Efficient circuit compression by multi-qudit entangling gates in linear optical quantum computation

• URL: http://arxiv.org/abs/2602.08394v1
• Date: Mon, 09 Feb 2026 08:52:41 GMT
• Title: Efficient circuit compression by multi-qudit entangling gates in linear optical quantum computation
• Authors: Apurav, Jaskaran Singh,
• Abstract summary: We show the existence of multi-level control ent-Z gates for qudits encoded in multiple modes in LOQC.<n>We present explicit linear optical schemes that realize such operations.<n>Our results improve upon a key scalability limitation and significantly improve the efficiency of LOQC architectures.
• Score: 1.9157770789584179
• License: http://creativecommons.org/licenses/by-sa/4.0/
• 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 $\mathcal{O}(2^{r_1}+2^{r_2})$ as compared to the existing bound of $\mathcal{O}(2^{r_1+r_2})$ where $r_1$ and $r_2$ are the number of qubits to be removed as control in the qudits. The success probability of the realization is $\frac{1}{2} \left(\frac{1}{8}\right)^{2^{r_1}+2^{r_2}}$. When combined with qudit circuit compression schemes, our results improve upon a key scalability limitation and significantly improve the efficiency of LOQC architectures.

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