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

Optics Letters

Refined Kerr-effect-based high-dimensional quantum gate

Fang‐Fang Du, Xue-Mei Ren, Gang Fan, Jing Guo

Published Jan 7, 2025• 30 citations
Publisher

Abstract

High-dimensional quantum gates not only extend the existing quantum computing framework but also serve as a vital component in a range of quantum technologies. In the study, a 4 × 4-dimensional controlled-NOT (CNOT) gate is presented based on the assistance of a weak cross-Kerr medium, utilizing only two degrees of freedom (DoFs) with two photons. Specifically, the control qudits are encoded in the photonic polarization DoF, while the target qudits are encoded in the path DoF of the two photons. Notably, the circuit is constructed using only two times of the Kerr medium, outperforming a previous design that required six times, which simplifies the entire circuits. Furthermore, the fidelity and success probability of the proposed protocol are near 1 when the influence factors take the appropriate value.

DOI
10.1364/ol.547224

Related papers

Linear-optics-based high-dimensional quantum gate with qudits

Zhi‐Guo Fan, Xue-Shuo Deng, Qiulin Tan +1 more

Implementing quantum logic gates with linear optical elements is a key approach in photon-based quantum information processing (QIP) due to its operational convenience and experimental flexibility. The adoption of high-dimensional (H-D) quantum computing with qudit encoding over conventional 2-D qubit encoding offers higher information encoding capability. In this paper, we present a linear-optics-based two-qudit 4×4-D (16-D) controlled-SUM (CSUM) gate for photon systems, where the polarization degrees of freedom (DoFs) of two photons encode the 4-D control qudit and the polarization and spatial DoFs of another single photon encode the 4-D target qudit. The 16-D CSUM gate demonstrates an efficiency of 1/243 and a theoretical average fidelity of 0.98395. Additionally, the H-D CSUM gate neither requires ancillary photons and pre-shared entanglement nor presents complex quantum circuits, thus significantly reducing the experimental overhead and enhancing its feasibility with current technology.

Optics Letters•Aug 11, 2025•11 citations

Qudit-based high-dimensional controlled-not gate

Fang‐Fang Du, Xue-Mei Ren, Ming Ma +1 more

High-dimensional quantum systems expand quantum channel capacity and information storage space. By implementing high-dimensional quantum logic gates, the speed of quantum computing can be practically enhanced. We propose a deterministic 4 × 4-dimensional controlled-not (CNOT) gate for a hybrid system without ancillary qudits required, where the spatial and polarization states of a single photon serve as a control qudit of four dimensions, whereas two electron-spin states in nitrogen-vacancy (NV) centers act as a four-dimensional target qudit. As the control qudits are easily operated employing simple optical elements and the target qudits are available for storage, the CNOT gate works in a deterministic way, and it can be flexibly extended to n × n-dimensional (n > 4) quantum gates for other hybrid systems or different photonic degrees of freedoms. The efficiency and fidelity of the CNOT gate are analyzed aligning with current technological capabilities, finding that they have satisfactory performances.

Optics Letters•Feb 7, 2024•65 citations

Error-heralded high-dimensional quantum gate with robust fidelity

Fang‐Fang Du, Xue-Mei Ren, Jing Guo

Quantum computing in high-dimensional spaces holds promise for a plethora of applications, i.e., handling more intricate information and executing wider quantum operations, in complex quantum information technologies (QITs). In the paper, we set up an error-heralded, resource-saving, circuit-simplified, and 4×4-dimensional controlled-not (CNOT) gate, where the polarized and spatial state of the flying photon (i.e., the control qudit) can effectively control the collective spin wave state of two atomic ensembles (i.e., the target qudit) in two double-sided cavities. Moreover, through meticulous analysis, the feasibility of the high-dimensional gate using existing technology boasts the exceptional performance including a near-unity fidelity and high efficiency exceeding 0.95, in principle, as the undesired performances originated from the little side leakage and the finite coupling strength, and the imperfect atom-ensemble-cavity interactions are heralded by single-photon detectors. Besides, auxiliary photons or atomic ensembles are unnecessary. Therefore, our protocol stands out for its simplicity, efficient resource utilization, and real-time error prediction, contributing significantly to the efficacy of QIT and charting a promising path towards the realization of high-dimensional quantum computing endowed with heightened capabilities.

