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Related papers: Minimum Synthesis Cost of CNOT Circuits

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We study two-qubit circuits over the Clifford+CS gate set, which consists of the Clifford gates together with the controlled-phase gate CS=diag(1,1,1,i). The Clifford+CS gate set is universal for quantum computation and its elements can be…

Quantum Physics · Physics 2021-06-21 Andrew N. Glaudell , Neil J. Ross , Jacob M. Taylor

Exact synthesis provides unconditional optimality and canonical structure, but is often limited to small, carefully scoped regimes. We present an exact synthesis framework for two-qubit circuits over the Clifford+$T$ gate set that optimizes…

A CNOT circuit is the key gadget for entangling qubits in quantum computing systems. However, the qubit connectivity of noisy intermediate-scale quantum (NISQ) devices is constrained by their {limited connectivity architecture}. To improve…

Quantum Physics · Physics 2023-02-03 Bujiao Wu , Xiaoyu He , Shuai Yang , Lifu Shou , Guojing Tian , Jialin Zhang , Xiaoming Sun

Resource-efficient and high-precision approximate synthesis of quantum circuits expressed in the Clifford+T gate set is vital for Fault-Tolerant quantum computing. Efficient optimal methods are known for single-qubit RZ unitaries, otherwise…

Quantum Physics · Physics 2026-04-27 Mathias Weiden , Justin Kalloor , John Kubiatowicz , Ed Younis , Costin Iancu

We provide a simple framework for the synthesis of quantum circuits based on a numerical optimization algorithm. This algorithm is used in the context of the trapped-ions technology. We derive theoretical lower bounds for the number of…

Emerging Technologies · Computer Science 2020-04-17 Timothée Goubault de Brugière , Marc Baboulin , Benoît Valiron , Cyril Allouche

For universal quantum computation, a major challenge to overcome for practical implementation is the large amount of resources required for fault-tolerant quantum information processing. An important aspect is implementing arbitrary unitary…

Quantum Physics · Physics 2021-02-17 Gary J. Mooney , Charles D. Hill , Lloyd C. L. Hollenberg

We show the applicability of the Cartan decomposition of Lie algebras to quantum circuits. This approach can be used to synthesize circuits that can efficiently implement any desired unitary operation. Our method finds explicit quantum…

We present a simple algorithm that implements an arbitrary $n$-qubit unitary operator using a Clifford+T circuit with T-count $O(2^{4n/3} n^{2/3})$. This improves upon the previous best known upper bound of $O(2^{3n/2} n)$, while the best…

Quantum Physics · Physics 2025-10-01 Xinyu Tan

We propose two Clifford+$T$ synthesis algorithms that are optimal with respect to $T$-count. The first algorithm, called deterministic synthesis, approximates any single-qubit unitary by a single-qubit Clifford+$T$ circuit with the minimum…

Quantum Physics · Physics 2025-10-09 Hayata Morisaki , Kaoru Sano , Seiseki Akibue

Quantum circuit optimization is a central task in Quantum Computing, as current Noisy Intermediate Scale Quantum devices suffer from error propagation that often scales with the number of operations. Among quantum operations, the CNOT gate…

Artificial Intelligence · Computer Science 2026-04-16 Jacopo Cossio , Daniele Lizzio Bosco , Riccardo Romanello , Giuseppe Serra , Carla Piazza

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…

Quantum Physics · Physics 2024-12-04 Wenqi Zhang , Jinyang Liu , Zixiang Zhou , Shuai Yang

Current noisy intermediate-scale quantum (NISQ) devices can only execute small circuits with shallow depth, as they are still constrained by the presence of noise: quantum gates have error rates and quantum states are fragile due to…

Quantum Physics · Physics 2024-06-11 Shihao Zhang , Kai Huang , Lvzhou Li

We present an algorithm for compiling arbitrary unitaries into a sequence of gates native to a quantum processor. As accurate CNOT gates are hard for the foreseeable Noisy- Intermediate-Scale Quantum devices era, our A* inspired algorithm…

Emerging Technologies · Computer Science 2019-12-09 Marc Grau Davis , Ethan Smith , Ana Tudor , Koushik Sen , Irfan Siddiqi , Costin Iancu

We developed a general framework for synthesizing target gates by using a finite set of basic gates, which is a crucial step in quantum compilation. When approximating a gate in SU($n$), a naive brute-force search requires a computational…

Quantum Physics · Physics 2025-10-10 Soichiro Yamazaki , Seiseki Akibue

Quantum squaring operation is a useful building block in implementing quantum algorithms such as linear regression, regularized least squares algorithm, order-finding algorithm, quantum search algorithm, Newton Raphson division, Euclidean…

Quantum Physics · Physics 2024-06-05 Afrin Sultana , Edgard Muñoz-Coreas

The optimal cost of a three-qubit Fredkin gate is 5 two-qubit entangling gates, and the overhead climbs to 8 when restricted to controlled-not (CNOT) gates. By harnessing higher-dimensional Hilbert spaces, we reduce the cost of a…

Quantum Physics · Physics 2020-06-24 Wen-Qiang Liu , Hai-Rui Wei

Circuit synthesis is the task of decomposing a given logical functionality into a sequence of elementary gates. It is (depth-)optimal if it is impossible to achieve the desired functionality with even shorter circuits. Optimal synthesis is…

Quantum Physics · Physics 2023-06-05 Tom Peham , Nina Brandl , Richard Kueng , Robert Wille , Lukas Burgholzer

We describe a new method for approximating an arbitrary $n$ qubit unitary with precision $\varepsilon$ using a Clifford and T circuit with $O(4^{n}n(\log(1/\varepsilon)+n))$ gates. The method is based on rounding off a unitary to a unitary…

Quantum Physics · Physics 2013-06-14 Vadym Kliuchnikov

We introduce an improved CNOT synthesis algorithm that considers nearest-neighbour interactions and CNOT gate error rates in noisy intermediate-scale quantum (NISQ) hardware. Compared to IBM's Qiskit compiler, it improves the fidelity of a…

Quantum Physics · Physics 2024-05-31 Dohun Kim , Minyoung Kim , Sarah Meng Li , Michele Mosca

In the era of noisy intermediate-scale quantum (NISQ), executing quantum algorithms on actual quantum devices faces unique challenges. One such challenge is that quantum devices in this era have restricted connectivity: quantum gates are…

Quantum Physics · Physics 2020-11-16 Yao Tang