Error correction optimisation in the presence of X/Z asymmetry

By taking into account the physical nature of quantum errors it is possible to improve the efficiency of quantum error correction. Here we consider an optimisation to conventional quantum error correction which involves exploiting asymmetries in the rates of X and Z errors by reducing the rate of X correction. As an example, we apply this optimisation to the [[7,1,3]] code and make a comparison with conventional quantum error correction. After two levels of concatenated error correction we demonstrate a circuit depth reduction of at least 43% and reduction in failure rate of at least 67%. This improvement requires no additional resources and the required error asymmetry is likely to be present in most physical quantum computer architectures.

[1]  Simon J. Devitt,et al.  Universal quantum computation under asymmetric quantum error correction , 2007 .

[2]  A. Fowler,et al.  Long-range coupling and scalable architecture for superconducting flux qubits , 2007, cond-mat/0702620.

[3]  L. Hollenberg,et al.  Robust controlled-NOT gate in the presence of large fabrication-induced variations of the exchange interaction strength , 2007, quant-ph/0701165.

[4]  Andrew W. Cross,et al.  Subsystem fault tolerance with the Bacon-Shor code. , 2006, Physical review letters.

[5]  D. DiVincenzo,et al.  Effective fault-tolerant quantum computation with slow measurements. , 2006, Physical review letters.

[6]  Marc Mézard,et al.  Asymmetric quantum error-correcting codes , 2006, quant-ph/0606107.

[7]  C. Eliasmith,et al.  Fault-tolerant Quantum Computation , 1995 .

[8]  J. Morton,et al.  Coherence of spin qubits in silicon , 2005, cond-mat/0512705.

[9]  D. DiVincenzo,et al.  Dephasing of a superconducting qubit induced by photon noise. , 2005, Physical review letters.

[10]  Jacob M. Taylor,et al.  Coherent Manipulation of Coupled Electron Spins in Semiconductor Quantum Dots , 2005, Science.

[11]  M. Head‐Gordon,et al.  Simulated Quantum Computation of Molecular Energies , 2005, Science.

[12]  D. Bacon.  Operator quantum error-correcting subsystems for self-correcting quantum memories , 2005, quant-ph/0506023.

[13]  J. Preskill,et al.  Quantum accuracy threshold for concatenated distance-3 codes , 2005, Quantum Inf. Comput..

[14]  F. Schmidt-Kaler,et al.  The coherence of qubits based on single Ca+ ions , 2002, quant-ph/0211059.

[15]  I. Chuang,et al.  Experimental realization of Shor's quantum factoring algorithm using nuclear magnetic resonance , 2001, Nature.

[16]  D. Gottesman.  Theory of fault-tolerant quantum computation , 1997, quant-ph/9702029.

[17]  A. Steane.  Active Stabilization, Quantum Computation, and Quantum State Synthesis , 1996, quant-ph/9611027.

[18]  Seth Lloyd,et al.  Universal Quantum Simulators , 1996, Science.

[19]  E. Knill,et al.  Concatenated Quantum Codes , 1996, quant-ph/9608012.

[20]  Lov K. Grover.  A fast quantum mechanical algorithm for database search , 1996, STOC '96.

[21]  A. Steane.  Multiple-particle interference and quantum error correction , 1996, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[22]  P. Shor.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[23]  K. Vahala.  Handbook of stochastic methods for physics, chemistry and the natural sciences , 1986, IEEE Journal of Quantum Electronics.

[24]  B. Muzykantskii,et al.  ON QUANTUM NOISE , 1995 .