Optics Express•Aug 9, 2024•30 citations

Robust-fidelity high-dimensional controlled-controlled-SUM gate with qudits

Fang‐Fang Du, Xin‐Shan Du, Zhuoya Bai +2 more

Abstract High-dimensional (HD) quantum systems are capable of processing more complex information and performing a wider array of quantum operations, in contrast to low-dimensional (LD) quantum systems, thereby improving the speed and fault tolerance of quantum computing. In the study, we propose a deterministic qudit-encoded $4\times 4\times 4$ 4 × 4 × 4 -dimensional (64D) controlled-controlled-SUM (CCSUM) gate based on weak Kerr effect. The 64D CCSUM gate leverages the polarization and spatial degrees of freedom (DoFs) of three photons to encode 4D control and target qudits, thereby optimizing quantum resources and reducing costs. Moreover, the HD CCSUM gate functionality is implemented in a deterministic way by employing the X-Homodyne detector to measure coherent states, combined with related classical feed-forward operations. Through detailed analyses, the proposed HD CCSUM gate, under current technological conditions, exhibits robust fidelity and feasibility, offering a promising path toward the realization of HD quantum computing.

EPJ Quantum Technology•Aug 6, 2025•0 citations

Heralded hyper-CNOT gates for two-photon systems assisted by quantum scattering in waveguides

Jing-Xue Zhang, Xue-Tong Sun, Lin-Xiong Wang +2 more

Abstract Photonic hyper-parallel quantum gates play a critical role in high-capacity quantum communication and fast quantum computing. Here, based on photon scattering in one-dimensional (1D) waveguides, we present some heralded schemes for constructing four-qubit hyper-controlled-not (hyper-CNOT) gates in two-photon systems. The qubits are encoded on both the polarization and spatial-mode degrees of freedoms (DOFs) of the photons, which can simplify the quantum circuit and reduce the quantum resource consumption. In our schemes, the faulty scattering events between photons and emitters caused by system imperfections can be filtered out and discarded. That is, our protocols for hyper-CNOT gates work in a heralded way. Our calculations show that, with great progress in the emitter-waveguide systems, our photonic hyper-CNOT gates may be experimentally feasible.

Communications in Theoretical Physics•Jul 31, 2024•2 citations

Deterministic Hyperparallel Control Gates with Weak Kerr Effects

Fang‐Fang Du, Gang Fan, Xue‐Mei Ren +1 more

Abstract By harnessing weak cross‐Kerr nonlinearities, it proposes two deterministic hyperparallel quantum control gates, including the hyperparallel controlled‐NOT (hyper‐CNOT) gate and hyperparallel Fredkin (hyper‐Fredkin) gate for photonic systems in the polarization and spatial degrees of freedom (DoFs), which are composed of two procedures for the implementations of the first polarized control (CNOT and Fredkin) gates and the second spatial control (CNOT and Fredkin) ones in turn. Moreover, compared with the two two‐photon CNOT gates (three‐photon Fredkin gates) in one DoF, the hyper‐CNOT (hyper‐Fredkin) gate is provided with more straightforward quantum circuits, lower computational costs of resource overhead (without the assistance of single photons or entangled states), less cross‐Kerr nonlinear interactions between three photons and the coherent states, and reduces the effect caused by photon‐loss noise. The success probabilities of two quantum control gates are approximated unit by performing the corresponding classical feed‐forward operations based on the different measuring outcomes of the X‐homodyne detectors to be aimed at the coherent states, and they are robust against the photon loss as well, which are feasible with the current technology and convenient in practical applications.

