Fusion Based Photonic Quantum Computing

Short answer: Fusion-based quantum computing (FBQC) is a model of universal quantum computation built on generating small, constant-sized entangled resource states and performing projective entangling measurements called fusions. Its authors propose it to simplify photonic hardware by using identical modules and low-depth operations on each qubit. It is a research architecture, supported so far by theory, numerical thresholds and small laboratory demonstrations of its building blocks.

Core Operational Principles

FBQC relies on two primitive operations: the generation of small, constant-sized entangled resource states and projective entangling measurements. These measurements, referred to as fusions, are performed on the qubits of the resource states. The central principle involves constructing fusion networks from these resource states and fusion measurements. This network forms the fabric of the computation, on which an algorithm is implemented by modifying the basis of at least some of the fusion measurements. Appropriately combining the outcomes of these fusion measurements yields the output of the computation.

In photonic implementations, the lack of photon-photon interactions makes deterministic two-qubit gates challenging. Consequently, entangling gates are probabilistically implemented through measurements. In the FBQC context, photons are continuously created in small entangled resource states and rapidly measured in shallow linear-optics circuits. The quantum information survives in the system via quantum teleportation through fusion gates. These gates are entangling two-photon measurements that may be implemented probabilistically with linear-optical circuits. The backbone of the computation is a fusion network consisting of multiple entangled resource states that are routed from sources and fused together.

Architectural Simplifications and Hardware

FBQC offers significant architectural simplifications for photonic systems. It enables hardware made up of many identical modules, which simplifies manufacturing and integration. The model requires an extremely low depth of operations on each physical qubit. Additionally, it reduces the classical processing requirements compared to other approaches. An example architecture creates the fusion network by having each qubit traverse the system from left to right through specific stages. Qubits are connected to fusions via a fusion network router, which can include time delays.

Fusion devices may be reconfigurable, allowing them to make projective measurements in different bases. Classical signals from fusion measurements are fed to a classical processor responsible for decoding and algorithmic logic. There can be feedforward from this processor to adjust subsequent operations. This structure allows the non-determinism of fusion to be directly dealt with by the quantum error correction protocol, along with other errors. By tailoring the fault-tolerance framework to the physical system, the scheme can achieve a higher threshold than previously reported schemes.

Fault Tolerance and Error Models

The 2021 FBQC paper (arXiv 2101.09310, published in Nature Communications in 2023) introduced a stabilizer formalism for analyzing fault tolerance and computation in FBQC schemes. This framework naturally captures the error structure that arises in certain physical systems for quantum computation, such as photonics. Two pedagogical examples of fault-tolerant schemes have been constructed within this framework. Their thresholds were numerically evaluated under a hardware-agnostic fusion error model that includes both erasure and Pauli error.

The study also examined an error model of linear optical quantum computing with probabilistic fusion and photon loss. This capability addresses the inherent probabilistic nature of photonic fusion gates. The quantum error correction protocol manages the non-determinism of fusion alongside other errors, ensuring the robustness of the computation. This approach allows for topological fault-tolerant quantum computation to be realized within the FBQC model.

Temporal Multiplexing and Resource Generation

A 2025 Nature Communications paper reports key functionalities by temporally fusing resource states. These states are deterministically generated using a solid-state spin-photon interface. Repetitive operation of the paper leads to sequential entanglement generation. Curiously, entanglement is created between the quantum states of the same spin at two different instances in time. This temporal multiplexing of photonic entanglement provides a resource-efficient route to scaling many-body entangled systems with photons.

This method addresses the requirement for near-deterministic generation and control of constant-size entangled states. It complements the probabilistic entangling measurements required for photonic fusion gates. By using a single quantum emitter to generate entanglement across time, the architecture avoids the need for multiple independent sources for each resource state. This approach supports the continuous creation of photons in small entangled resource states necessary for the fusion network. It represents a research-stage advancement in realizing the resource generation primitive of FBQC.

FAQ

What are the two primitive operations of FBQC?

The two primitive operations are the generation of small, constant-sized entangled resource states and projective entangling measurements. These measurements are referred to as fusions and are performed on the qubits of the resource states to construct the computation network.

How does FBQC handle probabilistic fusion gates?

The non-determinism of fusion is directly dealt with by the quantum error correction protocol. This protocol manages the probabilistic nature of the entangling measurements alongside other errors, ensuring the fault-tolerance of the overall computation scheme.

What architectural simplifications does FBQC provide?

FBQC enables hardware composed of many identical modules. It requires an extremely low depth of operations on each physical qubit and reduces the classical processing requirements, simplifying the overall photonic architecture.

How are resource states generated in recent demonstrations?

Researchers have demonstrated the temporal fusion of resource states deterministically generated using a solid-state spin-photon interface. This method creates entanglement between the quantum states of the same spin at two different instances in time.