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Advanced Quantum Technologies

Effective Implementation Of Nonadiabatic Geometric Swap Gate And Fredkin Gate Of Cat‐State Qubits Using An Auxiliary Ququart

Yi‐Hao Kang, Qingwei Wang, Yang Xiao, Dong-Sheng Li, S Liu, Lijiong Shen, Yu Wang, Yan Xia

Published Jun 1, 2026• 0 citations
Publisher

Abstract

ABSTRACT We propose a feasible approach to implement nonadiabatic geometric SWAP and Fredkin gates for cat‐state qubits using Kerr‐nonlinear resonators driven by two‐photon squeezing fields. By coupling an auxiliary ququart (a four‐level system) to the resonators, a resonator‐selective transition of the ququart is achieved through precise optical control. This selective transition enables conditional flipping of the states of target cat‐state qubits based on the state of control qubits, forming the basis for high‐fidelity multi‐qubit gate operations. Leveraging this mechanism, both SWAP and Fredkin gates are realized through a fixed operational sequence, with the number of steps remaining constant regardless of the number of involved cat‐state qubits. Numerical simulations confirm robust performance under realistic conditions, including parameter inaccuracies, imbalanced couplings, inter‐resonator crosstalk, and decoherence. Therefore, this approach offers a robust and practical method for implementing nonadiabatic geometric SWAP and Fredkin gates with cat‐state qubits.

