Parallelizing quantum circuit synthesis

Quantum circuit synthesis is the process in which an arbitrary unitary operation is decomposed into a sequence of gates from a universal set, typically one which a quantum computer can implement both efficiently and fault-tolerantly. As physical implementations of quantum computers improve, the need is growing for tools which can effectively synthesize components of the circuits and algorithms they will run. Existing algorithms for exact, multi-qubit circuit synthesis scale exponentially in the number of qubits and circuit depth, leaving synthesis intractable for circuits on more than a handful of qubits. Even modest improvements in circuit synthesis procedures may lead to significant advances, pushing forward the boundaries of not only the size of solvable circuit synthesis problems, but also in what can be realized physically as a result of having more efficient circuits. We present a method for quantum circuit synthesis using deterministic walks. Also termed pseudorandom walks, these are walks in which once a starting point is chosen, its path is completely determined. We apply our method to construct a parallel framework for circuit synthesis, and implement one such version performing optimal $T$-count synthesis over the Clifford+$T$ gate set. We use our software to present examples where parallelization offers a significant speedup on the runtime, as well as directly confirm that the 4-qubit 1-bit full adder has optimal $T$-count 7 and $T$-depth 3.

[1]  Paul C. van Oorschot,et al.  Improving Implementable Meet-in-the-Middle Attacks by Orders of Magnitude , 1996, CRYPTO.

[2]  Clifford Stein,et al.  Introduction to Algorithms, 2nd edition. , 2001 .

[3]  Y. Gurevich,et al.  Efficient decomposition of single-qubit gates intoVbasis circuits , 2013, 1303.1411.

[4]  M. Mosca,et al.  A Meet-in-the-Middle Algorithm for Fast Synthesis of Depth-Optimal Quantum Circuits , 2012, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems.

[5]  Michele Mosca,et al.  An algorithm for the T-count , 2013, Quantum Inf. Comput..

[6]  Dmitri Maslov,et al.  Practical Approximation of Single-Qubit Unitaries by Single-Qubit Quantum Clifford and T Circuits , 2012, IEEE Transactions on Computers.

[7]  Peter Selinger,et al.  Exact synthesis of multi-qubit Clifford+T circuits , 2012, ArXiv.

[8]  Michael A. Nielsen,et al.  The Solovay-Kitaev algorithm , 2006, Quantum Inf. Comput..

[9]  R. Stephenson.  A and V , 1962, The British journal of ophthalmology.

[10]  Dmitri Maslov,et al.  Asymptotically optimal approximation of single qubit unitaries by Clifford and T circuits using a constant number of ancillary qubits , 2012, Physical review letters.

[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]  Martin Rötteler,et al.  Efficient synthesis of universal Repeat-Until-Success circuits , 2014, Physical review letters.

[13]  Krysta Marie Svore,et al.  Efficient approximation of diagonal unitaries over the Clifford+T basis , 2014, Quantum Inf. Comput..

[14]  Martin Rötteler,et al.  Quantum arithmetic and numerical analysis using Repeat-Until-Success circuits , 2014, Quantum Inf. Comput..

[15]  Neal Koblitz,et al.  Advances in Cryptology — CRYPTO ’96 , 2001, Lecture Notes in Computer Science.

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

[17]  Peter Selinger,et al.  Efficient Clifford+T approximation of single-qubit operators , 2012, Quantum Inf. Comput..

[18]  S. Aaronson,et al.  Improved simulation of stabilizer circuits (14 pages) , 2004 .

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

[20]  I. Chuang,et al.  Quantum Computation and Quantum Information: Bibliography , 2010 .

[21]  Rolf Rabenseifner,et al.  Hybrid Parallel Programming: Performance Problems and Chances , 2003 .

[22]  Vadym Kliuchnikov,et al.  A framework for exact synthesis , 2015, ArXiv.

[23]  Georg Hager,et al.  Hybrid MPI/OpenMP Parallel Programming on Clusters of Multi-Core SMP Nodes , 2009, 2009 17th Euromicro International Conference on Parallel, Distributed and Network-based Processing.

[24]  Philippe Oechslin,et al.  Making a Faster Cryptanalytic Time-Memory Trade-Off , 2003, CRYPTO.

[25]  David McKinnon,et al.  Exact synthesis of single-qubit unitaries over Clifford-cyclotomic gate sets , 2015, 1501.04944.

[26]  Neil J. Ross,et al.  Optimal ancilla-free Clifford+T approximation of z-rotations , 2014, Quantum Inf. Comput..

[27]  Paul C. van Oorschot,et al.  Parallel Collision Search with Cryptanalytic Applications , 2013, Journal of Cryptology.

[28]  Dmitri Maslov,et al.  Fast and efficient exact synthesis of single-qubit unitaries generated by clifford and T gates , 2012, Quantum Inf. Comput..