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Proceedings of the ACM on Programming Languages

Modular Component-Based Quantum Circuit Synthesis

Chan Gu Kang, Hakjoo Oh

Published Apr 6, 2023• 11 citations
Publisher

Abstract

In this article, we present a novel method for synthesizing quantum circuits from user-supplied components. Given input-output state vectors and component quantum gates, our synthesizer aims to construct a quantum circuit that implements the provided functionality in terms of the supplied component gates. To achieve this, we basically use an enumerative search with pruning. To accelerate the procedure, however, we perform the search and pruning at the module level; instead of simply enumerating candidate circuits by appending component gates in sequence, we stack modules, which are groups of gate operations. With this modular approach, we can effectively reduce the search space by directing the search in a way that bridges the gap between the current circuit and the input-output specification. Evaluation on 17 benchmark problems shows that our technique is highly effective at synthesizing quantum circuits. Our method successfully synthesized 16 out of 17 benchmark circuits in 96.6 seconds on average. On the other hand, the conventional, gate-level synthesis algorithm succeeded in 10 problems with an average time of 639.1 seconds. Our algorithm increased the speed of the baseline by 20.3x for the 10 problems commonly solved by both approaches.

DOI
10.1145/3586039

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In this article, we present a novel method for synthesizing quantum circuits from user-supplied components. Given input-output state vectors and component quantum gates, our synthesizer aims to construct a quantum circuit that implements the provided functionality in terms of the supplied component gates. To achieve this, we basically use an enumerative search with pruning. To accelerate the procedure, however, we perform the search and pruning at the module level; instead of simply enumerating candidate circuits by appending component gates in sequence, we stack modules, which are groups of gate operations. With this modular approach, we can effectively reduce the search space by directing the search in a way that bridges the gap between the current circuit and the input-output specification. Evaluation on 17 benchmark problems shows that our technique is highly effective at synthesizing quantum circuits. Our method successfully synthesized 16 out of 17 benchmark circuits in 96.6 seconds on average. On the other hand, the conventional, gate-level synthesis algorithm succeeded in 10 problems with an average time of 639.1 seconds. Our algorithm increased the speed of the baseline by 20.3x for the 10 problems commonly solved by both approaches.
The quantum circuit synthesis problem bridges quantum algorithm design and quantum hardware implementation in the Noisy Intermediate-Scale Quantum (NISQ) era. In quantum circuit synthesis problems, diagonal unitary synthesis plays a crucial role due to its fundamental and versatile nature. Meanwhile, experimental results have shown that moderately approximating the original algorithm to conserve quantum resources can improve the fidelity of algorithms during quantum execution. Building on this insight, we propose a quantum circuit synthesis algorithm to design diagonal unitary implementations based on specified quantum resource limits. Our algorithm can synthesize diagonal unitary for quantum circuits with up to 15 qubits on an ordinary laptop. In algorithm efficiency, synthesizing an n-qubit unitary matrix with an exact algorithm requires 2n2^n2n CNOT gates as a baseline. Within the algorithm error $\varepsilon $ range of interest (0\%-12\%), our algorithm achieves a $3.2\varepsilon $ reduction in CNOT gates on average. In runtime, the algorithm efficiently performs, synthesizing 12-qubit diagonal unitary in an average of 6.57 seconds and 15-qubit in approximately 561.71 seconds.
Quantum unitary synthesis addresses the problem of translating abstract quantum algorithms into sequences of hardware-executable quantum gates. Solving this task exactly is infeasible in general due to the exponential growth of the underlying combinatorial search space. Existing approaches suffer from misaligned optimization objectives, substantial training costs and limited generalization across different qubit counts. We mitigate these limitations by using supervised learning to approximate the minimum description length of residual unitaries and combining this estimate with stochastic beam search to identify near optimal gate sequences. Our method relies on a lightweight model with zero-shot generalization, substantially reducing training overhead compared to prior baselines. Across multiple benchmarks, we achieve faster wall-clock synthesis times while exceeding state-of-the-art methods in terms of success rate for complex circuits.
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 that 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.
