Encoded recoupling and decoupling: An alternative to quantum error-correcting codes applied to trapped-ion quantum computation

A recently developed theory for eliminating decoherence and design constraints in quantum computers, 'encoded recoupling and decoupling', is shown to be fully compatible with a promising proposal for an architecture enabling scalable ion-trap quantum computation [D. Kielpinski et al., Nature (London) 417, 709 (2002)]. Logical qubits are encoded into pairs of ions. Logic gates are implemented using the Soerensen-Moelmer (SM) scheme applied to pairs of ions at a time. The encoding offers continuous protection against collective dephasing. Decoupling pulses, that are also implemented using the SM scheme directly to the encoded qubits, are capable of further reducing various other sources of qubit decoherence, such as due to differential dephasing and due to decohered vibrational modes. The feasibility of using the relatively slow SM pulses in a decoupling scheme quenching the latter source of decoherence follows from the observed 1/f spectrum of the vibrational bath.

[1]  Daniel A Lidar,et al.  Comprehensive encoding and decoupling solution to problems of decoherence and design in solid-state quantum computing. , 2002, Physical review letters.

[2]  C. Monroe,et al.  Experimental Issues in Coherent Quantum-State Manipulation of Trapped Atomic Ions , 1997, Journal of research of the National Institute of Standards and Technology.

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

[4]  P. Zanardi.  Symmetrizing Evolutions , 1998, quant-ph/9809064.

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

[6]  T Yamamoto,et al.  Charge echo in a cooper-pair box. , 2002, Physical review letters.

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

[8]  Ronnie Kosloff,et al.  Quantum computing by an optimal control algorithm for unitary transformations. , 2002, Physical review letters.

[9]  Klaus Molmer,et al.  Entanglement and quantum computation with ions in thermal motion , 2000 .

[10]  E. Knill,et al.  Resilient Quantum Computation , 1998 .

[11]  Gerard J. Milburn,et al.  Ion Trap Quantum Computing with Warm Ions , 2000 .

[12]  K. B. Whaley,et al.  Exact gate sequences for universal quantum computation using the XY interaction alone , 2001, quant-ph/0112014.

[13]  J. Levy.  Universal quantum computation with spin-1/2 pairs and Heisenberg exchange. , 2001, Physical review letters.

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

[15]  P. Zanardi,et al.  Error avoiding quantum codes , 1997, quant-ph/9710041.

[16]  K. B. Whaley,et al.  Encoded universality for generalized anisotropic exchange Hamiltonians , 2002, quant-ph/0204016.

[17]  Lorenza Viola.  Quantum control via encoded dynamical decoupling , 2002 .

[18]  Daniel A. Lidar,et al.  Qubits as Parafermions , 2001, OFC 2001.

[19]  Seth Lloyd,et al.  Resonant cancellation of off-resonant effects in a multilevel qubit , 2000 .

[20]  M. A. Rowe,et al.  A Decoherence-Free Quantum Memory Using Trapped Ions , 2001, Science.

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

[22]  G. J. Milburn,et al.  DECOHERENCE IN ION TRAPS DUE TO LASER INTENSITY AND PHASE FLUCTUATIONS , 1998 .

[23]  A. Leggett,et al.  Dynamics of the dissipative two-state system , 1987 .

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

[25]  Daniel A. Lidar,et al.  Bang–Bang Operations from a Geometric Perspective , 2001, Quantum Inf. Process..

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

[27]  D A Lidar,et al.  Universal fault-tolerant quantum computation in the presence of spontaneous emission and collective dephasing. , 2002, Physical review letters.

[28]  J. Preskill.  Reliable quantum computers , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[29]  Artur Ekert,et al.  Quantum computers and dissipation , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

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

[31]  C. Monroe,et al.  Experimental entanglement of four particles , 2000, Nature.

[32]  Alexandre Blais,et al.  Quantum Codes for Simplifying Design and Suppressing Decoherence in Superconducting Phase-Qubits , 2002, Quantum Inf. Process..

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

[34]  C. Monroe,et al.  Architecture for a large-scale ion-trap quantum computer , 2002, Nature.

[35]  David P. DiVincenzo,et al.  Encoded universality from a single physical interaction , 2001, Quantum Inf. Comput..

[36]  D. A. Lidar,et al.  Power of anisotropic exchange interactions: Universality and efficient codes for quantum computing , 2002 .

[37]  F. Schmidt-Kaler,et al.  Quantum State Engineering on an Optical Transition and Decoherence in a Paul Trap , 1999 .

[38]  Lorenza Viola,et al.  Implementation of universal control on a decoherence-free qubit , 2002 .

[39]  T. L. James,et al.  CHAPTER 2 – PRINCIPLES OF NUCLEAR MAGNETIC RESONANCE , 1975 .

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

[41]  Simon C. Benjamin.  Simple pulses for universal quantum computation with a Heisenberg ABAB chain , 2001 .

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

[43]  Knight,et al.  Quantum computing using dissipation to remain in a decoherence-free subspace , 2000, Physical review letters.

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

[45]  Masaki Aihara,et al.  Multipulse control of decoherence , 2002 .

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

[47]  Paolo Zanardi.  Computation on an error-avoiding quantum code and symmetrization , 1999 .

[48]  J. Cirac,et al.  Quantum Computations with Cold Trapped Ions. , 1995, Physical review letters.

[49]  Alex Brown.  Two-color pulsed laser excitation of dipolar molecules: Absolute laser carrier-phase effects , 2002 .

[50]  K. Mølmer,et al.  QUANTUM COMPUTATION WITH IONS IN THERMAL MOTION , 1998, quant-ph/9810039.

[51]  K. B. Whaley,et al.  Universal quantum computation with the exchange interaction , 2000, Nature.

[52]  C. F. Roos,et al.  Speed of ion-trap quantum-information processors , 2000, quant-ph/0003087.

[53]  M. A. Rowe,et al.  Heating of trapped ions from the quantum ground state , 2000 .

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

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

[56]  Daniel A. Lidar,et al.  Decoherence-Free Subspaces for Multiple-Qubit Errors: (II) Universal, Fault-Tolerant Quantum Computation , 2001 .

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

[58]  D A Lidar,et al.  Efficient universal leakage elimination for physical and encoded qubits. , 2002, Physical review letters.

[59]  M. Aihara.  Non-Markovian theory of nonlinear-optical phenomena associated with the extremely fast relaxation in condensed matter , 1982 .

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

[61]  A. G. White,et al.  Experimental verification of decoherence-free subspaces. , 2000, Science.

[62]  C. Monroe,et al.  Decoherence of quantum superpositions through coupling to engineered reservoirs , 2000, Nature.

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