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arXiv:2608.11733

A 12-CNOT Double Qubit Excitation Gate

Irfansha Shaik

quant-phcs.AISubmitted Aug 12, 2026• Announced Aug 13, 2026• 0 citations• Revised Aug 18, 2026 (v2)
v1 · Aug 12, 2026v2 · Aug 18, 2026v3 · Aug 27, 2026
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Abstract

In this work, we presented, to the best of our knowledge, the first reported 12-CNOT decomposition of the double qubit excitation operator. We compared our new circuit with the previous SOTA 13-CNOT circuits in 4 different metrics. Our new circuit has the lowest CNOT count (12), lowest CNOT depth (8, roughly 27% reduction), and lowest total circuit depth (15, 25% reduction) among all the previous SOTA circuits. Further, we only added 2 extra one-qubit gates compared to the lowest one-qubit gate count (11) among the previous SOTA circuits. As the double qubit excitation operator can be used as a building block hundreds or thousands of times in practical quantum algorithms, any reduction in such primitives compounds over the full circuit, resulting in significant overall resource savings.

Comments
4 pages, 5 figures, 1 table, (update figures from version 1, improved results)

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In this work, we presented, to the best of our knowledge, the first reported 12-CNOT decomposition of the double qubit excitation operator. We compared our new circuit with the previous SOTA 13-CNOT circuits in 4 different metrics. Our new circuit has the lowest CNOT count (12), lowest CNOT depth (8, roughly 27% reduction), and lowest total circuit depth (15, 25% reduction) among all the previous SOTA circuits. Further, we only added 2 extra one-qubit gates compared to the lowest one-qubit gate count (11) among the previous SOTA circuits. As the double qubit excitation operator can be used as a building block hundreds or thousands of times in practical quantum algorithms, any reduction in such primitives compounds over the full circuit, resulting in significant overall resource savings.
The preparation of nnn-qubit quantum states is a cross-cutting subroutine for many quantum algorithms, and the effort to reduce its circuit complexity is a significant challenge. In the literature, the quantum state preparation algorithm by Sun et al. is known to be optimally bounded, defining the asymptotically optimal width-depth trade-off bounds with and without ancillary qubits. In this work, a simpler algebraic decomposition is proposed to separate the preparation of the real part of the desired state from the complex one, resulting in a reduction in terms of circuit depth, total gates, and CNOT count when mmm ancillary qubits are available. The reduction in complexity is due to the use of a single operator ΛΛΛ for each uniformly controlled gate, instead of the three in the original decomposition. Using the PennyLane library, this new algorithm for state preparation has been implemented and tested in a simulated environment for both dense and sparse quantum states, including those that are random and of physical interest. Furthermore, its performance has been compared with that of Möttönen et al.'s algorithm, which is a de facto standard for preparing quantum states in cases where no ancillary qubits are used, highlighting interesting lines of development.
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Clifford circuit optimization is an important step in the quantum compilation pipeline. Major compilers employ heuristic approaches. While they are fast, their results are often suboptimal. Minimization of noisy gates, like 2-qubit CNOT gates, is crucial for practical computing. Exact approaches have been proposed to fill the gap left by heuristic approaches. Among these are SAT based approaches that optimize gate count or depth, but they suffer from scalability issues. Further, they do not guarantee optimality on more important metrics like CNOT count or CNOT depth. A recent work proposed an exhaustive search only on Clifford circuits in a certain normal form to guarantee CNOT count optimality. But an exhaustive approach cannot scale beyond 6 qubits. In this paper, we incorporate search restricted to Clifford normal forms in a SAT encoding to guarantee CNOT count optimality. By allowing parallel plans, we propose a second SAT encoding that optimizes CNOT depth. By taking advantage of flexibility in SAT based approaches, we also handle connectivity restrictions in hardware platforms, and allow for qubit relabeling. We have implemented the above encodings and variations in our open source tool Q-Synth. In experiments, our encodings significantly outperform existing SAT approaches on random Clifford circuits. We consider practical VQE and Feynman benchmarks to compare with TKET and Qiskit compilers. In all-to-all connectivity, we observe reductions up to 32.1% in CNOT count and 48.1% in CNOT depth. Overall, we observe better results than TKET in the CNOT count and depth. We also experiment with connectivity restrictions of major quantum platforms. Compared to Qiskit, we observe up to 30.3% CNOT count and 35.9% CNOT depth further reduction.
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Currently, computing paradigm is ruled by the laws of classical physics and will continue till the dimensions of transistors reaches the size of atomic particles. Quantum computing (QC) is a new technology that employs laws of quantum mechanics to address issues such as irreversibility and power dissipation that are outside the scope of conventional computing models. QC offers a powerful stage for solving complex and compound problems like searching and number factoring. A critical task in utilizing quantum physics in many application fields is circuit design using reversible quantum gates. Unitary decomposition is a popular scheme for mapping quantum algorithms to any set of elementary quantum operations. Using decomposition techniques enables transformation of unitary matrices into fundamental quantum gates, which is critical for running algorithms on prevailing quantum computers. Any 3x3 reversible quantum gate can be decomposed into single-qubit rotation gates and two qubit CNOT gates. This paper is the first to present quantum implementations of FRSG1 and JTF1 gates into CNOT gates and single qubit U3 gates with different optimization levels on a platform provided by IBM. These gates are important in a variety of practical applications like Stochastic computing and parity generation circuits. In FRSG1 the implementation count of single qubit gates decreases by 56% and the count of two qubit gates by 15% after optimization, whereas in JTF1 gate the single qubit gate count reduces by 71% and the number of two qubit gates reduces by 41%.
Multi-controlled gates are fundamental components in the design of quantum algorithms, where efficient decompositions of these operators can enhance algorithm performance. The best asymptotic decomposition of an n-controlled X gate with one borrowed ancilla into single qubit and CNOT gates produces circuits with degree 3 polylogarithmic depth and employs a divide-and-conquer strategy. In this paper, we reduce the number of recursive calls in the divide-and-conquer algorithm and decrease the depth of n-controlled X gate decomposition to a degree of 2.799 polylogarithmic depth. With this optimized decomposition, we also reduce the depth of n-controlled SU(2) gates and approximate n-controlled U(2) gates. Decompositions described in this work achieve the lowest asymptotic depth reported in the literature. We also perform an optimization in the base of the recursive approach. Starting at 52 control qubits, the proposed n-controlled X gate with one borrowed ancilla has the shortest circuit depth in the literature. One can reproduce all the results with the freely available open-source code provided in a public repository.