Below-threshold error reduction in single photons through photon distillation

TL;DR

This work addresses the resource-intensive challenge of correcting photon indistinguishability errors in measurement-based photonic quantum computing by introducing and experimentally validating photon distillation as a scalable, bosonic error-mitigation method. The authors establish a fundamental, optimal scaling law, showing that distilling N copies reduces the indistinguishability error as $\epsilon_{\text{indist}}' = \frac{1}{N} \epsilon_{\text{indist}} + O(\epsilon_{\text{indist}}^2)$, with Fourier-interferometer architectures achieving this bound. In a silicon-nitride photonic processor, they demonstrate a 2.2× reduction in indistinguishability (from $0.076$ to $0.034$) and a net-gain total-error reduction of about 1.2× after accounting for gate noise, demonstrating below-threshold operation. Resource estimates indicate that, for state-of-the-art sources, a photon-distillation circuit can reduce the photon-cost of a logical qubit by up to a factor of four (e.g., at $N \approx 12$), enabling substantial overhead reductions when combined with quantum error correction. The findings suggest photon distillation as a practical, complementary tool for scalable, fault-tolerant photonic quantum computing and motivate further exploration of intrinsically bosonic error-reduction strategies.

Abstract

Photonic quantum computers use the bosonic statistics of photons to construct, through quantum interference, the large entangled states required for measurement-based quantum computation. Therefore, any which-way information present in the photons will degrade quantum interference and introduce errors. While quantum error correction can address such errors in principle, it is highly resource-intensive and operates with a low error threshold, requiring numerous high-quality optical components. We experimentally demonstrate scalable, optimal photon distillation as a substantially more resource-efficient strategy to reduce indistinguishability errors in a way that is compatible with fault-tolerant operation. Photon distillation is an intrinsically bosonic, coherent error-mitigation technique which exploits quantum interference to project single photons into purified internal states, thereby reducing indistinguishability errors at both a higher efficiency and higher threshold than quantum error correction. We observe unconditional error reduction (i.e., below-threshold behaviour) consistent with theoretical predictions, even when accounting for noise introduced by the distillation gate, thereby achieving actual net-gain error mitigation under conditions relevant for fault-tolerant quantum computing. We anticipate photon distillation will find uses in large-scale quantum computers. We also expect this work to inspire the search for additional intrinsically bosonic error-reduction strategies, even for fault-tolerant architectures.

Figures (8)

• Figure 1: Schematic overview of measurement-based quantum computing without (left) and with (right) photon distillation. In both versions, single photons (depicted as particles) are consolidated into small resource states which are probabilistically combined into a larger resource state, on which a computation is performed by measurement (not shown). Photons carrying indistinguishability errors, shown as red particles, accumulate in the cluster, necessitating error correction to produce logical qubits (shown as Bloch spheres above the cluster). Photon distillation results in a smaller cluster able nonetheless to support more logical qubits due to the suppressed indistinguishability error.
• Figure 2: Schematic of the experimental platform. A laser resonantly excites an InGaAs quantum-dot single-photon source, whose photons are demultiplexed from the time domain into spatial modes and synchronised using fibre delays. A 20-mode quantum photonic processor coherently manipulates the photons according to user-specified transformations. Each output mode is individually monitored by a superconducting nanowire single-photon detector, whose signal is read out by a time-tagger to record coincident photon arrivals.
• Figure 3: Characterisation of the implemented photon-distillation gate. A) Measured indistinguishability errors and the corresponding improvements predicted by a numerical model based on the characterisation of the implemented linear interferometric transformation. B) Schematic of the implemented photon-distillation gate (top) and the characterised indistinguishability errors $\epsilon_{\text{indist}}$ of the raw input photons $\rho$ and the distilled output photons $\rho^\prime$ (bottom). Gate success is indicated by simultaneous single-photon detection at both measured outputs. Excess noise contributions are expressed as effective indistinguishability errors (interferometric transformation infidelity $\epsilon_{\text{unitary}}$, multiphoton error $\epsilon_{\text{multi}}$), which together induce the total indistinguishability error $\epsilon_{\text{tot}} \simeq \epsilon_{\text{indist}} + (1-\epsilon_{\text{indist}})\epsilon_{\text{multi}}$somhorst2025extracting. C) Simplified depiction of the preparation of a measurement-based photonic quantum computer. The lightning bolts illustrate the different steps where indistinguishability errors can compromise the computation. Throughout this figure, error bars indicate 95% confidence intervals.
• Figure 4: Effect of distillation on quantum computer resource cost. A) Resource use as a function of indistinguishability error (normalised to threshold) for different sizes $N$ of the photon-distillation scheme. Each distillation isoline shows the number of photons required to achieve a logical error $p_{\text{L}} = 10^{-10}$, with $N = 1$ representing no distillation, normalised to the requirements of the currently best-performing source. Solid lines indicate where linear error reduction, as in Eq. (\ref{['eq:OptimalFourierAsympt']}), is valid within 2%; dashed lines are shown otherwise. The points mark three state-of-the-art photon sources (SPS) [A] PsiQuantumPlatform, [B] paesani2020near, and [C] zhai2022quantum, with green squares marking probabilistic sources and orange diamonds marking deterministic sources. Inset: zoom-in to the area around source [A]. B) Resource cost for photon source [A] as a function of photon-distillation scheme size $N$, illustrating that a complementary $N = 12$ photon-distillation scheme can reduce costs by a factor of four, relative to standalone QEC. Filled markers indicate where linear error reduction is valid within 2%; open markers are shown otherwise.
• Figure 5: Transformation model for non-uniform loss simulation.$\rho(\epsilon)$ = injected photon with indistinguishability error $\epsilon$; $D_{\text{in (out)}}$ = sub-unitary diagonal matrices capturing non-uniform losses as reported in Eq. (\ref{['eq:MatrixCharacterFull']}); $U_D$ = distillation transformation matrix as reported in Eq. (\ref{['eq:MatrixU_D_Exp']}) $U_B$ = two-mode balanced beam splitter for HOM interference experiment.

Theorems & Definitions (2)

• Theorem 1: Optimality of the Fourier transform
• proof