Mitigating quantum operation infidelity through engineering the distribution of photon losses

TL;DR

The paper addresses how photon-loss distributions in multiport interferometers influence the fidelity of linear-optical quantum operations. It develops a framework based on lossy transformations $T$, their purified representations, and metrics such as $\mathcal{F}(U,T)$ and $\Lambda$ to evaluate performance under symmetric (rectangular) versus asymmetric (triangular) loss configurations. Across boson sampling, photon distillation, and GHZ-state generation, asymmetric loss distributions can improve fidelity and uniformity of heralded outputs, though they may reduce overall success probability, a trade-off that can be mitigated by multiplexing. The work provides a design-oriented framework for optimizing loss distributions in photonic circuits and highlights when unbalanced losses may yield practical gains for high-fidelity quantum photonic operations.

Abstract

Multiport interferometers can be constructed from two-port components in various configurations. We investigate how these configurations influence the performance of quantum operations through asymmetries in optical losses. Using numerical simulations, we analyze the effect of photon-loss distributions on the fidelity of operations involving measurements. For both full- and partial-measurement protocols, we compare rectangular (symmetric-loss) and triangular (asymmetric-loss) architectures. Our results show that asymmetric loss configurations can reduce operation infidelity in several cases, revealing a quantifiable trade-off between fidelity and success probability, with implications for the design of high-fidelity photonic circuits.

Figures (8)

• Figure 1: Classification of linear optical quantum operations. A quantum channel $\rho \rightarrow \mathcal{T}(\rho)$ is implemented via a multiport interferometer executing a linear transformation $T$ on creation operators, followed by projective measurements. (A) Full-measurement operation: all output modes are measured, yielding classical information. (B) Partial-measurement operation: one or more output modes are measured. Postselection on specific outcomes produces a heralded state $\rho^\prime$, representing the conditional quantum information output.
• Figure 2: Universal 5-port interferometer designs. Blue rectangles are configurable two-mode unit cells, and green rectangles are static single-mode identity transformations used to equalize path lengths. Orange rectangles represent uniform local loss channels with transmission efficiency $\eta$. A) Rectangular design (top) and its equivalent loss-commuted network (bottom), producing symmetric losses. B) Triangular design (top) and its equivalent loss-commuted network (bottom), producing asymmetric losses; not all loss elements can be commuted to the input. C) Commutation rules for uniform loss elements oszmaniec2018classicalbrod2020classical used to construct the equivalent networks in A and B. D) Local transformation rule for a subcircuit of two-mode unit cells, enabling conversion between the illustrated designs clement2022lov.
• Figure 3: Single-photon fidelity in 5-mode interferometers under loss. Non-postselected single-photon fidelity, $\tilde{\mathcal{F}}$, as a function of single-photon transmission efficiency per unit cell, $\eta$. Triangular designs show higher average fidelity than rectangular designs. Rectangular designs maintain uniform fidelity across all output modes, while triangular designs exhibit variation, indicated by the spread between maximum and minimum fidelities. Each point averages over 500 Haar-random unitary samples. Inset: Detailed view of the high-efficiency regime.
• Figure 4: Conditional transmittance in a 5-photon Fourier transform distillation circuit. Conditional transmittance $\Lambda$ is plotted as a function of single-photon transmission efficiency $\eta$ for rectangular and triangular designs. Triangular designs yield higher conditional transmittance than rectangular designs for $0 < \eta < 1$.
• Figure 5: Conditional transmittance of qubits in heralded 3-qubit GHZ states. The rectangular design exhibits symmetric losses, yet the marginal conditional qubit transmittance $\Lambda$ is non-uniform. Transitioning to a triangular design reduces this non-uniformity, particularly for qubits 2 and 3. Calculations assume unit cell efficiency $\eta = 0.9848$.