Universal Refocusing of Systematic Quantum Noise

Refocusing of a quantum system in NMR and quantum information processing can be achieved by application of short pulses according to the methods of spin echo and dynamical decoupling. However, these methods are strongly limited by the requirement that the evolution of the system between pulses be suitably small. Here we show how refocusing may be achieved for arbitrary (but time-independent) evolution of the system between pulses. We first illustrate the procedure with one-qubit systems, and then generalize to $d$-dimensional quantum systems. We also give an application of this result to quantum computation, proving a new version of the Solovay-Kitaev theorem that does not require inverse gates.

[1]  S. Das Sarma,et al.  Concatenated dynamical decoupling in a solid-state spin bath , 2007, 0707.1037.

[2]  D. DiVincenzo,et al.  The Physical Implementation of Quantum Computation , 2000, quant-ph/0002077.

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

[4]  D. Suter,et al.  Iterative rotation scheme for robust dynamical decoupling , 2012 .

[5]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[6]  Nan Zhao,et al.  Dynamical decoupling design for identifying weakly coupled nuclear spins in a bath , 2014 .

[7]  M. Mosca,et al.  Approximating fractional time quantum evolution , 2008, 0810.3843.

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

[9]  A. Haar.  Der Massbegriff in der Theorie der Kontinuierlichen Gruppen , 1933 .

[10]  H. Weyl.  Quantenmechanik und Gruppentheorie , 1927 .

[11]  I. Gohberg,et al.  Basic Operator Theory , 1981 .

[12]  S. Szarek.  Metric Entropy of Homogeneous Spaces , 1997, math/9701213.

[13]  Wen Yang,et al.  Preserving qubit coherence by dynamical decoupling , 2010, 1007.0623.

[14]  Michael A. Nielsen,et al.  The Solovay-Kitaev algorithm , 2006, Quantum Inf. Comput..

[15]  Daniel A. Lidar,et al.  Quadratic dynamical decoupling: Universality proof and error analysis , 2011, 1106.2151.

[16]  Robin K. Harris,et al.  Spin choreography: Basic steps in high resolution NMR , 1997 .

[17]  E. Hahn,et al.  Spin Echoes , 2011 .

[18]  D. Lidar,et al.  Fault-tolerant quantum dynamical decoupling , 2004, 2005 Quantum Electronics and Laser Science Conference.