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arXiv:2311.18179

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

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

Published Nov 30, 2023• 0 citations
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Abstract

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 $X_4$ gate, Pauli $Z_4$ 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-$X_4$ gate and all of its integer powers. We have achieved both the ultra-high average gate fidelity $99.73\%$ and efficiency $99.47\%$, 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.

DOI
10.48550/arxiv.2311.18179

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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.
Universal quantum computers require fault-tolerant logical qudits, as qudits naturally align with the simulation of multi-level physical systems. Here, we present a general framework and working examples for encoding fault-tolerant logical qudits in finite-dimensional spin systems. We construct distance-333, distance-555 codewords, and general 2t+12t+12t+1-distance codes that can be implemented using a single physical qudit or a small number of coupled qudits for higher distances, while requiring a Hilbert space dimension significantly smaller than conventional constructions based on multiple logical qubits. Logical operations and error correction protocols can be implemented with polynomial scaling in the number of elementary operations. We further discuss schematic designs for physical implementation and required single-gate fidelities, which are compatible with current spin qudit platforms. This strategy provides a resource-efficient path toward realizing fault-tolerant logical qudits in finite multi-level physical systems.
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High-dimensional degrees of freedom of photons can encode more quantum information than their two-dimensional counterparts. While the increased information capacity has advantages in quantum applications (such as quantum communication), controlling and manipulating these systems has been challenging. Here we show a method to perform deterministic arbitrary high-dimensional Pauli XXX gates for single photons carrying orbital angular momentum. The XXX gate consists of a cyclic permutation of qudit basis vectors and, together with the ZZZ gate, forms the basis for performing arbitrary transformations. The proposed experimental setups only use two basic optical elements such as mode sorters and mode shifters and thus could be implemented in any system where these experimental tools are available. Furthermore the number of involved interferometers scales logarithmically with the dimension, which is important for practical implementation.