of such controls as a means for providing more reliable quantum information processing. PACS: 0.365.Yz, 03.67.Lx, 03.67-a

[1]  D. DiVincenzo,et al.  Quantum computation with quantum dots , 1997, cond-mat/9701055.

[2]  D A Lidar,et al.  Reducing constraints on quantum computer design by encoded selective recoupling. , 2002, Physical review letters.

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

[4]  D. Vitali,et al.  Heating and decoherence suppression using decoupling techniques , 2001, quant-ph/0108007.

[5]  I. Chuang,et al.  Quantum Computation and Quantum Information: Introduction to the Tenth Anniversary Edition , 2010 .

[6]  M. Tinkham.  Group Theory and Quantum Mechanics , 1964 .

[7]  M. Byrd.  Differential geometry on SU(3) with applications to three state systems , 1998, math-ph/9807032.

[8]  S. Lloyd,et al.  DYNAMICAL SUPPRESSION OF DECOHERENCE IN TWO-STATE QUANTUM SYSTEMS , 1998, quant-ph/9803057.

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

[10]  D. Vitali,et al.  Using parity kicks for decoherence control , 1998, quant-ph/9808055.

[11]  Seth Lloyd,et al.  Universal Control of Decoupled Quantum Systems , 1999 .

[12]  G. Bodenhausen,et al.  Principles of nuclear magnetic resonance in one and two dimensions , 1987 .

[13]  D A Lidar,et al.  Creating decoherence-free subspaces using strong and fast pulses. , 2002, Physical review letters.

[14]  V. Jurdjevic.  Geometric control theory , 1996 .

[15]  Viola,et al.  Theory of quantum error correction for general noise , 2000, Physical review letters.

[16]  G. Guo,et al.  Suppressing environmental noise in quantum computation through pulse control , 1999 .

[17]  Lloyd,et al.  Dynamical generation of noiseless quantum subsystems , 2000, Physical review letters.

[18]  Paolo Zanardi.  Stabilizing quantum information , 2000 .

[19]  K. B. Whaley,et al.  Theory of decoherence-free fault-tolerant universal quantum computation , 2000, quant-ph/0004064.

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

[21]  Hoi-Kwong Lo,et al.  Introduction to Quantum Computation Information , 2002 .

[22]  Rainer Wawer,et al.  Quantum Networks: Dynamics of Open Nanostructures , 1998, VLSI Design.

[23]  E. Knill,et al.  DYNAMICAL DECOUPLING OF OPEN QUANTUM SYSTEMS , 1998, quant-ph/9809071.

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