Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

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 27, 2026 (v3)
v1 · Aug 12, 2026v2 · Aug 18, 2026v3 · Aug 27, 2026
arXivHTMLPDF

Abstract

Effective implementation of high-level quantum gates is essential for practical quantum computing. 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. With output qubit relabeling, the CNOT depth can be further reduced to 7 (roughly 36% reduction from 11). Further, we only added 2 extra 1q gates (from 11 to 13) compared to the best of the 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
5 pages, 6 figures, 1 table, (update figures from version 2, improved results)

Related papers

Algebraic Reduction to Improve an Optimally Bounded Quantum State Preparation Algorithm

Giacomo Belli, Michele Amoretti

The preparation of $n$-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 $m$ ancillary qubits are available. The reduction in complexity is due to the use of a single operator $Λ$ 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.

quant-pharXiv:2602.06535•Feb 9, 2026•0 citations

Quantum-state preparation with universal gate decompositions

Martin Plesch, Časlav Brukner

In quantum computation every unitary operation can be decomposed into quantum circuits---a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-not(cnot) gates. Two measures are important when judging the complexity of the circuit: the total number of cnot gates needed to implement it and the depth of the circuit, measured by the minimal number of computation steps needed to perform it. Here we give an explicit and simple quantum circuit scheme for preparation of arbitrary quantum states, which can directly utilize any decomposition scheme for arbitrary full quantum gates, thus connecting the two problems. Our circuit reduces the depth of the best currently known circuit by a factor of $2$. It also reduces the total number of cnot gates from ${2}^{n}$ to $\frac{23}{24}{2}^{n}$ in the leading order for even number of qubits. Specifically, the scheme allows us to decrease the upper bound from $11$ cnot gates to $9$ and the depth from $11$ to $5$ steps for four qubits. Our results are expected to help in designing and building small-scale quantum circuits using present technologies.

arXiv:1003.5760•Physical Review A•Mar 3, 2011•335 citations

Linear-Scaling Quantum Circuits for Computational Chemistry

Ilias Magoulas, Francesco A. Evangelista

High Resolution Image Download MS PowerPoint Slide We have recently constructed compact, CNOT-efficient, quantum circuits for Fermionic and qubit excitations of arbitrary many-body rank [Magoulas, I.; Evangelista, F. A. J. Chem. Theory Comput. 2023, 19, 822]. Here, we present approximations of these circuits that substantially reduce the CNOT counts even further. Our preliminary numerical data, using the selected projective quantum eigensolver approach, show up to a 4-fold reduction in CNOTs. At the same time, there is practically no loss of accuracy in the energies compared to the parent implementation, while the ensuing symmetry breaking is essentially negligible.

arXiv:2304.12870•Journal of Chemical Theory and Computation•Jul 6, 2023•11 citations

Optimal Quantum Circuit Decomposition of Reversible Gates on IBM quantum computer

Hilal Ahmad Bhat, Farooq Ahmad Khanday, Khurshed Ahmad Shah

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%.

International Conference on Multimedia, Signal Processing and Communication Technologies (IMPACT)•Nov 26, 2022•3 citations

Low-depth Quantum Circuit Decomposition of Multi-controlled Gates

Thiago Melo D. Azevedo, Jefferson D. S. Silva, Adenilton José da Silva

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.

arXiv:2407.05162•Jul 6, 2024•0 citations

Reconfigurable Quantum Instruction Set Computers for High Performance Attainable on Hardware

Zhaohui Yang, Dawei Ding, Qi Ye +3 more

The performance of current quantum hardware is severely limited. While expanding the quantum ISA with high-fidelity, expressive basis gates is a key path forward, it imposes significant gate calibration overhead and complicates compiler optimization. As a result, even though more powerful ISAs have been designed, their use remains largely conceptual rather than practical. To move beyond these hurdles, we introduce the concept of "reconfigurable quantum instruction set computers" (ReQISC), which incorporates: (1) a unified microarchitecture capable of directly implementing arbitrary 2Q gates equivalently, i.e., SU(4) modulo 1Q rotations, with theoretically optimal gate durations given any 2Q coupling Hamiltonians; (2) a compilation framework tailored to ReQISC primitives for end-to-end synthesis and optimization, comprising a program-aware pass that refines high-level representations, a program-agnostic pass for aggressive circuit-level optimization, and an SU(4)-aware routing pass that minimizes hardware mapping overhead. We detail the hardware implementation to demonstrate the feasibility, in terms of both pulse control and calibration of this superior gate scheme on realistic hardware. By leveraging the expressivity of SU(4) and the time minimality realized by the underlying microarchitecture, the SU(4)-based ISA achieves remarkable performance, with a 4.97-fold reduction in average pulse duration to implement arbitrary 2Q gates, compared to the usual CNOT/CZ scheme on mainstream flux-tunable transmons. Supported by the end-to-end compiler, ReQISC outperforms the conventional CNOT-ISA, SOTA compiler, and pulse implementation counterparts, in significantly reducing 2Q gate counts, circuit depth, pulse duration, qubit mapping overhead, and program fidelity losses. For the first time, ReQISC makes the theoretical benefits of continuous ISAs practically feasible.

