Architecture-aware synthesis of phase polynomials for NISQ devices

We propose a new algorithm to synthesise quantum circuits for phase polynomials, which takes into account the qubit connectivity of the quantum computer. We focus on the architectures of currently available NISQ devices. Our algorithm generates circuits with a smaller CNOT depth than the algorithms currently used in Staq and t$|$ket$\rangle$, while improving the runtime with respect the former.

[1]  Aleks Kissinger,et al.  CNOT circuit extraction for topologically-constrained quantum memories , 2019, Quantum Inf. Comput..

[2]  Robert Wille,et al.  An Efficient Methodology for Mapping Quantum Circuits to the IBM QX Architectures , 2017, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[3]  Ross Duncan,et al.  t|ket⟩: a retargetable compiler for NISQ devices , 2020, Quantum Science and Technology.

[4]  Jialin Zhang,et al.  Optimization of CNOT circuits on topological superconducting processors , 2019 .

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

[6]  Mathias Soeken Using ZDDs in the mapping of quantum circuits , 2019, QPL.

[7]  Robert Wille,et al.  Mapping Quantum Circuits to IBM QX Architectures Using the Minimal Number of SWAP and H Operations , 2019, 2019 56th ACM/IEEE Design Automation Conference (DAC).

[8]  John P. Hayes,et al.  Optimal synthesis of linear reversible circuits , 2008, Quantum Inf. Comput..

[9]  Michele Mosca,et al.  On the controlled-NOT complexity of controlled-NOT–phase circuits , 2018, Quantum Science and Technology.

[10]  Matthew Amy,et al.  staq -- A full-stack quantum processing toolkit , 2019 .

[11]  Dmitri Maslov,et al.  Polynomial-Time T-Depth Optimization of Clifford+T Circuits Via Matroid Partitioning , 2013, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[12]  Richard M. Karp,et al.  Reducibility Among Combinatorial Problems , 1972, 50 Years of Integer Programming.

[13]  Aleks Kissinger,et al.  Picturing Quantum Processes: A First Course in Quantum Theory and Diagrammatic Reasoning , 2017 .

[14]  Michael A. Nielsen,et al.  Quantum computing and polynomial equations over the finite field Z 2 , 2004 .

[15]  Michael A. Nielsen,et al.  Quantum computing and polynomial equations over the finite field Z2 , 2005, Quantum Inf. Comput..

[16]  Bob Coecke,et al.  Interacting quantum observables: categorical algebra and diagrammatics , 2009, ArXiv.

[17]  Ross Duncan,et al.  Phase Gadget Synthesis for Shallow Circuits , 2019, QPL.

[18]  Michele Mosca,et al.  Quantum circuit optimizations for NISQ architectures , 2019, Quantum Science and Technology.

[19]  Ross Duncan,et al.  On the qubit routing problem , 2019, TQC.