Fusion-Based Photonic Qubit

Figure

Description

Fusion-based quantum computing (FBQC) is a photonic architecture proposed by Bartolucci et al. (2023) and developed primarily by PsiQuantum. Rather than building large entangled cluster states deterministically and then measuring them (as in standard measurement-based QC), FBQC uses small, constant-size entangled photonic resource states that are stitched together at computation time via probabilistic fusion gates.

A Type II fusion gate is a destructive Bell-state measurement on one photon from each of two resource states, projecting the remaining photons into a larger entangled state. Each fusion succeeds with probability $\le 50\%$ using linear optics alone (boosted to $\sim 75\%$ with ancilla photons). The architecture is designed to tolerate this high failure rate: the resource states (e.g., 6-ring states or small graph states) are chosen so that the resulting entanglement structure remains percolated and supports fault-tolerant computation even when roughly half of all fusions fail.

The key advantage of FBQC is that it requires only constant-depth optical circuits: resource state generation is a fixed-size problem (not scaling with computation size), and fusions are local two-photon operations. This is compatible with photonic chip manufacturing, where reproducing many identical small circuits is far easier than building one large reconfigurable circuit.

Hamiltonian

Photonic qubits are non-interacting; computation is performed through measurement. The relevant formalism is the fusion gate operation rather than a Hamiltonian.

A Type II fusion on two photonic qubits (one from each resource state) implements a projective Bell-state measurement:

${\Pi }_{\text{fusion}}^{\pm }=|{\Phi }^{\pm }⟩⟨{\Phi }^{\pm }|$

where $|{\Phi }^{\pm }⟩=\frac{1}{\sqrt{2}}(|00⟩\pm |11⟩)$ in the dual-rail encoding.

The fusion succeeds with probability $p_{\text{success}}\le 1/2$ (linear optics bound) or $p_{\text{success}}\le 3/4$ with single ancilla photon boosting:

$p_{\text{success}}^{\text{boosted}}=\frac{1}{2}+\frac{1}{4}{\eta }_{\text{ancilla}}$

The resource state is a small entangled graph state:

$|G⟩={\prod }_{(i,j)\in E}C{Z}_{ij}|+{⟩}^{\otimes n}$

where $E$ is the edge set of the resource graph (e.g., a 6-ring: $n=6$, $E=\{(1,2),(2,3),\dots ,(6,1)\}$).

Motivation

Photonic quantum computing offers room-temperature operation, high clock speeds, and natural connectivity to quantum networks. However, photon-photon interactions are negligible, making deterministic two-qubit gates impossible with linear optics (KLM theorem). FBQC embraces this probabilistic nature: instead of demanding deterministic gates, it designs a fault-tolerant architecture around probabilistic fusion operations, tolerating failure rates up to $\sim 50\%$ through topological redundancy in the resource state structure. This makes large-scale photonic quantum computing architecturally viable using only single-photon sources, linear optical circuits, and photon detectors — all of which are amenable to semiconductor manufacturing.

Key Findings

• Fault-tolerant threshold of $\sim 50\%$ fusion failure rate demonstrated theoretically, matching the linear optical bound (Bartolucci et al. 2023).
• Topological fault tolerance via Raussendorf lattice or foliated surface code structure survives below-threshold fusion failures and photon loss (Bombin et al. 2021).
• 6-ring resource states identified as minimal resource states sufficient for universal fault-tolerant FBQC.
• Architecture requires $O(1)$ optical depth per resource state, enabling chip-scale photonic manufacturing.
• PsiQuantum targeting $>10^6$ photonic qubits using silicon photonic chips with integrated single-photon sources and detectors.

Key Metrics

Metric	Value	Notes	Fidelity reference
Fusion success probability	~50% (linear optics)	Up to ~75% with boosting	Bartolucci et al. 2023
Loss tolerance threshold	~2–3% per photon	Below this photon loss rate, fault tolerance achieved	Bombin et al. 2021
Resource state size	6 photons (6-ring)	Minimal for fault-tolerant FBQC	Bartolucci et al. 2023
Optical depth per resource state	$O(1)$	Constant, does not scale with computation	Bartolucci et al. 2023
Clock speed	~GHz	Limited by photon generation and detection rates	—
Operating temperature	300 K (photonic) / 1–4 K (detectors)	SNSPDs require cryogenics	—
Target qubit count	>10⁶	PsiQuantum silicon photonic platform	—

Linked Papers

• bartolucci-2023-fbqc
• bombin-2021-interleaving

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