Quantum circuit synthesis is one of the major areas of current research in the field of quantum computing.Analogous to its Boolean counterpart, the task involves constructing arbitrary quantum gates using only those available within a small set of universal gates that can be realized physically.However, unlike the latter, there are an infinite number of single qubit quantum gates, all of which constitute the special unitary group SU(2).Realizing any given single qubit gate using a given universal gate family is a complex task.Although gates can be synthesized to arbitrary degree of precision as long as the set of finite strings of the gate family is a dense subset of SU(2), it is desirable to accomplish the highest level of precision using only the minimum number of universal gates within the string approximation.Almost all algorithms that have been proposed for this purpose are based on the Solovay-Kitaev algorithm.The crux of the Solovay-Kitaev algorithm is the use of a procedure to decompose a given quantum gate into a pair of group commutators with the pair being synthesized separately.The Solovay-Kitaev algorithm involves group commutator decomposition in a recursive manner, with a direct approximation of a gate into a string of universal gates being performed only at the last level, i.e. in the leaf nodes of the search tree representing the execution of the Solovay-Kitaev algorithm.The main contribution of this research is in integrating conventional optimization procedures within the Solovay-Kitaev algorithm.Two specific directions of research have been studied.Firstly, optimization is incorporated within the group commutator decomposition, so that a more optimal pair of group commutators are obtained.As the degree of precision of the synthesized gate is explicitly minimized by means of this optimization procedure, the enhanced algorithm allows for more accurate quantum gates to be synthesized than what the original Solovay-Kitaev algorithm achieves.Simulation results with random gates indicate that the obtained accuracy is an order of magnitude better than before.Two versions of the new algorithm are examined, with the optimization in the first version being invoked only at the bottom level of Solovay-Kitaev algorithm and when carried out across all levels of the search tree in the next.Extensive simulations show that the second version yields better results despite equivalent computation times.Theoretical analysis of the proposed algorithm is able to provide a more formal, quantitative explanation underlying the experimentally observed phenomena.The other direction of investigation of this research involves formulating the group commutator decomposition in the form of bi-criteria optimization.This phase of research relaxed the equality constraint in the previous approach and with relaxation, a bi-criteria optimization is proposed.This optimization algorithm is new and has been devised primarily when the objective needs to be relaxed in different stages.This bi-criteria approach is able to provide comparably accurate synthesis as the previous approach.
Reversible quantum logic plays an important role in quantum computing. In this paper, we propose an approach to optimally synthesize quantum circuits by symbolic reachability analysis where the primary inputs are purely binary. we use symbolic reachability analysis, a technique most commonly used in model checking (a way of formal verification), to synthesize the optimum quantum circuits. We present an exact synthesis method with optimal quantum cost and a speedup method with non-optimal quantum cost. Both our methods guarantee the synthesizeability of all reversible circuits. Unlike previous works which use permutative reversible gates, we use a lower level library which includes non-permutative quantum gates. For the first time, problems in quantum logic synthesis have been reduced to those of multiple-valued logic synthesis thus reducing the search space and algorithm complexity. We synthesized quantum circuits for gate, half-adder, full-adder, etc. with the smallest cost.. Our approach obtains the minimum cost quantum circuits for Miller's gate, half-adder, and full-adder, which are better than previous results. In addition, we prove the minimum quantum cost (using our elementary quantum gates) for Fredkin, Peres, and Toffoli gates. Our work constitutes the first successful experience of applying satisfiability with formal methods to quantum logic synthesis.
Quantum computers, more specifically quantum circuits, take on the eyes with their computational promises such as reversibility. In this paper, we perform synthesis and optimization of quantum circuits. In the first part, we propose a fast synthesis algorithm that implements any given reversible Boolean function with quantum gates. Instead of an exhaustive search on every given function, our algorithm creates a library of essential functions and performs sorting. As an example, to implement 4 bit circuits we only use 120 essential functions out of all 20922789888000 functions. In the second part, we optimize our circuits by using new templates. The proposed templates mainly consist of Toffoli gates with negative and positive controlling lines. These templates also show us that optimum area solutions proposed in the literature are not actually optimum; they can be improved.