quant-pharXiv:2511.06746•International Conference on Architectural Support for Programming Languages and Operating Systems (ASPLOS)•Nov 11, 2025•0 citations
Effective implementation of high-level quantum gates is essential for practical quantum computing. 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. With output qubit relabeling, the CNOT depth can be further reduced to 7 (roughly 36% reduction from 11). Further, we only added 2 extra 1q gates (from 11 to 13) compared to the best of the 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.
In quantum computation every unitary operation can be decomposed into quantum circuits---a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-not(cnot) gates. Two measures are important when judging the complexity of the circuit: the total number of cnot gates needed to implement it and the depth of the circuit, measured by the minimal number of computation steps needed to perform it. Here we give an explicit and simple quantum circuit scheme for preparation of arbitrary quantum states, which can directly utilize any decomposition scheme for arbitrary full quantum gates, thus connecting the two problems. Our circuit reduces the depth of the best currently known circuit by a factor of 222. It also reduces the total number of cnot gates from 2n{2}^{n}2n to 23242n\frac{23}{24}{2}^{n}2423​2n in the leading order for even number of qubits. Specifically, the scheme allows us to decrease the upper bound from 111111 cnot gates to 999 and the depth from 111111 to 555 steps for four qubits. Our results are expected to help in designing and building small-scale quantum circuits using present technologies.
High Resolution Image Download MS PowerPoint Slide We have recently constructed compact, CNOT-efficient, quantum circuits for Fermionic and qubit excitations of arbitrary many-body rank [Magoulas, I.; Evangelista, F. A. J. Chem. Theory Comput. 2023, 19, 822]. Here, we present approximations of these circuits that substantially reduce the CNOT counts even further. Our preliminary numerical data, using the selected projective quantum eigensolver approach, show up to a 4-fold reduction in CNOTs. At the same time, there is practically no loss of accuracy in the energies compared to the parent implementation, while the ensuing symmetry breaking is essentially negligible.
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.
The performance of current quantum hardware is severely limited. While expanding the quantum ISA with high-fidelity, expressive basis gates is a key path forward, it imposes significant gate calibration overhead and complicates compiler optimization. As a result, even though more powerful ISAs have been designed, their use remains largely conceptual rather than practical. To move beyond these hurdles, we introduce the concept of "reconfigurable quantum instruction set computers" (ReQISC), which incorporates: (1) a unified microarchitecture capable of directly implementing arbitrary 2Q gates equivalently, i.e., SU(4) modulo 1Q rotations, with theoretically optimal gate durations given any 2Q coupling Hamiltonians; (2) a compilation framework tailored to ReQISC primitives for end-to-end synthesis and optimization, comprising a program-aware pass that refines high-level representations, a program-agnostic pass for aggressive circuit-level optimization, and an SU(4)-aware routing pass that minimizes hardware mapping overhead. We detail the hardware implementation to demonstrate the feasibility, in terms of both pulse control and calibration of this superior gate scheme on realistic hardware. By leveraging the expressivity of SU(4) and the time minimality realized by the underlying microarchitecture, the SU(4)-based ISA achieves remarkable performance, with a 4.97-fold reduction in average pulse duration to implement arbitrary 2Q gates, compared to the usual CNOT/CZ scheme on mainstream flux-tunable transmons. Supported by the end-to-end compiler, ReQISC outperforms the conventional CNOT-ISA, SOTA compiler, and pulse implementation counterparts, in significantly reducing 2Q gate counts, circuit depth, pulse duration, qubit mapping overhead, and program fidelity losses. For the first time, ReQISC makes the theoretical benefits of continuous ISAs practically feasible.