Impact of qubit connectivity on quantum algorithm performance

Quantum computing hardware is undergoing rapid development from proof-of-principle devices to scalable machines that could eventually challenge classical supercomputers on specific tasks. On platforms with local connectivity, the transition from one- to two-dimensional arrays of qubits is seen as a natural technological step to increase the density of computing power and to reduce the routing cost of limited connectivity. Here we map and schedule representative algorithmic workloads - the Quantum Fourier Transform (QFT) relevant to factoring, the Grover diffusion operator relevant to quantum search, and Jordan-Wigner parity rotations relevant to simulations of quantum chemistry and materials science - to qubit arrays with varying connectivity. In particular we investigate the impact of restricting the ideal all-to-all connectivity to a square grid, a ladder and a linear array of qubits. Our schedule for the QFT on a ladder results in running time close to that of a system with all-to-all connectivity. Our results suggest that some common quantum algorithm primitives can be optimized to have execution times on systems with limited connectivities, such as a ladder and linear array, that are competitive with systems that have all-to-all connectivity

[1]  John M. Martinis,et al.  Logic gates at the surface code threshold: Superconducting qubits poised for fault-tolerant quantum computing , 2014 .

[2]  Katherine Bourzac,et al.  Chemistry is quantum computing’s killer app , 2017 .

[3]  Héctor Bombín.  Structure of 2D Topological Stabilizer Codes , 2011 .

[4]  Lov K. Grover.  Quantum Mechanics Helps in Searching for a Needle in a Haystack , 1997, quant-ph/9706033.

[5]  S. Lloyd,et al.  Quantum Algorithm Providing Exponential Speed Increase for Finding Eigenvalues and Eigenvectors , 1998, quant-ph/9807070.

[6]  C. Monroe,et al.  Co-designing a scalable quantum computer with trapped atomic ions , 2016, npj Quantum Information.

[7]  Robert Wille,et al.  Optimal SWAP gate insertion for nearest neighbor quantum circuits , 2014, 2014 19th Asia and South Pacific Design Automation Conference (ASP-DAC).

[8]  Amílcar Sernadas,et al.  Quantum Computation and Information , 2006 .

[9]  Simon J. Devitt,et al.  Implementation of Shor's algorithm on a linear nearest neighbour qubit array , 2004, Quantum Inf. Comput..

[10]  R. Barends,et al.  Superconducting quantum circuits at the surface code threshold for fault tolerance , 2014, Nature.

[11]  Jonas Helsen,et al.  A crossbar network for silicon quantum dot qubits , 2017, Science Advances.

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

[13]  J. Preskill,et al.  Topological quantum memory , 2001, quant-ph/0110143.

[14]  С.И. Доронин,et al.  РЕШЕНИЕ СИСТЕМ ЛИНЕЙНЫХ УРАВНЕНИЙ НА КВАНТОВОМ ПРОЦЕССОРЕ IBM QUANTUM EXPERIENCE , 2020 .

[15]  Masaki Nakanishi,et al.  An Efficient Method to Convert Arbitrary Quantum Circuits to Ones on a Linear Nearest Neighbor Architecture , 2009, 2009 Third International Conference on Quantum, Nano and Micro Technologies.

[16]  Gian Giacomo Guerreschi,et al.  Two-step approach to scheduling quantum circuits , 2018, Quantum Science and Technology.

[17]  John M. Martinis,et al.  State preservation by repetitive error detection in a superconducting quantum circuit , 2015, Nature.

[18]  E. Knill,et al.  Quantum algorithms for fermionic simulations , 2000, cond-mat/0012334.

[19]  Alireza Shafaei,et al.  Optimization of quantum circuits for interaction distance in linear nearest neighbor architectures , 2013, 2013 50th ACM/EDAC/IEEE Design Automation Conference (DAC).

[20]  Simon J. Devitt,et al.  Blueprint for a microwave trapped ion quantum computer , 2015, Science Advances.

[22]  L. DiCarlo,et al.  Scalable Quantum Circuit and Control for a Superconducting Surface Code , 2016, 1612.08208.

[23]  Isaac L. Chuang,et al.  Quantum Computation and Quantum Information (10th Anniversary edition) , 2011 .

[24]  Stephen Brierley,et al.  Efficient implementation of quantum circuits with limited qubit interactions , 2015, Quantum Inf. Comput..

[25]  Alán Aspuru-Guzik,et al.  Error Sensitivity to Environmental Noise in Quantum Circuits for Chemical State Preparation. , 2016, Journal of chemical theory and computation.

[26]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[27]  Raymond Laflamme,et al.  Erratum: Quantum algorithms for fermionic simulations [Phys. Rev. A 64, 022319 2001)] , 2002 .

[28]  S. Debnath,et al.  Demonstration of a small programmable quantum computer with atomic qubits , 2016, Nature.

[29]  Dieter Suter,et al.  Efficient implementations of the Quantum Fourier Transform: an experimental perspective , 2002 .

[30]  Peter W. Shor,et al.  Polynomial-Time Algorithms for Prime Factorization and Discrete Logarithms on a Quantum Computer , 1995, SIAM Rev..

[31]  J. Whitfield,et al.  Simulation of electronic structure Hamiltonians using quantum computers , 2010, 1001.3855.

[32]  Takao Namiki,et al.  at quantum , 2002 .

[33]  Mozammel H. A. Khan,et al.  Cost Reduction in Nearest Neighbour Based Synthesis of Quantum Boolean Circuits , 2008, Eng. Lett..

[34]  Dieter Suter,et al.  Efficient implementations of the quantum Fourier transform , 2005 .

[35]  Alireza Shafaei,et al.  Qubit placement to minimize communication overhead in 2D quantum architectures , 2014, 2014 19th Asia and South Pacific Design Automation Conference (ASP-DAC).

[36]  Alán Aspuru-Guzik,et al.  Quantum Simulation of Electronic Structure with Linear Depth and Connectivity. , 2017, Physical review letters.

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

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

[39]  Travis S. Humble,et al.  Quantum supremacy using a programmable superconducting processor , 2019, Nature.

[40]  J. R. Petta,et al.  Scalable gate architecture for a one-dimensional array of semiconductor spin qubits , 2016, 1607.07025.

[41]  Barenco,et al.  Elementary gates for quantum computation. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[42]  Angelo Bassi,et al.  Noise gates for decoherent quantum circuits , 2008, 0802.1639.

[43]  O. Gühne,et al.  03 21 7 2 3 M ar 2 00 6 Scalable multi-particle entanglement of trapped ions , 2006 .