Sufficient condition on noise correlations for scalable quantum computing

I study the effectiveness of fault-tolerant quantum computation against correlated Hamiltonian noise, and derive a sufficient condition for scalability. Arbitrarily long quantum computations can be executed reliably provided that noise terms acting collectively on k system qubits are sufficiently weak, and decay sufficiently rapidly with increasing k and with increasing spatial separation of the qubits.

[1]  Robert Alicki,et al.  Quantum memory as a perpetuum mobile of the second kind , 2009 .

[2]  E. Knill,et al.  Resilient quantum computation: error models and thresholds , 1997, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[3]  A. Leggett,et al.  Quantum tunnelling in a dissipative system , 1983 .

[4]  Dorit Aharonov,et al.  Fault-tolerant Quantum Computation with Constant Error Rate * , 1999 .

[5]  Robert Alicki,et al.  Quantum error correction fails for Hamiltonian models , 2004, quant-ph/0411008.

[6]  Ben Reichardt.  Fault-Tolerance Threshold for a Distance-Three Quantum Code , 2006, ICALP.

[7]  Daniel Gottesman,et al.  Stabilizer Codes and Quantum Error Correction , 1997, quant-ph/9705052.

[8]  Barbara M. Terhal,et al.  Fault-tolerant quantum computation for local non-Markovian noise , 2005 .

[9]  John Preskill,et al.  Quantum accuracy threshold for concatenated distance-3 codes , 2006, Quantum Inf. Comput..

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

[11]  Mikhail I. Dyakonov,et al.  Is Fault-Tolerant Quantum Computation Really Possible? , 2006, quant-ph/0610117.

[12]  Andrew P. Hines,et al.  Decoherence in quantum walks and quantum computers , 2007, 0711.1555.

[13]  John Preskill,et al.  Fault-tolerant quantum computation with long-range correlated noise. , 2006, Physical review letters.

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

[15]  A. Kitaev.  Quantum computations: algorithms and error correction , 1997 .

[16]  D. Gottesman.  An Introduction to Quantum Error Correction and Fault-Tolerant Quantum Computation , 2009, 0904.2557.

[17]  E. Mucciolo,et al.  Bound on quantum computation time: Quantum error correction in a critical environment , 2010, 1004.3247.

[18]  Ben W. Reichardt.  Threshold for the distance three Steane quantum code , 2005 .

[19]  Gil Kalai.  Detrimental Decoherence , 2008 .

[20]  Gil Kalai,et al.  Quantum Computers: Noise Propagation and Adversarial Noise Models , 2009, 0904.3265.

[21]  Gil Kalai,et al.  How Quantum Computers Fail: Quantum Codes, Correlations in Physical Systems, and Noise Accumulation , 2011, ArXiv.

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

[23]  Resilient quantum computation in correlated environments: a quantum phase transition perspective. , 2006, Physical review letters.

[24]  Michal Horodecki,et al.  Dynamical description of quantum computing: Generic nonlocality of quantum noise , 2002 .

[25]  Dorit Aharonov,et al.  Fault-tolerant quantum computation with constant error , 1997, STOC '97.

[26]  Gil Kalai,et al.  How Quantum Computers Can Fail , 2006, quant-ph/0607021.

[27]  G. Kalai.  Thoughts on Noise and Quantum Computation , 2005, quant-ph/0508095.

[28]  John Preskill,et al.  Combining dynamical decoupling with fault-tolerant quantum computation , 2009, 0911.3202.

[29]  Peter W. Shor,et al.  Fault-tolerant quantum computation , 1996, Proceedings of 37th Conference on Foundations of Computer Science.

[30]  M. Ben-Or,et al.  Limitations of Noisy Reversible Computation , 1996, quant-ph/9611028.

[31]  John Preskill,et al.  Fault-tolerant quantum computation versus Gaussian noise , 2008, 0810.4953.

[32]  Eduardo R. Mucciolo,et al.  Hamiltonian Formulation of Quantum Error Correction and Correlated Noise , 2007, ArXiv.

[33]  R. Alicki.  Comment on "Resilient Quantum Computation in Correlated Environments: A Quantum Phase Transition Perspective" and "Fault-tolerant Quantum Computation with Longe-range Correlated Noise" , 2007, quant-ph/0702050.

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

[35]  Yu.,et al.  Quantum tunneling in a dissipative system. , 1996, Physical review. A, Atomic, molecular, and optical physics.

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

[37]  G. Hooft.  Quantum gravity as a dissipative deterministic system , 1999, gr-qc/9903084.