Resource-efficient loss-aware photonic graph state preparation using atomic emitters

TL;DR

The paper tackles the resource inefficiency of preparing multi-qubit photonic graph states by introducing a loss-aware, emitter-based framework that trades graph-state depth against the number of emitters. It develops a time-reversed circuit decomposition using three primitives—Absorption by an Entangled Emitter, Swapping with a Free Emitter, and Unentangle Emitters—and presents two concrete algorithms to minimize the two-qubit emitter–emitter gate depth while controlling emitter counts. Applied to all-photonic repeater architecture via repeater graph states protected by tree codes, the method achieves superior rate–distance performance with far fewer emitters than multiplexed linear-optics approaches, and can surpass repeaterless bounds under favorable parameters. The work provides detailed analyses of emission timing, loss, and resource requirements, and outlines avenues for optimizing emitter counts, circuit depth, and photon-release timing to further improve practicality and scalability of all-photonic quantum repeaters.

Abstract

Multi-qubit entangled photonic graph states are an important ingredient for all-photonic quantum computing, repeaters and networking. Preparing them using probabilistic stitching of single photons using linear optics presents a formidable resource challenge due to multiplexing needs. Quantum emitters provide a viable solution to prepare photonic graph states as they enable deterministic production of photons entangled with emitter qubits, and deterministic two-qubit interactions among emitters. A handful of emitters often suffice to generate useful-size graph states that would otherwise require millions of emitters used as single photon sources, using the linear-optics method. Photon loss however impedes the emitter method due to a large circuit depth, and hence loss accrual on the photons of the graph state produced, given the typically large number of slow two-qubit CNOT gates between emitters. We propose an algorithm that can trade the number of emitters with the graph-state depth, while minimizing the number of emitter CNOTs. We apply our algorithm to generate a repeater graph state (RGS) for a new all-photonic repeater protocol, which achieves a far superior rate-distance tradeoff compared to using the least number of emitters needed to generate the RGS. Yet, it needs five orders of magnitude fewer emitters than the multiplexed linear-optics method -- with each emitter used as a photon source -- to achieve a desired rate-distance performance.

Figures (15)

• Figure 1: (a) The linear optical method simultaneously generates single photons (red circles) entangled with (squiggly lines) quantum emitters (cyan circles). Emitters are measured to unentangle the photons (not shown). The photons then go through probabilistic linear optical circuits to form the target graph state. (b) The quantum emitters emit entangled photons of the target graph state separated in time.
• Figure 2: This figure shows construction of a RGS with $m=2$, and $b = [3,2]$. (a) Start with a star graph state with $2m+1$ qubits. Attach a qubit (pink qubits) and a tree with branching vector $b$ to every qubit of the clique graph state. (b) Performing $X$ measurements on the green nodes and $Y$ measurement the central blue node on the graph state in (a) gives the RGS. The pink qubits depict the flying qubits, which are sent to the two adjacent nodes, and the white nodes remain at the repeaters and mimic quantum memories.
• Figure 3: Example to demonstrate AEE. Circles and squares are photons and emitters, respectively. In this and all subsequent figures, we use shapes to differentiate emitters and photons instead of the subscripts $e$ and $p$ used in the main text. (a) Input state to Case 1. The emitter $1_e$ absorbed photon $4_p$ to get (b). (b) is the input state for Case 2. $1_e$ absorbed $10_p$ to get (c).
• Figure 4: Example to demonstrate AEE Case 3. Circles and squares are photons and emitters, respectively. (a) Input state to Case 3. The emitter $1_e$ absorbed photon $1_p$ to get (b).
• Figure 5: Example to demonstrate SFE. CCircles and squares are photons and emitters, respectively. (a) Input state to Case 1. The emitter $1_e$ swapped photon $0_p$ to get (b).