Tools for Reducing Service Time in Near-Term Quantum Networks

Abstract: Architectures have been proposed to control entanglement generation in multi-user quantum networks. To allow time for local operations and classical communication at end nodes, these architectures insert fixed separations between consecutive batches of entanglement generation attempts. This reduces network utilization when attempts fail, leaving the network idle during the scheduled separation. To address this limitation, we propose a novel method to reclaim this idle time by shortening the scheduled separation between attempts while respecting hardware constraints. The method uses an analytical execution model to optimize the separation and reduce the total network service time of an application. Evaluations within the Arqon architecture show network service time reductions of up to 42 minutes (7.6%) for single applications and 16-29 minutes (26-30%) per application when co-scheduled. The approach applies broadly to quantum network architectures that share hardware between entanglement generation and local operations, and the method can be used online by network schedulers.

• The paper presents an analytical method that computes the optimal shortened separation between consecutive packet generation attempts (PGA) by leveraging an optimized ingress $\alpha$.
• The key methodology involves parameterizing the ingress using local operations and computing constraints to ensure worst-case single-skip and maximum feasible service levels.
• The results show that by reducing service time using the proposed analytical techniques, substantial speedup is achieved around 2.7% to 5.8%. These findings are validated for hardware configurations of trapped-ion and solid-state systems.

Problem and context

Quantum network architectures that coordinate entanglement delivery for multi-user applications must respect a minimum separation between successive packet deliveries: because the end-node hardware that participates in entanglement consumption also performs local operations and classical communication (LOCC), consecutive consumptions must be spaced by at least the LOCC duration. Existing schedulers, including Arqon (Gauthier et al., 9 Apr 2026), conservatively reserve this full minimum separation after every scheduled block of entanglement generation attempts. Since each block succeeds only probabilistically, many blocks fail and leave both the network and the end nodes idle for an interval during which no LOCC is actually required.

Smith et al. quantify how significant this over-provisioning is on current hardware: demonstrated heralded entanglement rates are $2.22$ Hz in trapped-ion systems [liu2026long] and $0.022$ Hz in solid-state platforms [stolk2024metropolitan] over 10 km links, so at the trapped-ion rate successive consumptions occur every $\sim 450$ ms — comparable to a representative minimum separation of roughly $500$ ms derived from coherence budgets ($t_{\text{coh}}/2$) plus LOCC overheads. In this regime, the conservative separation constrains essentially every consumption event. The paper's contribution is a lightweight analytical method that computes the optimal shortened separation between consecutive packet generation attempts (PGAs), trading reclaimed idle time against the risk that a late-generated packet forces an end node to skip its next block.

Method: ingress parameterization and Markov chain session model

The central object is the PGA ingress $\alpha = (t^{\text{minsep}} - T')/E \in [0,1]$, where $E$ is the PGA duration and $T'$ the reduced scheduled separation. A packet generated within the violation zone $((1-\alpha)E, E]$ triggers a skip of the following PGA. Two constraints bound admissible separations:

• Single-skip guarantee: $2T' + E \geq t^{\text{minsep}}$, ensuring worst-case violations skip only one PGA rather than cascading, yielding the lower bound $0.022$0.
• Service feasibility: the expected packet count must reach $0.022$1 within the allocated PGAs $0.022$2.

Because the distribution of packet generation times within a PGA admits no closed form, the conditional violation probability $0.022$3 is precomputed into lookup tables via Monte Carlo simulation of link arrivals as a Poisson process with rate $0.022$4 under a sliding-window criterion ($0.022$5 successful trials per configuration). Given these tables, session execution under reduced separation is modeled as a Markov chain $0.022$6 over executed/skipped steps, with skip transition probability $0.022$7. The expected number of executed PGAs after $0.022$8 steps resolves to the closed form

$0.022$9

and the smallest $\sim 450$0 achieving the required packet count defines a conservative upper bound $\sim 450$1 on expected session time. Using the stationary distribution of the reduced two-state chain, the authors derive a closed-form speedup decomposition that makes the tradeoff structure explicit:

$\sim 450$2

where the first term is the release-time reduction if no skips occurred and the second is the fraction of that savings lost to compensating skipped PGAs. Speedup is positive only when the former exceeds the latter. All quantities reduce to table lookups and closed-form expressions, making the optimizer suitable for runtime use by network schedulers without repeated simulation — a notable practical property relative to simulation-driven scheduling approaches (Maiti et al., 4 Feb 2026).

Single-session results

Evaluation covers two hardware regimes: the state-of-the-art trapped-ion regime ($\sim 450$3 Hz, $\sim 450$4 ms) and an optimistic regime ($\sim 450$5 Hz, $\sim 450$6 s), with sessions of $\sim 450$7 instances simulated over $\sim 450$8 trials. The results expose a sharp dependence on the demand's z-score $\sim 450$9, which measures how many standard deviations the requested link count lies above the mean arrivals per window.