DOI
10.1002/qute.70347

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ABSTRACT We propose a feasible approach to implement nonadiabatic geometric SWAP and Fredkin gates for cat‐state qubits using Kerr‐nonlinear resonators driven by two‐photon squeezing fields. By coupling an auxiliary ququart (a four‐level system) to the resonators, a resonator‐selective transition of the ququart is achieved through precise optical control. This selective transition enables conditional flipping of the states of target cat‐state qubits based on the state of control qubits, forming the basis for high‐fidelity multi‐qubit gate operations. Leveraging this mechanism, both SWAP and Fredkin gates are realized through a fixed operational sequence, with the number of steps remaining constant regardless of the number of involved cat‐state qubits. Numerical simulations confirm robust performance under realistic conditions, including parameter inaccuracies, imbalanced couplings, inter‐resonator crosstalk, and decoherence. Therefore, this approach offers a robust and practical method for implementing nonadiabatic geometric SWAP and Fredkin gates with cat‐state qubits.
Abstract We propose an effective protocol for the implementation of nonadiabatic geometric quantum gates of cat-state qubits in Kerr-nonlinear resonators driven by two-photon squeezing drives. Coupling the Kerr-nonlinear resonators with an auxiliary qutrit with proper coupling strengths, the selective transition of the auxiliary qutrit is realized. The selective transition can be exploited in the implementation of a set of useful quantum gates, including the phase gates, the NOT gates, the controlled-phase gates, the controlled NOT gates, and the Toffoli gates. Numerical simulations show the implementations of different types of gates are robust against systematic errors, random noise, and decoherence. Therefore, the protocol may be helpful for robust and scalable quantum computation based on cat-state qubits.
Implementation of quantum logic gates with linear optical elements plays a prominent role in quantum computing due to the relatively easier manipulation and realization. We present efficient schemes to implement controlled-NOT (CNOT) gate and controlled-swap (Fredkin) gate by solely using linear optics. We encode the control qubits and target qudits in photonic polarization (two-level) and spatial degrees of freedom (ddd-level), respectively. Based on the hybrid encoding, CNOT and Fredkin gates are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Remarkably, the number of linear optics required to implement a CNOT gate has been reduced to one polarization beam splitter (PBS), while only ddd PBSs are necessary to implement a generalized Fredkin gate. The optical depths of all schemes are reduced to one and dimension-independent. Besides, the fidelity of our three-qubit Fredkin gate is higher than 99.7\% under realistic conditions, which is higher than the previous schemes.
Implementation of quantum logic gates with linear optical elements plays a prominent role in quantum computing due to their relatively easy manipulation and realization. We present efficient schemes to implement controlled-not (cnot) gates and controlled-swap (Fredkin) gates by using solely linear optics. We encode the control qubits and target qudits in photonic polarization (two-level) and spatial degrees of freedom (ddd level), respectively. On the basis of the hybrid encoding, cnot and Fredkin gates are constructed in a deterministic way without any borrowed ancillary photons or measurement-induced nonlinearities. Remarkably, the number of linear optics required to implement a cnot gate has been reduced to one polarizing beam splitter, while only ddd polarizing beam splitters are necessary to implement a generalized Fredkin gate. The optical depths of all schemes are reduced to 1 and and are dimension independent. Besides, the fidelity of our three-qubit Fredkin gate is higher than 99.7% under realistic conditions, which is higher than in previous schemes.
Summary form only given. Photonic qubit logic provides flexible, low noise scheme for quantum information processing. However, implementation of increasing scale requires numbers of resources beyond what is readily available. A recent demonstration [1] has shown how to add a control operation to existing unitary transformations, providing a practical method for moving to medium-scale quantum circuits. Here we use the entanglement-based version of this scheme to implement a complex quantum gate - the Fredkin, or 3-qubit swap gate - with significantly less resources than its decomposition into a 2-qubit gate array.In the technique proposed in [1], the Hilbert space is expended in order to have a four-level system for each qubit. Each system is composed of a qubit sub-system on which the target operation acts, and a second qubit sub-system, which remains unaffected. The control is added by gates that switch between the different subsystems according to the control qubit. Despite its conceptual simplicity, this technique still uses too many gates for practical implementations with current photonic technology. A more feasible way is a version that replaces the gates with pre-existing entanglement between the gates with qubit system and the second subsystem. The experiment is based on four possible photon pairs -called x, o, s and e - with photons either only in x and e, leading to the swapping, or only in o and s, leading to no swapping (Fig. 1). Each qubit is encoded twice and the two last modes are only used for triggering. The coincidences and the polarization beam splitter on two first mode ensure that the possibilities for the origin of the photons are linked to the state of the control qubit.The four possible photon pairs are encoding in the polarization mode coming from two polarization entangling down-conversion crystals. One crystal give a photon pair either in modes x or o and the second one a pair in mode s or e . We then separate spatially the polarization mode using beam displacer or Sagnac interferometers to preserve the phase stability (Fig . 2) . From the simulation we expect a fidelity around 85% for the truth table.
We propose a protocol to realize nonadiabatic geometric quantum computation of small-amplitude Schr\"odinger cat qubits via invariant-based reverse engineering. We consider a system with a two-photon driven Kerr nonlinearity, which can generate a pair of dressed even and odd coherent states (i.e., Schr\"odinger cat states) for fault-tolerant quantum computations. An additional coherent field is applied to linearly drive a cavity mode, to induce oscillations between dressed cat states. By designing this linear drive with invariant-based reverse engineering, we show how to implement nonadiabatic geometric quantum computation with cat qubits. The performance of the protocol is estimated by taking into account the influence of systematic errors, additive white Gaussian noise, 1/f1/f1/f noise, and decoherence including photon loss and dephasing. Numerical results demonstrate that our protocol is robust against these negative factors. Therefore, this protocol may provide a feasible method for nonadiabatic geometric quantum computation in bosonic systems.
We propose the generation of effective three-body interactions in superconducting circuits by coupling qubits or resonators to a bus qubit. Such interactions are characterized by energy exchange between two qubits or resonators depending on the state of the bus qubit. We show that a controlled-iswap (-iswap\sqrt{\mathrm{i}swap}iswap​) gate can be naturally implemented based on the three-body interactions and it can be used to construct a quantum Fredkin (controlled-swap) gate. A generalized Fredkin gate which controls the swapping of photons between two resonators can be realized in a similar way. It can be used to generate the entangled state of a high number of photons. This proposal is promising to be demonstrated with superconducting circuits previously reported and will stimulate the implementation of multiqubit quantum gates based on many-body interactions.