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Quantum Science and Technology

Applications of the CCZS gate in quantum circuit synthesis

Fudong Liu, Tailyu Fan, Guo-Qiang Shu, Chunyan Zhang, Weilong Wang, Xuyan Qi, Xinxin Zhu, Hongru Yang, Yangyang Fei

Published Jul 3, 2025• 2 citations
Publisher

Abstract

Abstract Limited by the decoherence of qubits as well as the errors of quantum gates, near-term superconducting quantum computers can only run low-depth quantum circuits to achieve acceptable fidelity. One possible way to overcome these limitations is to construct quantum circuits with additional high-fidelity expressive multi-qubit gates. Recently, a new three-qubit gate, denoted as Controlled-CPHASE-SWAP (CCZS), has been implemented through simultaneous Controlled-Z (CZ) gates. The CCZS gate takes less time than a single CZ gate and can be implemented at the coherence limit. However, how to use the CCZS gate in quantum circuit synthesis remains unexplored. In this paper, we construct the quantum fan-out/parity gates, the controlled-phase gate and the locally fully connected CZ gates with the CCZS gate, respectively. Furthermore, applications of the CCZS gate in quantum error correction, quantum Fourier transform and quantum approximate optimization algorithm are also proposed. We evaluate the performance of the CCZS gate in quantum circuit synthesis through simulation and explore its potential advantages over CZ gates.

