Minimizing resource overhead in fusion-based quantum computation using hybrid spin-photon devices

TL;DR

The paper analyzes three resource-state generation schemes for fusion-based photonic quantum computation to build a 24-photon Shor-encoded (2,2) 6-ring state and assesses their loss tolerance and hardware overhead. By comparing all-photonic, caterpillar, and repeat-until-success (RUS) architectures across resource and transmission efficiency metrics, it shows that deterministic spin-photon sources with RUS gates dramatically reduce the required number of photon sources and overall resource overhead. The results indicate that a 12-source RUS-based approach can achieve near-deterministic generation with moderate loss tolerance, offering a pathway to industrial-scale fault-tolerant photonic quantum computation far more efficiently than heralded-photon-based schemes. The discussion highlights practical rate constraints, the impact of component losses, and the potential for future hardware developments to shift the balance in favor of hybrid spin-photonic approaches.

Abstract

We present three schemes for constructing a (2,2)-Shor-encoded 6-ring photonic resource state for fusion-based quantum computing, each relying on a different type of photon source. We benchmark these architectures by analyzing their ability to achieve the loss tolerance threshold for fusion-based quantum computation using the target resource state. More precisely, we estimate their minimum hardware requirements for fault-tolerant quantum computation in terms of the number of photon sources to achieve on-demand generation of resource states with a desired generation period. Notably, we find that a group of 12 deterministic single-photon sources containing a single matter qubit degree of freedom can produce the target resource state near-deterministically by exploiting entangling gates that are repeated until success. The approach is fully modular, eliminates the need for lossy large-scale multiplexing, and reduces the overhead for resource-state generation by several orders of magnitude compared to architectures using heralded single-photon sources and probabilistic linear-optical entangling gates. Our work shows that the use of deterministic single-photon sources embedding a qubit substantially shortens the path toward fault-tolerant photonic quantum computation.

Figures (10)

• Figure 1: Stages of fusion-based quantum computation. Single photons can be combined using linear optics and measurements to produce entangled seed states, such as a linear-cluster state or a Greenberger–Horne–Zeilinger (GHZ) state. The black lines connecting photons indicate that a control-Z operation (CZ) was applied to the two photonic qubits each initially prepared in the $\ket{+}=(\ket{0}+\ket{1})/\sqrt{2}$ state. States which can be described using this representation are called graph states. Multiple seed states can be combined to construct a larger graph state, the target resource state, that is sent to a fusion network to implement fusion-based quantum computation. This work focuses on the stages up to and including the target state production.
• Figure 2: Four different sources of quantum photonic states.a. A heralded single-photon source (SPS) constructed using intense laser pulses interacting with a non-linear material to induce four-wave mixing, whereby two pump laser photons are converted into a pair of photons of different frequencies. By filtering the light in frequency and detecting the idler photon, the presence of the single-photon signal is heralded. b. A deterministic SPS constructed from a quantum dot (QD) embedded in a micropillar cavity. The QD is excited using off-resonant laser pulses and triggered to emit a single photon at its resonance frequency, which can be separated from scattered laser photons using a highly transmittive beam splitter and filter. c. A deterministic source of caterpillar graph states constructed from a deterministic SPS containing an additional matter qubit degree of freedom such as an electron spin. The source's qubit mediates entanglement between a chosen degree of freedom in successive photons such as polarization or time bin, producing a caterpillar graph state. d. A repeat-until-success (RUS) module where a switch is used to route photons entangled with the source's qubit to an entangling circuit implementing a unitary transformation $U$. Afterward, the photons are measured, and, upon success, a CZ gate is applied on the two source's qubits, thus allowing the construction of more complex graphs using fewer photons. In some case, local corrections on the source's qubits are required, which is handled by classical feedforward communication to the lasers controlling the sources.
• Figure 3: Three different schemes for constructing a Shor-encoded (2,2) 6-ring resource state. When several states need to be combined to progress to the next stage, the number is appended to the arrows. The fusion operations are boosted by generating and measuring additional auxiliary photons which are omitted for simplicity. a. An all-photonic architecture using single-photon sources that are either heralded or deterministic followed by probabilistic entanglement generation and fusion gates. b. Using a deterministic source of caterpillar graph states followed by fusion gates. c. Using a group of at least 12 deterministic caterpillar sources and repeat-until-success (RUS) CZ gates and local complementations (LC).
• Figure 4: Resource efficiency and maximal loss that each architecture can tolerate.a. The regimes where fault-tolerant quantum computing is possible using the 24-photon Shor-encoded (2, 2) 6-ring resource state are indicated by shaded areas. The square points represent the hypothetical optimal implementations presented in Table \ref{['tab:optimal']}. The curves illustrate the simulated trade-off between resource efficiency and maximal loss per component when using MUX strategies to reach RSG success probability $p_\mathrm{rsg}=99.9\%$. For the HSPS, we assume a photon generation success probability of $p_s=5\%$, representing realistic improvements over current technology. For the RUS scheme, the solid line represents a single 12-source RSG while the dashed line represents the maximum resource efficiency achieved when using spatial multiplexing to reach $r=r_0$ at the cost of increased depth $D=2$. Both RUS curves consider only temporal resource sharing. b. The number of sources needed to reach $p_\mathrm{rsg}=99.9\%$ at $r=r_0=1$ GHz for the best (RUS) and worst (HSPS) architectures shown in panel a using resource sharing, spatial multiplexing, and a maximal loss per component of $x=0.1\%$. In both plots, we define the hypothetical ideal RSG architecture represented by the star point as an RSG that is able to produce resource states with perfect resource efficiency ($\eta_R=1$) and without photons passing through any optical components after being collected from source ($\eta_x=1$) so that the loss is purely determined by the collection efficiency $\beta$.
• Figure 5: Basic linear cluster generation process. Starting with the emitter's qubit in the $\ket{+}_{qe}$ state (small purple square), a Bell state $\ket{\Psi}$ is created via the emission of a photon (small orange circle) and then transformed into a cluster state with a Hadamard gate applied to the SPS's qubit. The middle circle containing two elements represents the Bell state as a redundantly-encoded $\ket{+}$ state.