Optimization of CNOT circuits on topological superconducting processors

We focus on optimization of the depth/size of CNOT circuits under topological connectivity constraints. We prove that any $n$-qubit CNOT circuit can be paralleled to $O(n)$ depth with $n^2$ ancillas for $2$-dimensional grid structure. For the high dimensional grid topological structure in which every quibit connects to $2\log n$ other qubits, we achieves the asymptotically optimal depth $O(\log n)$ with only $n^2$ ancillas. We also consider the synthesis without ancillas. We propose an algorithm uses at most $2n^2$ CNOT gates for arbitrary connected graph, considerably better than previous works. Experiments also confirmed the performance of our algorithm. We also designed an algorithm for dense graph, which is asymptotically optimal for regular graph. All these results can be applied to stabilizer circuits.

[1]  Xiaobo Zhu,et al.  Propagation and Localization of Collective Excitations on a 24-Qubit Superconducting Processor. , 2019, Physical review letters.

[2]  J. Vartiainen,et al.  Efficient decomposition of quantum gates. , 2003, Physical review letters.

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

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

[5]  P. Oscar Boykin,et al.  A new universal and fault-tolerant quantum basis , 2000, Inf. Process. Lett..

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

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

[8]  Scott Aaronson,et al.  Improved Simulation of Stabilizer Circuits , 2004, ArXiv.

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

[10]  Demetres Christofides The asymptotic complexity of matrix reduction over finite fields , 2014, ArXiv.

[11]  D. D. Awschalom,et al.  Quantum information processing using quantum dot spins and cavity QED , 1999 .

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

[13]  V.V. Shende,et al.  Synthesis of quantum-logic circuits , 2006, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[14]  Shang-Hua Teng,et al.  Optimal Space-Depth Trade-Off of CNOT Circuits in Quantum Logic Synthesis , 2019, SODA.

[15]  Yaoyun Shi Both Toffoli and controlled-NOT need little help to do universal quantum computing , 2003, Quantum Inf. Comput..

[16]  Simon J. Devitt,et al.  Mapping of Topological Quantum Circuits to Physical Hardware , 2014, Scientific Reports.

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

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

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

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

[21]  H. Neven,et al.  Characterizing quantum supremacy in near-term devices , 2016, Nature Physics.

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

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

[24]  Peter Dankelmann,et al.  Upper bounds on the Steiner diameter of a graph , 2012, Discret. Appl. Math..

[25]  Simon J. Devitt,et al.  Synthesis of Arbitrary Quantum Circuits to Topological Assembly , 2016, Scientific Reports.