We describe a family of recursive methods for the synthesis of qubit permutations on quantum computers with limited qubit connectivity. Two objectives are of importance: circuit size and depth. In each case we combine a scalable heuristic with a non-scalable, yet exact, synthesis.

This work presents tweedledum-an extensible open-source library aiming at narrowing the gap between high-level algorithms and physical devices by enhancing the expressive power of existing frameworks. For example, it allows designers to insert classical logic (defined at a high abstraction level, e.g., a Python function) directly into quantum circuits. We describe its design principles, concrete implementation, and, in particular, the library's core: An intuitive and flexible intermediate representation (IR) that supports different abstraction levels across the same circuit structure.

We present a flow for synthesizing quantum operations that are defined by classical combinational functions. The discussion will focus on out-of-place computation, i.e.,$U_{f}$:$\vert x\rangle\vert y\rangle\vert 0\rangle^{k}\rightarrow\vert x\rangle\vert y\oplus f(x)\rangle\vert 0\rangle^{k}$. Our flow allows users to express this function at a high level of abstraction. At its core, there is an improved version of the current state-of-the-art algorithm for synthesizing oracles [1]. As a result, our synthesized circuits use up to 25 % fewer qubits and up to 43 % fewer Clifford gates. Crucially, these improvements are possible without increasing the number of$T$gates nor the execution time.

We propose a flow for automated quantum compilation. Our flow takes a Boolean function implemented in Python as input and translates it into a format appropriate for reversible logic synthesis. We focus on two quantum compilation tasks: uniform state preparation and oracle synthesis. To illustrate the use of our flow, we solve IBM's virtual hackathon challenge of 2019, called the Zed city problem, an instance of vertex coloring, by using quantum search algorithms. The expressiveness of Python in combination with automated compilation algorithms allows us to express quantum algorithms at a high level of abstraction, which reduces the effort to implement them, and leads to better and more flexible implementations. We show that our proposed flow generates a lower-cost circuit implementation of the oracle needed to solve IBM's challenge when compared to the winning submission.

In this paper we consider the compilation of quantum state permutations into quantum gates for physical quantum computers. A sequence of generic single-target gates, which realize the input permutation, are extracted using a decomposition based reversible logic synthesis algorithm. We present a compilation algorithm that translates single-target gates into a quantum circuit composed of the elementary quantum gate sets that are supported by IBM's 5-qubit and 16-qubit, and Rigetti's 8-qubit and 19-qubit superconducting transmon QPUs. Compared to generic state-of-the-art compilation techniques, our technique improves gate volume and gate depth by up to 59% and 53%, respectively.

This paper proposes a fast SAT-based algorithm for recovering area applicable to an already technology mapped circuit. The algorithm considers a sequence of relatively small overlapping regions, called windows, in a mapped network and tries to improve the current mapping of each window using a SAT solver. Delay constraints are considered by interfacing the SAT solver with a timer. Experimental results are given for benchmarks that have been mapped already into 6-LUTs by a high-effort area-only synthesis/mapping flow. The new mapper starting from these results, many of which represented the best known area results at the time, achieved an additional average area reduction of 3-4%, while for some benchmarks the area reduction exceeded 10%. Runtime for any example was only a few seconds.

The fast-extract algorithm is a well-known algebraic method for factoring and decomposing Boolean expressions. Since it uses pairwise comparisons between cubes to find factors, the runtime is degraded for networks whose primary outputs are expressed in terms of primary inputs and have Boolean functions with thousands of cubes. This paper describes a new implementation of the fast-extract algorithm, fxch, having complexity linear in the number of cubes. The reduction in complexity is achieved by hashing sub-cubes and using the hash table to find good factors to extract. Experimental results on industrial benchmarks show superior runtime and scalability of the proposed algorithm, compared to the available solutions.