Session	$500$0	$500$1	Markov bound $500$2 [%]	Simulated $500$3 [%]	Service time saving
$500$4	1.8	0.063	2.0	$500$5	2.3 min
$500$6	3.1	0.095	5.2	$500$7	11.1 min
$500$8	4.3	0.082	6.1	$500$9	41.9 min
$t_{\text{coh}}/2$0	0.0	0.049	0.8	$t_{\text{coh}}/2$1	3.2 min
$t_{\text{coh}}/2$2	1.8	0.062	2.5	$t_{\text{coh}}/2$3	18.1 min
$t_{\text{coh}}/2$4	3.1	0.069	5.1	$t_{\text{coh}}/2$5	2.8 hr

Two findings deserve emphasis. First, the benefit is bounded by opposing effects of the z-score: demands with large $t_{\text{coh}}/2$6 have long PGAs ($t_{\text{coh}}/2$7), which shrinks the geometric ceiling on release-time reduction to $t_{\text{coh}}/2$8 for $t_{\text{coh}}/2$9, but their generation times spread across the PGA so violations accumulate slowly and the ceiling is nearly reached; near $\alpha = (t^{\text{minsep}} - T')/E \in [0,1]$0 ($\alpha = (t^{\text{minsep}} - T')/E \in [0,1]$1), the ceiling is a generous $\alpha = (t^{\text{minsep}} - T')/E \in [0,1]$2, yet fast violation growth holds the realized reduction to $\alpha = (t^{\text{minsep}} - T')/E \in [0,1]$3. Second, a high packet success probability eliminates any benefit: demand $\alpha = (t^{\text{minsep}} - T')/E \in [0,1]$4 with $\alpha = (t^{\text{minsep}} - T')/E \in [0,1]$5 yields no speedup at any feasible ingress, because the skip penalty dominates across the entire admissible range. This gives schedulers a simple diagnostic for when separation reduction is indicated.

The analytical machinery tracks simulation closely: the stationary approximation agrees with the exact Markov bound to within $\alpha = (t^{\text{minsep}} - T')/E \in [0,1]$6 percentage points, and the Markov bound underestimates simulated speedup by only $\alpha = (t^{\text{minsep}} - T')/E \in [0,1]$7–$\alpha = (t^{\text{minsep}} - T')/E \in [0,1]$8 percentage points while remaining a valid lower bound. Monte Carlo verification confirms that all tested configurations meet their requested service probability at the optimal ingress — though, as discussed below, this is empirical rather than guaranteed by the framework.

Multi-session co-scheduling

The strongest quantitative result arises when two sessions share the network under round-robin scheduling. Intervening PGAs from the other session provide natural separation, so the effective ingress contributing to violations shrinks to $\alpha = (t^{\text{minsep}} - T')/E \in [0,1]$9, and when $E$0 no violations are possible at all and the separation can be fully eliminated.

Co-scheduling $E$1 with $E$2 raises the Markov-bound speedup from $E$3 to $E$4 and from $E$5 to $E$6 respectively, corresponding to service time reductions of $E$7 and $E$8 minutes per session ($E$9 and $T'$0). The mechanism is that each co-scheduled PGA fills most of the round-robin cycle alone: the residual ingresses collapse to $T'$1 and $T'$2, nearly eliminating skip penalties. The Markov bound here underestimates simulation by at most $T'$3 percentage points. The implication is that multi-tenant resource sharing and separation optimization are complementary rather than competing scheduling objectives — a nontrivial conclusion given that partitioned resource regions (as in Arqon's path partition) would deny sessions co-scheduled partners and revert them to single-session gains.

Limitations and open questions

The paper is explicit about several assumptions and gaps. The probabilistic service agreement — that $T'$4 packets are generated with probability at least $T'$5 — is not formally enforced by the optimization; the feasibility constraint $T'$6 is necessary but not sufficient, and compliance is verified only empirically by simulation. Formalizing the relationship between $T'$7 and $T'$8 is left open, as is jointly optimizing separation and block allocation under stricter (smaller-$T'$9) service regimes, where additional blocks must compensate for violations.

The analysis is restricted to the single-skip regime, which holds only when Eq. (single-skip constraint) bounds $((1-\alpha)E, E]$0 away from cascading failures; adaptive policies that begin consumption mid-block or allocate extra blocks adaptively could outperform uniform reduction but are not modeled. The lookup-table approach assumes tables computed for nearby link counts $((1-\alpha)E, E]$1 approximate one another when $((1-\alpha)E, E]$2 is large, but interpolation error across configurations is unquantified. Finally, evaluation uses a relaxed service probability ($((1-\alpha)E, E]$3 in single-session experiments) to isolate the separation effect, and qubit decoherence after delivery is assumed away by construction of the window $((1-\alpha)E, E]$4. Testbed demonstration of the optimizer within Arqon itself remains future work.

Conclusion

This work converts a previously implicit hardware constraint — shared end-node hardware between entanglement consumption and LOCC — into a tractable constrained scheduling problem with a runtime-solvable solution. The closed-form speedup decomposition identifies precisely when separation reduction helps (moderate-to-high $((1-\alpha)E, E]$5, low $((1-\alpha)E, E]$6) and when it cannot ($((1-\alpha)E, E]$7 near unity), and the co-scheduling analysis shows that gains can grow by more than an order of magnitude when intervening PGAs absorb the required separation. The main open problem is converting the empirically verified service probability into a formal guarantee, which would make the optimized separation deployable under strict service agreements in near-term quantum networks.