Multi-qubit correction for quantum annealers

We present multi-qubit correction (MQC) as a novel postprocessing method for quantum annealers that views the evolution in an open-system as a Gibbs sampler and reduces a set of excited states to a new synthetic state with lower energy value. After sampling from the ground state of a given (Ising) Hamiltonian, MQC compares pairs of excited states to recognize virtual tunnels—i.e., a group of qubits that changing their states simultaneously can result in a new state with lower energy value—and successively converges to the ground state. Experimental results using D-Wave 2000Q quantum annealers demonstrate that MQC finds samples with notably lower energy values and improves the reproducibility of results when compared to recent hardware/software advances in the realm of quantum annealing, such as spin-reversal transforms, classical postprocessing techniques, and increased inter-sample delay between successive measurements.

[1]  A. Ganti,et al.  Family of [[6k,2k,2]] codes for practical and scalable adiabatic quantum computation , 2013, 1309.1674.

[2]  M. W. Johnson,et al.  Quantum annealing with manufactured spins , 2011, Nature.

[3]  Daniel A. Lidar,et al.  Adiabatic quantum optimization with the wrong Hamiltonian , 2013, 1310.0529.

[4]  Daniel A. Lidar,et al.  Mean Field Analysis of Quantum Annealing Correction. , 2015, Physical review letters.

[5]  D. McMahon Adiabatic Quantum Computation , 2008 .

[6]  Ryan Babbush,et al.  What is the Computational Value of Finite Range Tunneling , 2015, 1512.02206.

[7]  Hristo Djidjev,et al.  Optimizing the Spin Reversal Transform on the D-Wave 2000Q , 2019, 2019 IEEE International Conference on Rebooting Computing (ICRC).

[8]  John Fulcher,et al.  Computational Intelligence: An Introduction , 2008, Computational Intelligence: A Compendium.

[9]  Cang Hui,et al.  Non-equilibrium dynamics , 2017 .

[10]  J. Straub,et al.  Global energy minimum searches using an approximate solution of the imaginary time Schroedinger equation , 1993 .

[11]  Daniel A. Lidar,et al.  Error-corrected quantum annealing with hundreds of qubits , 2013, Nature Communications.

[12]  Masayuki Ohzeki,et al.  Quantum annealing: An introduction and new developments , 2010, 1006.1696.

[13]  Dmitri V. Averin,et al.  Decoherence induced deformation of the ground state in adiabatic quantum computation , 2012, Scientific Reports.

[14]  Wojciech H. Zurek,et al.  Defects in Quantum Computers , 2017, Scientific Reports.

[15]  John E. Dorband,et al.  Extending the D-Wave with support for Higher Precision Coefficients , 2018, ArXiv.

[16]  Moinuddin K. Qureshi,et al.  Mitigating Measurement Errors in Quantum Computers by Exploiting State-Dependent Bias , 2019, MICRO.

[17]  Peter Norvig,et al.  Artificial Intelligence: A Modern Approach , 1995 .

[18]  Aidan Roy,et al.  A practical heuristic for finding graph minors , 2014, ArXiv.

[19]  Daniel A. Lidar,et al.  Towards fault tolerant adiabatic quantum computation. , 2007, Physical review letters.

[20]  Daniel A. Lidar,et al.  Quantum annealing correction for random Ising problems , 2014, 1408.4382.

[21]  Rita Almeida Ribeiro,et al.  Adaptive Imitation Scheme for Memetic Algorithms , 2011, DoCEIS.

[22]  Andrew Lucas,et al.  Ising formulations of many NP problems , 2013, Front. Physics.

[23]  Andries P. Engelbrecht,et al.  Computational Intelligence: An Introduction , 2002 .

[24]  Tim Finin,et al.  Reinforcement Quantum Annealing: A Hybrid Quantum Learning Automata , 2020, Scientific Reports.

