Photonic Hybrid Quantum Computing

TL;DR

This review surveys hybrid photonic quantum computing, which exploits multiple photonic degrees of freedom to combine the complementary strengths of discrete and bosonic encodings, thereby significantly mitigating the challenge of weak photon-photon interactions.

Abstract

Photons are a ubiquitous carrier of quantum information: they are fast, suffer minimal decoherence, and do not require huge cryogenic facilities. Nevertheless, their intrinsically weak photon-photon interactions remain a key obstacle to scalable quantum computing. This review surveys hybrid photonic quantum computing, which exploits multiple photonic degrees of freedom to combine the complementary strengths of discrete and bosonic encodings, thereby significantly mitigating the challenge of weak photon-photon interactions. We first outline the basic principles of discrete-variable, native continuous-variable, and bosonic-encoding paradigms. We then summarise recent theoretical advances and state-of-the-art experimental demonstrations with particular emphasis on the hybrid approach. Its unique advantages, such as efficient generation of resource states and nearly ballistic (active-feedforward-free) operations, are highlighted alongside remaining technical challenges. To facilitate a clear comparison, we explicitly present the error thresholds and resource overheads required for fault-tolerant quantum computing. Our work offers a focused overview that clarifies how the hybrid approach enables scalable and compatible architectures for quantum computing.

Figures (5)

• Figure 1: BSM schemes for three types of encoding. (a) DV BSM, $\textrm{B}_\textrm{II}$, consisting of polarizing beam splitters (PBSs), a half waveplate (HWP), two quarter waveplates (QWPs), and four on-off detectors. (b) BSM in coherent-state basis, $\textrm{B}_\alpha$, implemented by a beam splitter (BS) and two PNR detectors. (c) HBSM, $\textrm{B}_\textrm{H}$, realized by separately performing two BSMs $\textrm{B}_\textrm{I}$ and $\textrm{B}_\alpha$. The red (blue) circles represent single-photon (cat-state) qubits. While the success probability of $\textrm{B}_\textrm{II}$ is 1/2, those of $\textrm{B}_\alpha$ and $\textrm{B}_\textrm{H}$ can be made arbitrarily high by increasing coherent amplitude $\alpha$.
• Figure 2: Wigner function of logical states $| 0_\textrm{L} \rangle$, $| 1_\textrm{L} \rangle$, and $| +_\textrm{L} \rangle$ for bosonic encoding schemes: (a) cat-state qubit, (b) four-headed cat code, (c) GKP code. Blue (red) regions represent positive (negative) Wigner function and orange circles show unoccupied logical space.
• Figure 3: Major steps for hybrid quantum computing. (a) In HTQC, three-qubit cluster states, two $| \mathcal{C}_3 \rangle$'s and one $| \mathcal{C}_{3^\prime} \rangle$, are fused using HBSMs to ballistically form $| \mathcal{C}_\ast \rangle$. (b) In PHTQC, two $| \mathcal{C}_\ast \rangle$'s are fused along with a $| \mathcal{C}_{3^\prime} \rangle$ to form a $| \mathcal{C}_\ast \rangle_8$ and the process can be extended to form a $| \mathcal{C}_\ast \rangle_{4n}$, where $n>2$. Here, the states are post-selected over all BSMs being successful. (c) Physical implementation of HTQC and PHTQC-$n$ requires two layers of RHG lattice to be present and the other layers are formed as the FTQC progresses by layer-by-layer measurement of qubits in $X$-basis, $M_X$. The layers are formed and interconnected by placing $| \mathcal{C}_\ast \rangle$ ($| \mathcal{C}_\ast \rangle_{4n}$) on the nodes forming edges by performing HBSMs ($n$ repeated HBSMs).
• Figure 4: Schemes for generating photonic hybrid entanglement. Single-rail hybrid entanglement is generated via (a) conditional photon addition Jeong2014a and (b) photon subtraction Morin2014a. Dual-rail hybrid entanglement is generated via (c) heralded photon detection after a DV-entangled state and a cat state pass through a beam splitter Kwon2015, and (d) coherent mixing of a cat state and superposed DV modes through a polarizing beam splitter Sychev2018a.
• Figure 5: (a) Loss-resilient entanglement swapping using hybrid pairs and $\textrm{B}_\alpha$Lim2016a. Here, $\textrm{B}_\alpha$ can be displaced with other measurements strategies such as homodyne detection for better performance depending on the loss environment Lim2016a. (b) Tele-amplification of a cat-state qubit for loss-resilient communication NeergaardNielsen2013. Teleporation (c) from a single-photon qubit to a cat-state qubit Sychev2018aDarras2023a and (d) from a cat-sate to a single-photon qubit Ulanov2017a.