N ov 2 01 2 Efficient Distributed Quantum Computing

We provide algorithms for efficiently moving and addressing quantum memory in parallel. These imply that the standard circuit model can be simulated with low overhead by the more realistic model of a distributed quantum computer. As a result, the circuit model can be used by algorithm designers without worrying whether the underlying architecture supports the connectivity of the circuit. In addition, we apply our results to existing memory intensive quantum algorithms. We present a parallel quantum search algorithm and improve the time-space trade-off for the Element Distinctness and Collision Finding problems.

[1]  E. Szemerédi,et al.  O(n LOG n) SORTING NETWORK. , 1983 .

[2]  Leslie G. Valiant,et al.  Optimally universal parallel computers , 1988 .

[3]  Leslie G. Valiant,et al.  A bridging model for parallel computation , 1990, CACM.

[4]  E T. Leighton,et al.  Introduction to parallel algorithms and architectures , 1991 .

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

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

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

[8]  J. Cirac,et al.  Quantum State Transfer and Entanglement Distribution among Distant Nodes in a Quantum Network , 1996, quant-ph/9611017.

[9]  Charles M. Grinstead,et al.  Introduction to probability , 1999, Statistics for the Behavioural Sciences.

[10]  R. Cleve,et al.  SUBSTITUTING QUANTUM ENTANGLEMENT FOR COMMUNICATION , 1997, quant-ph/9704026.

[11]  Gilles Brassard,et al.  An exact quantum polynomial-time algorithm for Simon's problem , 1997, Proceedings of the Fifth Israeli Symposium on Theory of Computing and Systems.

[12]  Donald E. Knuth,et al.  The art of computer programming, volume 3: (2nd ed.) sorting and searching , 1998 .

[13]  Colin P. Williams,et al.  Nested Quantum Search and NP-Hard Problems , 2000, Applicable Algebra in Engineering, Communication and Computing.

[14]  G. Brassard,et al.  Quantum Amplitude Amplification and Estimation , 2000, quant-ph/0005055.

[15]  Frédéric Magniez,et al.  Quantum algorithms for element distinctness , 2000, Proceedings 16th Annual IEEE Conference on Computational Complexity.

[16]  S. Girvin,et al.  Cavity quantum electrodynamics for superconducting electrical circuits: An architecture for quantum computation , 2004, cond-mat/0402216.

[17]  Andris Ambainis,et al.  Quantum walk algorithm for element distinctness , 2003, 45th Annual IEEE Symposium on Foundations of Computer Science.

[18]  Lov K. Grover,et al.  How significant are the known collision and element distinctness quantum algorithms? , 2004, Quantum Inf. Comput..

[19]  Andris Ambainis,et al.  Quantum search algorithms , 2004, SIGA.

[20]  S. Girvin,et al.  Strong coupling of a single photon to a superconducting qubit using circuit quantum electrodynamics , 2004, Nature.

[21]  Frédéric Magniez,et al.  Quantum algorithms for the triangle problem , 2005, SODA '05.

[22]  Mike Paterson,et al.  Improved sorting networks withO(logN) depth , 1990, Algorithmica.

[23]  Mark Oskin,et al.  Architectural implications of quantum computing technologies , 2006, ACM J. Emerg. Technol. Comput. Syst..

[24]  Thierry Paul,et al.  Quantum computation and quantum information , 2007, Mathematical Structures in Computer Science.

[25]  Alain Tapp Quantum Algorithm for the Collision Problem , 2008, Encyclopedia of Algorithms.

[26]  Rodney Van Meter,et al.  Arithmetic on a distributed-memory quantum multicomputer , 2006, JETC.

[27]  Dmitri Maslov,et al.  Quantum Circuit Placement , 2008, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[28]  S. Lloyd,et al.  Architectures for a quantum random access memory , 2008, 0807.4994.

[29]  Seth Lloyd,et al.  Quantum random access memory. , 2007, Physical review letters.

[30]  D. Bernstein Cost analysis of hash collisions : will quantum computers make SHARCS obsolete? , 2009 .

[31]  R. V. Meter,et al.  DISTRIBUTED QUANTUM COMPUTATION ARCHITECTURE USING SEMICONDUCTOR NANOPHOTONICS , 2009, 0906.2686.

[32]  H. Thapliyal,et al.  Design of a comparator tree based on reversible logic , 2010, 10th IEEE International Conference on Nanotechnology.

[33]  Rodney Van Meter,et al.  On the Effect of Quantum Interaction Distance on Quantum Addition Circuits , 2008, JETC.

[34]  Masaki Nakanishi,et al.  An efficient conversion of quantum circuits to a linear nearest neighbor architecture , 2011, Quantum Inf. Comput..

[35]  Dmitri Maslov,et al.  Reversible Circuit Optimization Via Leaving the Boolean Domain , 2011, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[36]  G. Rempe,et al.  An elementary quantum network of single atoms in optical cavities , 2012, Nature.

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

[38]  Aleksandrs Belovs,et al.  Span programs for functions with constant-sized 1-certificates: extended abstract , 2011, STOC '12.

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

[40]  C. Monroe,et al.  Large-scale modular quantum-computer architecture with atomic memory and photonic interconnects , 2012, 1208.0391.