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Physical Review A

Experimental realization of high-dimensional quantum gates with ultrahigh fidelity and efficiency

Zhe Meng, Wen‐Qiang Liu, Bo-Wen Song, Xiaoyun Wang, An‐Ning Zhang, Zhang‐qi Yin

Published Feb 20, 2024• 26 citations
Publisher

Abstract

Qudit, a high-dimensional quantum system, can provide a larger Hilbert space, and it has been shown that the larger Hilbert space has remarkable advantages over the smaller one in quantum information processing. However, it is a great challenge to realize the high-fidelity quantum gates with qudits. Here we theoretically propose and experimentally demonstrate the four-dimensional quantum gates (including the generalized Pauli ${X}_{4}$ gate, Pauli ${Z}_{4}$ gate, and all of their integer powers) with optical qudits based on the polarization-spatial degree of freedom of the single photon. Furthermore, we also realize the polarization-controlled eight-dimensional controlled-${X}_{4}$ gate and all of its integer powers. The experimental results achieve both the ultrahigh average gate fidelity $99.73%$ and efficiency $99.47%$, which are above the error threshold for fault-tolerant quantum computation. Our work paves the way for the large-scale high-dimensional fault-tolerant quantum computation with a polynomial resource cost.

DOI
10.1103/physreva.109.022612

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Qudit, a high-dimensional quantum system, provides a larger Hilbert space to process the quantum information and has shown remarkable advantages over the qubit counterparts. It is a great challenge to realize the high fidelity universal quantum gates with qudits. Here we theoretically propose and experimentally demonstrate a set of universal quantum gates for a single optical qudit with four dimensions (including the generalized Pauli X4X_4X4​ gate, Pauli Z4Z_4Z4​ gate, and all of their integer powers), which are encoded in the polarization-spatial degree of freedom without multiple unstable cascaded interferometers. Furthermore, we also realize the controlled-X4X_4X4​ gate and all of its integer powers. We have achieved both the ultra-high average gate fidelity 99.73%99.73\%99.73% and efficiency 99.47%99.47\%99.47%, which are above the the error threshold for fault-tolerant quantum computation. Our work paves a way for the large-scale high-dimensional fault-tolerant quantum computation with a polynomial resource cost.
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The controlled quantum gate is an essential element for the realization of quantum computer and has been implemented in various types of two-level systems. However, high-dimensional controlled quantum gates are rarely investigated both theoretically and experimentally although high-dimensional quantum systems exhibit remarkable advantages over two-level systems for some of quantum information and computing tasks. Here we experimentally demonstrate the four-dimensional controlled X gate and its unique higher orders based on orbital-angular-momentum and polarization degrees of freedom of a single photon. The controlled gates have been examined with various input states, and all the conversion efficiency of the unitary operations are above 93% with 100% utility of photons. This work is an important step towards the goal of achieving arbitrary d-dimensional quantum circuit and paves a way for the implementation of quantum communication, computation in high-dimensional quantum systems.
Abstract Quantum gates are essential for the realization of quantum computer and have been implemented in various types of two-level systems. However, high-dimensional quantum gates are rarely investigated both theoretically and experimentally even that high-dimensional quantum systems exhibit remarkable advantages over two-level systems for some quantum information and quantum computing tasks. Here we experimentally demonstrate the four-dimensional X gate and its unique higher orders with the average conversion efficiency 93%. All these gates are based on orbital-angular-momentum degree of freedom (DoF) of single photons. Besides, a set of controlled quantum gates is implemented by use of polarization DoF. Our work is an important step toward the goal of achieving arbitrary high-dimensional quantum circuit and paves a way for the implementation of high-dimensional quantum communication and computation.
Abstract In high-dimensional quantum systems, qudits offer a richer resource than traditional two-dimensional qubits, increasing the capacity of quantum channels and enhancing the efficiency of fault-tolerant quantum computation. These advantages can be utilized to solve complex problems across various fields. In the paper, we propose a 2-qudit controlled-NOT (CNOT) gate in a 4 × 4 -dimensional space and a 3-qudit controlled-controlled-NOT (Toffoli) gate in a 4 × 4 × 4 -dimensional space, both equipped with error-heralded units. Our designs do not require auxiliary photons or extra negatively charged nitrogen-vacancy (NV−) center, resulting in saving resources. Moreover, since the imperfect NV−-cavity interaction processes are predicted in real-time by sensitive single-photon detectors, both high-dimensional CNOT and Toffoli gates boast robust fidelities using existing technology. Furthermore, our protocols simplify circuits with error-heralded units, significantly contributing to the effectiveness of quantum information technology and paving the way for advanced high-dimensional quantum computing.
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.