Advanced Quantum Technologies•Aug 1, 2023•41 citations
High-dimensional quantum gates not only extend the existing quantum computing framework but also serve as a vital component in a range of quantum technologies. In the study, a 4 × 4-dimensional controlled-NOT (CNOT) gate is presented based on the assistance of a weak cross-Kerr medium, utilizing only two degrees of freedom (DoFs) with two photons. Specifically, the control qudits are encoded in the photonic polarization DoF, while the target qudits are encoded in the path DoF of the two photons. Notably, the circuit is constructed using only two times of the Kerr medium, outperforming a previous design that required six times, which simplifies the entire circuits. Furthermore, the fidelity and success probability of the proposed protocol are near 1 when the influence factors take the appropriate value.
Implementing quantum logic gates with linear optical elements is a key approach in photon-based quantum information processing (QIP) due to its operational convenience and experimental flexibility. The adoption of high-dimensional (H-D) quantum computing with qudit encoding over conventional 2-D qubit encoding offers higher information encoding capability. In this paper, we present a linear-optics-based two-qudit 4×4-D (16-D) controlled-SUM (CSUM) gate for photon systems, where the polarization degrees of freedom (DoFs) of two photons encode the 4-D control qudit and the polarization and spatial DoFs of another single photon encode the 4-D target qudit. The 16-D CSUM gate demonstrates an efficiency of 1/243 and a theoretical average fidelity of 0.98395. Additionally, the H-D CSUM gate neither requires ancillary photons and pre-shared entanglement nor presents complex quantum circuits, thus significantly reducing the experimental overhead and enhancing its feasibility with current technology.
High-dimensional quantum systems expand quantum channel capacity and information storage space. By implementing high-dimensional quantum logic gates, the speed of quantum computing can be practically enhanced. We propose a deterministic 4 × 4-dimensional controlled-not (CNOT) gate for a hybrid system without ancillary qudits required, where the spatial and polarization states of a single photon serve as a control qudit of four dimensions, whereas two electron-spin states in nitrogen-vacancy (NV) centers act as a four-dimensional target qudit. As the control qudits are easily operated employing simple optical elements and the target qudits are available for storage, the CNOT gate works in a deterministic way, and it can be flexibly extended to n × n-dimensional (n > 4) quantum gates for other hybrid systems or different photonic degrees of freedoms. The efficiency and fidelity of the CNOT gate are analyzed aligning with current technological capabilities, finding that they have satisfactory performances.
Quantum computing in high-dimensional spaces holds promise for a plethora of applications, i.e., handling more intricate information and executing wider quantum operations, in complex quantum information technologies (QITs). In the paper, we set up an error-heralded, resource-saving, circuit-simplified, and 4×4-dimensional controlled-not (CNOT) gate, where the polarized and spatial state of the flying photon (i.e., the control qudit) can effectively control the collective spin wave state of two atomic ensembles (i.e., the target qudit) in two double-sided cavities. Moreover, through meticulous analysis, the feasibility of the high-dimensional gate using existing technology boasts the exceptional performance including a near-unity fidelity and high efficiency exceeding 0.95, in principle, as the undesired performances originated from the little side leakage and the finite coupling strength, and the imperfect atom-ensemble-cavity interactions are heralded by single-photon detectors. Besides, auxiliary photons or atomic ensembles are unnecessary. Therefore, our protocol stands out for its simplicity, efficient resource utilization, and real-time error prediction, contributing significantly to the efficacy of QIT and charting a promising path towards the realization of high-dimensional quantum computing endowed with heightened capabilities.
Abstract High-dimensional (HD) quantum systems are capable of processing more complex information and performing a wider array of quantum operations, in contrast to low-dimensional (LD) quantum systems, thereby improving the speed and fault tolerance of quantum computing. In the study, we propose a deterministic qudit-encoded 4×4×44\times 4\times 44×4×4 4 × 4 × 4 -dimensional (64D) controlled-controlled-SUM (CCSUM) gate based on weak Kerr effect. The 64D CCSUM gate leverages the polarization and spatial degrees of freedom (DoFs) of three photons to encode 4D control and target qudits, thereby optimizing quantum resources and reducing costs. Moreover, the HD CCSUM gate functionality is implemented in a deterministic way by employing the X-Homodyne detector to measure coherent states, combined with related classical feed-forward operations. Through detailed analyses, the proposed HD CCSUM gate, under current technological conditions, exhibits robust fidelity and feasibility, offering a promising path toward the realization of HD quantum computing.
Abstract Photonic hyper-parallel quantum gates play a critical role in high-capacity quantum communication and fast quantum computing. Here, based on photon scattering in one-dimensional (1D) waveguides, we present some heralded schemes for constructing four-qubit hyper-controlled-not (hyper-CNOT) gates in two-photon systems. The qubits are encoded on both the polarization and spatial-mode degrees of freedoms (DOFs) of the photons, which can simplify the quantum circuit and reduce the quantum resource consumption. In our schemes, the faulty scattering events between photons and emitters caused by system imperfections can be filtered out and discarded. That is, our protocols for hyper-CNOT gates work in a heralded way. Our calculations show that, with great progress in the emitter-waveguide systems, our photonic hyper-CNOT gates may be experimentally feasible.
Abstract By harnessing weak cross‐Kerr nonlinearities, it proposes two deterministic hyperparallel quantum control gates, including the hyperparallel controlled‐NOT (hyper‐CNOT) gate and hyperparallel Fredkin (hyper‐Fredkin) gate for photonic systems in the polarization and spatial degrees of freedom (DoFs), which are composed of two procedures for the implementations of the first polarized control (CNOT and Fredkin) gates and the second spatial control (CNOT and Fredkin) ones in turn. Moreover, compared with the two two‐photon CNOT gates (three‐photon Fredkin gates) in one DoF, the hyper‐CNOT (hyper‐Fredkin) gate is provided with more straightforward quantum circuits, lower computational costs of resource overhead (without the assistance of single photons or entangled states), less cross‐Kerr nonlinear interactions between three photons and the coherent states, and reduces the effect caused by photon‐loss noise. The success probabilities of two quantum control gates are approximated unit by performing the corresponding classical feed‐forward operations based on the different measuring outcomes of the X‐homodyne detectors to be aimed at the coherent states, and they are robust against the photon loss as well, which are feasible with the current technology and convenient in practical applications.