Quantum circuit optimization by topological compaction in the surface code

The fragile nature of quantum information limits our ability to construct large quantities of quantum bits suitable for quantum computing. An important goal, therefore, is to minimize the amount of resources required to implement quantum algorithms, many of which are serial in nature and leave large numbers of qubits idle much of the time unless compression techniques are used. Furthermore, quantum error-correcting codes, which are required to reduce the effects of noise, introduce additional resource overhead. We consider a strategy for quantum circuit optimization based on topological deformation in the surface code, one of the best performing and most practical quantum error-correcting codes. Specifically, we examine the problem of minimizing computation time on a two-dimensional qubit lattice of arbitrary, but fixed dimension, and propose two algorithms for doing so.

[1]  Austin G. Fowler,et al.  Topological code Autotune , 2012, 1202.6111.

[2]  R. V. Meter,et al.  Layered architecture for quantum computing , 2010, 1010.5022.

[3]  Robert Raussendorf,et al.  Fault-tolerant quantum computation with high threshold in two dimensions. , 2007, Physical review letters.

[4]  Checking the error correction strength of arbitrary surface code logical gates , 2012, 1210.4249.

[5]  Austin G. Fowler,et al.  Surface code with decoherence: An analysis of three superconducting architectures , 2012, 1210.5799.

[6]  S. Bravyi,et al.  Magic-state distillation with low overhead , 2012, 1209.2426.

[7]  Ben W. Reichardt,et al.  Error-detection-based quantum fault tolerance against discrete pauli noise , 2006 .

[8]  Hans-J. Briegel,et al.  Computational model underlying the one-way quantum computer , 2002, Quantum Inf. Comput..

[9]  J. Britton,et al.  Toward scalable ion traps for quantum information processing , 2009, 0909.2464.

[10]  Cody Jones,et al.  Multilevel distillation of magic states for quantum computing , 2012, 1210.3388.

[11]  T. M. Hsieh,et al.  Two-dimensional layout compaction by simulated annealing , 1988, 1988., IEEE International Symposium on Circuits and Systems.

[12]  Robert Wille,et al.  Synthesis of quantum circuits for linear nearest neighbor architectures , 2011, Quantum Inf. Process..

[13]  Martin Nilsson,et al.  Parallel Quantum Computation and Quantum Codes , 2001, SIAM J. Comput..

[14]  Guntram Scheithauer.  Algorithms for the Container Loading Problem , 1992 .

[15]  A. Fowler,et al.  A bridge to lower overhead quantum computation , 2012, 1209.0510.

[16]  Pinaki Mazumder,et al.  VLSI cell placement techniques , 1991, CSUR.

[17]  Stephen G. Kobourov,et al.  Spring Embedders and Force Directed Graph Drawing Algorithms , 2012, ArXiv.

[18]  E. Knill.  Quantum Computing with Very Noisy Devices , 1998 .

[19]  David P. DiVincenzo,et al.  Fault-tolerant architectures for superconducting qubits , 2009, 0905.4839.

[20]  Austin G. Fowler,et al.  A primer on surface codes: Developing a machine language for a quantum computer , 2012 .

[21]  D. Loss,et al.  Prospects for Spin-Based Quantum Computing in Quantum Dots , 2012, 1204.5917.

[22]  M. Mariantoni,et al.  Surface codes: Towards practical large-scale quantum computation , 2012, 1208.0928.

[23]  Richard Cleve,et al.  Fast parallel circuits for the quantum Fourier transform , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[24]  Thomas G. Draper,et al.  A new quantum ripple-carry addition circuit , 2004, quant-ph/0410184.

[25]  Simon J. Devitt,et al.  Surface code implementation of block code state distillation , 2013, Scientific Reports.

[26]  Rainer Blatt,et al.  Two-dimensional arrays of radio-frequency ion traps with addressable interactions , 2011, 1103.5428.

[27]  Austin G. Fowler,et al.  Cavity grid for scalable quantum computation with superconducting circuits , 2007, 0706.3625.

[28]  Elham Kashefi,et al.  Parallelizing quantum circuits , 2007, Theor. Comput. Sci..

[29]  Jeremy Levy,et al.  Quantum-dot cluster-state computing with encoded qubits , 2005, quant-ph/0506032.

[30]  Jeremy Levy.  Quantum-information processing with ferroelectrically coupled quantum dots , 2001 .

[31]  Robert D. Carr,et al.  Implications of electronics constraints for solid-state quantum error correction and quantum circuit failure probability , 2011, 1105.0682.

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

[33]  Robert Raussendorf,et al.  Topological fault-tolerance in cluster state quantum computation , 2007 .

[34]  Chak-Kuen Wong,et al.  An Algorithm to Compact a VLSI Symbolic Layout with Mixed Constraints , 1983, 20th Design Automation Conference Proceedings.

[35]  E. Knill.  Quantum computing with realistically noisy devices , 2005, Nature.

[36]  Austin G. Fowler,et al.  Time-optimal quantum computation , 2012, 1210.4626.

[37]  W. Munro,et al.  Architectural design for a topological cluster state quantum computer , 2008, 0808.1782.

[38]  Ben Reichardt,et al.  Fault-tolerant ancilla preparation and noise threshold lower bounds for the 23-qubit Golay code , 2011, Quantum Inf. Comput..

[39]  L. Kauffman.  Knots And Physics , 1991 .

[40]  Gerhard W. Dueck,et al.  Quantum Circuit Simplification and Level Compaction , 2006, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[41]  A. Kitaev,et al.  Universal quantum computation with ideal Clifford gates and noisy ancillas (14 pages) , 2004, quant-ph/0403025.

[42]  Emanuel Knill,et al.  Magic-state distillation with the four-qubit code , 2012, Quantum Inf. Comput..

[43]  A. Fowler.  Low-overhead surface code logical H , 2012 .

[44]  Elham Kashefi,et al.  Global Quantum Circuit Optimization , 2013, 1301.0351.

[45]  Andrew M. Steane,et al.  Fast fault-tolerant filtering of quantum codewords , 2008 .

[46]  Chak-Kuen Wong,et al.  An algorithm for optimal two-dimensional compaction of VLSI layouts , 1983, Integr..