Efficient circuit compression by multiqudit entangling gates in linear optical quantum computation

2026/02/28 by Apurav Tehri, Jaskaran Singh
Computer Science · Engineering · Physics and Astronomy · #Optical Network Technologies #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #quant-ph

paper · pdf · doi:10.1103/cx92-c6cm

published as Phys. Rev. A 113, 062622 (2026) · 7+7 pages, 6 figures. Comments are welcome!

openalex publication_date 2026/06/11 · openalex created_date 2026/06/12 · openalex updated_date 2026/07/28 · arxiv created 2026/07/30 · arxiv updated 2026/07/31

Abstract

Linear optical quantum computation (LOQC) offers a promising platform for scalable quantum information processing, but its scalability is fundamentally constrained by the probabilistic nature of non-local entangling gates. Qudit circuit compression schemes mitigate this issue by encoding multiple qubits onto qudits. However, these schemes become inefficient when only a subset of the encoded qubits is required to participate in the non-local entangling gate, leading to an exponential increase in the number of non-local gates. In this Letter, we address this bottleneck by demonstrating the existence of multi-level control-Z (CZ) gates for qudits encoded in multiple spatial modes in LOQC. Unlike conventional two-level CZ gates, which act only on a single pair of modes, multi-level CZ gates impart a conditional phase shift for an arbitrarily chosen subset of the spatial modes. We present two explicit linear optical schemes that realize such operations, illustrating a fundamental trade-off between prior information about the input quantum state and the physical resources required. The first scheme is realized with a constant success probability of 1/8 independent of the qudit dimension using a single non-local entangling gate, at the cost of state dependence, which is significantly better than the current success probability of 1/9. Our second scheme provides a fully state independent realization reducing the number of non-local gates to O(2^r₁+2^r₂) as compared to the existing bound of O(2^r₁+r₂) where r₁ and r₂ are the number of qubits to be removed as control in the qudits. The success probability of the realization is (1)/(2) ((1)/(8))^2^r₁+2^r₂. When combined with qudit circuit compression schemes, our results improve upon a key scalability limitation and significantly improve the efficiency of LOQC architectures.

Citations

• Quantum circuit compression using qubit logic on qudits
• Heralded High-Dimensional Photon-Photon Quantum Gate
• Scalable improvement of the generalized Toffoli gate realization using trapped-ion-based qutrits
• A manufacturable platform for photonic quantum computing
• Experimental realization of universal quantum gates and six-qubit entangled state using photonic quantum walk
• Qudits for decomposing multiqubit gates and realizing quantum algorithms
• Why I am optimistic about the silicon-photonic route to quantum computing
• An Optimal Design for Universal Multiport Interferometers
• The Computational Complexity of Linear Optics
• Quantum computation with linear optics

Related

• Heralded High-Dimensional Photon-Photon Quantum Gate
• Quantum circuit compression using qubit logic on qudits
• Efficient qudit based scheme for photonic quantum computing
• Multi-Photon, Multi-Dimensional Hyper-Entanglement using Higher-Order Radix qudits with Applications to Quantum Computing, QKD and Quantum Teleportation
• Hybrid Path-Transverse Electric Mode Qudit Encoding on an Integrated Photonic Chip