DOI
10.1088/2058-9565/adebac

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Abstract Limited by the decoherence of qubits as well as the errors of quantum gates, near-term superconducting quantum computers can only run low-depth quantum circuits to achieve acceptable fidelity. One possible way to overcome these limitations is to construct quantum circuits with additional high-fidelity expressive multi-qubit gates. Recently, a new three-qubit gate, denoted as Controlled-CPHASE-SWAP (CCZS), has been implemented through simultaneous Controlled-Z (CZ) gates. The CCZS gate takes less time than a single CZ gate and can be implemented at the coherence limit. However, how to use the CCZS gate in quantum circuit synthesis remains unexplored. In this paper, we construct the quantum fan-out/parity gates, the controlled-phase gate and the locally fully connected CZ gates with the CCZS gate, respectively. Furthermore, applications of the CCZS gate in quantum error correction, quantum Fourier transform and quantum approximate optimization algorithm are also proposed. We evaluate the performance of the CCZS gate in quantum circuit synthesis through simulation and explore its potential advantages over CZ gates.
While the common practice of decomposing general quantum algorithms into a collection of single- and two-qubit gates is conceptually simple, in many cases it is possible to have more efficient solutions where quantum gates engaging multiple qubits are used. In the noisy intermediate-scale quantum (NISQ) era where a universal error correction is still unavailable, this strategy is particularly appealing since it can significantly reduce the computational resources required for executing quantum algorithms. In this work, we experimentally investigate a three-qubit Controlled-CPHASE-SWAP (CCZS) gate on superconducting quantum circuits. By exploiting the higher energy levels of superconducting qubits, we are able to realize a Fredkin-like CCZS gate with a duration of 40 ns, which is comparable to typical single- and two-qubit gates realized on the same platform. By performing quantum process tomography for the two target qubits, we obtain a process fidelity of 86.0% and 81.1% for the control qubit being prepared in ∣0〉 and ∣1〉, respectively. We also show that our scheme can be readily extended to realize a general CCZS gate with an arbitrary swap angle. The results reported here provide valuable additions to the toolbox for achieving large-scale hardware-efficient quantum circuits.
Efficient decompositions of multi-qubit gates are essential in NISQ applications, where the number of gates or the circuit depth is limited. This paper presents efficient decompositions of CCZ and CCCZ gates, typical multi-qubit gates, under several qubit connectivities. We can construct the CCZ gate with only four CZ-depth when the qubit is square-shaped, including one auxiliary qubit. In T-shaped qubit connectivity, which has no closed loop, we can decompose the CCCZ gate with 17 CZ gates. While previous studies have shown a CCCZ gate decomposition with 14 CZ gates for the fully connected case, we found only four connections are sufficient for 14 CZ gates' implementation. The search for constraint-sufficient decompositions is aided by an optimization method we devised to bring the parameterized quantum circuit closer to the target quantum gate. We can apply this scheme to decompose any quantum gates, not only CCZ and CCCZ. Such decompositions of multi-qubit gates, together with the newly found CCZ and CCCZ decompositions, shorten the execution time of quantum circuits and improve the accuracy of complex quantum algorithms on near future QPUs.
Quantum circuit synthesis describes the process of converting arbitrary unitary operations into a gate sequence of a fixed universal gate set, usually defined by the operations native to a given hardware platform. Most current synthesis algorithms are designed to synthesize towards a set of single qubit rotations and an additional entangling two qubit gate, such as CX, CZ, or the Molmer Sorensen gate. However, with the emergence of neutral atom based hardware and their native support for gates with more than two qubits, synthesis approaches tailored to these new gate sets become necessary. In this work, we present an approach to synthesize multi controlled phase gates using ZX calculus. By representing quantum circuits as graph like ZX diagrams, one can utilize the distinct graph structure of diagonal gates to identify multi controlled phase gates inherently present in some quantum circuits even if none were explicitly defined in the original circuit. We evaluate the approach on a wide range of benchmark circuits and compare them to the standard Qiskit synthesis regarding its circuit execution time for neutral atom based hardware with native support of multi controlled gates. Our results show possible advantages for current state of the art hardware and represent the first exact synthesis algorithm supporting arbitrary sized multi controlled phase gates.
Abstract Variational algorithms such as the quantum approximate optimization algorithm have attracted attention due to their potential for solving problems using near-term quantum computers. The ZZ interaction typically generates the primitive two-qubit gate in such algorithms applied for a time, typically a variational parameter, γ. Different compilation techniques exist with respect to the implementation of two-qubit gates. Due to the importance of the ZZ-gate, we present an error analysis comparing the continuous-angle controlled phase gate (CP) against the fixed angle controlled Z-gate (CZ). We analyze both techniques under the influence of coherent over-rotation and depolarizing noise. We show that CP and CZ compilation techniques achieve comparable ZZ-gate fidelities if the incoherent error is below 0.03% and the coherent error is below 0.8%. Thus, we argue that for small coherent and incoherent error a non-parameterized two-qubit gate such as CZ in combination with virtual Z decomposition for single-qubit gates could lead to a significant reduction in the calibration required and, therefore, a less error-prone quantum device. We show that above a coherent error of 0.04π (2%), the CZ gate fidelity depends significantly on γ.
Three-qubit gates are highly beneficial operations in quantum computing, enabling compact implementations of quantum algorithms and efficient generation of multipartite entangled states. However, realizing such gates with high fidelity remains challenging due to crosstalk, complex control requirements, and the overhead of parametric or tunable couplers. In this work, we propose and analyze the implementation of fast, high-fidelity three-qubit gates using giant atoms -- artificial atoms coupled to a waveguide at multiple spatially separated points. By leveraging interference effects intrinsic to the giant-atom architecture, we demonstrate that native three-qubit gates, such as the controlled-CZ-SWAP (CCZS) and the dual-iSWAP (DIV), can be realized through simple frequency tuning, without the need for complex pulse shaping or additional hardware. We evaluate gate performance under realistic decoherence and show that fidelities exceeding 99.5% are achievable with current experimental parameters in superconducting circuits. As an application, we present a scalable protocol for preparing three- and five-qubit GHZ states using minimal gate depth, achieving high state fidelity within sub-300ns timescales. Our results position giant-atom systems as a promising platform for entangled-state preparation and low-depth quantum circuit design in near-term quantum computers and quantum simulators.
Creation and manipulation of entanglement with low error is essential in quantum information systems. In practice, two-qubit entangling gates constitute a dominant error source, limiting circuit depths and performance in fault-tolerant architectures. Using a neutral-atom quantum processor, we realize entangling CZ gates with a high Rabi frequency smooth-amplitude pulse, employing state-selective readout and qubit reuse for fast calibration, and achieve state-of-the-art fidelities of 99.854(4)% which improve to 99.941(3)% upon loss postselection, with stable performance for 10 hours. We then use these low-error gates in quantum circuits with coherent atom rearrangement. We first benchmark performance by creating and disentangling cluster states, and subsequently implement scrambling circuits featuring longer-range connectivity to study non-locally entangled states generated through chaotic dynamics. These results pave the way towards deep-circuit, efficient fault-tolerant quantum computation.