To implement quantum algorithms on quantum computers it is crucial to decompose their operators into the limited gate set supported by those computers. Unfortunately, existing works automating this essential task are generally slow and only applicable to narrow use cases.We present Synthetiq, a method to synthesize quantum circuits implementing a given specification over arbitrary finite gate sets, which is faster and more versatile than existing works. Synthetiq utilizes Simulated Annealing instantiated with a novel, domain-specific energy function that allows developers to leverage partial specifications for better efficiency. Synthetiq further couples this synthesis method with a custom simplification pass, to ensure efficiency of the found circuits. We experimentally demonstrate that Synthetiq can generate better implementations than were previously known for multiple relevant quantum operators including RCCCX, CCT, CCiSWAP, C√SWAP, and C√iSWAP. Our extensive evaluation also demonstrates Synthetiq frequently outperforms a wide variety of more specialized tools in their own domains, including (i) the well-studied task of synthesizing fully specified operators in the Clifford+T gate set, (ii) є-approximate synthesis of multi-qubit operators in the same gate set, and (iii) synthesis tasks with custom gate sets. On all those tasks, Synthetiq is typically one to two orders of magnitude faster than previous state-of-the-art and can tackle problems that were previously out of the reach of any synthesis tool.
To implement quantum algorithms on quantum computers it is crucial to decompose their operators into the limited gate set supported by those computers. Unfortunately, existing works automating this essential task are generally slow and only applicable to narrow use cases.We present Synthetiq, a method to synthesize quantum circuits implementing a given specification over arbitrary finite gate sets, which is faster and more versatile than existing works. Synthetiq utilizes Simulated Annealing instantiated with a novel, domain-specific energy function that allows developers to leverage partial specifications for better efficiency. Synthetiq further couples this synthesis method with a custom simplification pass, to ensure efficiency of the found circuits. We experimentally demonstrate that Synthetiq can generate better implementations than were previously known for multiple relevant quantum operators including RCCCX, CCT, CCiSWAP, C√SWAP, and C√iSWAP. Our extensive evaluation also demonstrates Synthetiq frequently outperforms a wide variety of more specialized tools in their own domains, including (i) the well-studied task of synthesizing fully specified operators in the Clifford+T gate set, (ii) є-approximate synthesis of multi-qubit operators in the same gate set, and (iii) synthesis tasks with custom gate sets. On all those tasks, Synthetiq is typically one to two orders of magnitude faster than previous state-of-the-art and can tackle problems that were previously out of the reach of any synthesis tool.
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.
It is important to construct quantum algorithms within shallow-depth quantum circuits due to the current imperfections and decoherence in quantum devices. Efficient quantum circuit synthesis and optimization are critical tasks that generate relatively small quantum circuits tailored to specific requirements. However, an efficient circuit may vary depending on the physical realization platforms of quantum computers. For example, the Clifford+T gate library has recently gained prominence for its superior fault tolerance and error correction capabilities, but the T gate dominates circuit execution time. Therefore, the objectives of synthesis algorithms in this gate set include reducing T-depth and T-count, as well as overall circuit depth and gate count. Most traditional synthesis methods produce a single optimized circuit. In contrast, this study introduces a multi-objective quantum-inspired tabu search algorithm in quantum circuit synthesis to construct a diverse set of optimized circuits based on four distinct metrics. The values of these metrics in the optimized circuit display the entanglement relationship, and the proposed method simulates the formula to assist in building the entangled optimal circuit. Results show that the construction of the Pareto front can flexibly offer a variety of functionally equivalent circuits that adapt to advancements in quantum technology. Providing multiple optimized circuit structures facilitates circuit replacement and further simplification, thereby enhancing the development of quantum computing.
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 2n 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.
This work contains the analysis of results received after running synthesized quantum circuits for training perceptron neural networks. The training is performed by creating a Grover’s algorithm with a custom oracle function. The concept of synthesizing quantum circuits was showcased in the process of generating training circuits for three perceptron topologies, which were designed to test the accuracy of the synthesis process. The test circuits serve to prove that the proposed synthesis approach could be scaled to utilize more complex quantum computing systems and to solve more practical tasks. IBM’s 100-qubit cloud quantum simulator was used as the debugging environment. Quantum circuits for described algorithms are generated by the "Naginata" quantum synthesizer, its source code is published and further documented on GitHub along with the code for the provided example algorithms. The article describes the processes behind the algorithm for synthesizing quantum circuits that perform the training process of single-layer perceptrons by finding their weights by filtering all possible input values through a predefined accuracy criterion. Since quantum computing is still in its early development phase, quantum circuits are created mainly by manual placement of logic elements. Implementing quantum algorithms, especially more use-case specific ones, directly on the quantum circuit level could lead to the circuit easily becoming too complex for human comprehension. Quantum Circuit Synthesizer "Naginata" was created to simplify the development and debugging process of quantum algorithms, by adding better clarity to their development process. In our case, better clarity for the development process is achieved by composing functions for commonly used operations performed in the implemented quantum algorithm. The programmer could now implement the quantum algorithm as a set of functions, instead of manually creating a circuit from single logic elements. After this, the synthesizer would handle the task of creating the data for placing logic elements on the circuit. This enables an opportunity of implementing quantum algorithms with higher-level commands. In the scope of this work, parametrically generated generic blocks for frequently used operations such as: the adder, multiplier and digital comparator were created and utilized to form the training circuits. The test results, proved that with the help of the proposed quantum synthesizer, these compositions could be used efficiently as building blocks for implementing quantum algorithms. And by visually comparing sizes of both code and circuit representations of the synthesized circuits, to the code examples used to synthesize these circuits, it is determined that the proposed approach for implementing quantum circuits greatly simplifies the processes of development and debugging a quantum algorithm.
The primary objective of quantum circuit synthesis is to efficiently and accurately realize specific quantum algorithms or operations utilizing a predefined set of quantum gates, while also optimizing the circuit size. It holds a pivotal position in Noisy Intermediate-Scale Quantum (NISQ) computation. Historically, most synthesis efforts have predominantly utilized CNOT or CZ gates as the 2-qubit gates. However, the SQiSW gate, also known as the square root of iSWAP gate, has garnered considerable attention due to its outstanding experimental performance with low error rates and high efficiency in 2-qubit gate synthesis. In this paper, we investigate the potential of the SQiSW gate in various synthesis problems by utilizing only the SQiSW gate along with arbitrary single-qubit gates, while optimizing the overall circuit size. For exact synthesis, the upper bound of SQiSW gates to synthesize arbitrary 3-qubit and n -qubit gates are 24 and 139 192 4 n ( 1 + o ( 1 ) ) respectively, which relies on the properties of SQiSW gate in Lie theory and Quantum Shannon Decomposition. We also introduce an exact synthesis scheme for Toffoli gate using only 8 SQiSW gates, which is grounded in numerical observation. More generally, with respect to numerical approximations, we provide a theoretical analysis of a pruning algorithm to reduce the size of the searching space in numerical experiment to 1 12 + o ( 1 ) of previous size, helping us reach the result that 11 SQiSW gates are enough in arbitrary 3-qubit gates synthesis up to an acceptable numerical error.