[25]  Firas Hamze,et al.  Glassy Chimeras could be blind to quantum speedup: Designing better benchmarks for quantum annealing machines , 2014, 1401.1546.

[26]  Gili Rosenberg,et al.  Boosting quantum annealer performance via sample persistence , 2016, Quantum Inf. Process..

[27]  Ari Mizel Fault-tolerant, Universal Adiabatic Quantum Computation , 2014 .

[28]  John E. Dorband,et al.  A Method of Finding a Lower Energy Solution to a QUBO/Ising Objective Function , 2018, ArXiv.

[29]  Ramin Ayanzadeh,et al.  Leveraging Artificial Intelligence to Advance Problem-Solving with Quantum Annealers , 2020 .

[30]  Ajinkya Borle,et al.  On Post-Processing the Results of Quantum Optimizers , 2019, TPNC.

[31]  Sebastian Deffner,et al.  Quantum fluctuation theorem for error diagnostics in quantum annealers , 2018, Scientific Reports.

[32]  Daniel A. Lidar,et al.  Quantum annealing correction with minor embedding , 2015, 1507.02658.

[33]  Daniel A. Lidar,et al.  Adiabatic quantum computation , 2016, 1611.04471.

[34]  Daniel A. Lidar,et al.  Performance of two different quantum annealing correction codes , 2015, Quantum Inf. Process..

[35]  John Preskill,et al.  Quantum Computing in the NISQ era and beyond , 2018, Quantum.

[36]  Adam D. Bookatz,et al.  Error suppression in Hamiltonian-based quantum computation using energy penalties , 2014, 1407.1485.

[37]  Andrew D. King,et al.  Degeneracy, degree, and heavy tails in quantum annealing , 2015, 1512.07325.

[38]  Timothy W. Finin,et al.  Quantum Annealing Based Binary Compressive Sensing with Matrix Uncertainty , 2019, ArXiv.

[39]  H. Nishimori,et al.  Quantum annealing in the transverse Ising model , 1998, cond-mat/9804280.

[40]  Andrew D. King,et al.  Algorithm engineering for a quantum annealing platform , 2014, ArXiv.

[41]  Daniel O'Malley,et al.  Pre- and post-processing in quantum-computational hydrologic inverse analysis , 2019, ArXiv.

[42]  Jérémie Roland,et al.  Anderson localization makes adiabatic quantum optimization fail , 2009, Proceedings of the National Academy of Sciences.

[43]  Daniel A. Lidar,et al.  Nested quantum annealing correction , 2015, npj Quantum Information.

[44]  J. Doll,et al.  Quantum annealing: A new method for minimizing multidimensional functions , 1994, chem-ph/9404003.

[45]  B. Chakrabarti,et al.  Colloquium : Quantum annealing and analog quantum computation , 2008, 0801.2193.

[46]  Daniel A. Lidar,et al.  Nested quantum annealing correction at finite temperature: p -spin models , 2018, Physical Review A.

[47]  Hidetoshi Nishimori,et al.  Exponential Enhancement of the Efficiency of Quantum Annealing by Non-Stoquastic Hamiltonians , 2016, Frontiers ICT.

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

[49]  Kevin C. Young,et al.  Error suppression and error correction in adiabatic quantum computation: non-equilibrium dynamics , 2013, 1307.5892.

[50]  Kevin C. Young,et al.  Error suppression and error correction in adiabatic quantum computation I: techniques and challenges , 2013, 1307.5893.

[51]  Itay Hen,et al.  Practical engineering of hard spin-glass instances , 2016, 1605.03607.

[52]  Catherine C. McGeoch,et al.  Theory versus practice in annealing-based quantum computing , 2020, Theor. Comput. Sci..

[53]  Tim Finin,et al.  Quantum-Assisted Greedy Algorithms , 2019 .

[54]  P. Shor,et al.  Error Correcting Codes For Adiabatic Quantum Computation , 2005, quant-ph/0512170.