Advantage in distributed quantum computing with slow interconnects

TL;DR

The paper addresses whether slow interconnects between multiple QPUs can outperform a monolithic QPU for distributed quantum computing. It proposes distributed CliNR, a variant of partial error correction that parallelizes resource-state preparation across QPUs connected in a circular network and uses remote gates, enabling depth reduction and improved fidelity under realistic entanglement constraints. The authors demonstrate via circuit-level simulations that distributed CliNR can achieve lower logical error rates and shallower depths than both direct and monolithic CliNR implementations for $\tau_e$ up to 5, with 85-qubit Clifford circuits distributed over four modules. In the asymptotic regime, they show that with $O\left(\frac{t}{\ln t}\right)$ parallel Bell-pair generation and relaxed assumptions, distributed CliNR avoids stalling independently of qubit counts per QPU, indicating a viable near-term pathway to distributed quantum advantage on multi-QPU devices.

Abstract

The main bottleneck for distributed quantum computing is the rate at which entanglement is produced between quantum processing units (QPUs). In this work, we prove that multiple QPUs connected through slow interconnects can outperform a monolithic architecture made with a single QPU. We consider a distributed quantum computing model with the following assumptions: (1) each QPU is linked to only two other QPUs, (2) each link produces only one Bell pair at a time, (3) the time to generate a Bell pair is $τ_e$ times longer than the gate time. We propose a distributed version of the CliNR partial error correction scheme respecting these constraints and we show through circuit level simulations that, even if the entanglement generation time $τ_e$ is up to five times longer than the gate time, distributed CliNR can achieve simultaneously a lower logical error rate and a shorter depth than both the direct implementation and the monolithic CliNR implementation of random Clifford circuits. In the asymptotic regime, we relax assumption (2) and we prove that links producing $O(t/\ln t)$ Bell pairs in parallel, where $t$ is the number of QPUs, is sufficient to avoid stalling distributed CliNR, independently of the number of qubits per QPU. This demonstrates the potential of distributed CliNR for near-term multi-QPU devices. Moreover, we envision a distributed quantum superiority experiment based on the conjugated Clifford circuits of Bouland, Fitzsimons and Koh implemented with distributed CliNR.

Figures (3)

• Figure 1: The three modules of a QPU $Q_k$ in a distributed architecture connected to two other QPU $Q_{k\pm1}$.
• Figure 2: Distributed $\mathop{\mathrm{CliNR}}\nolimits$. (a) The three components of $\mathop{\mathrm{CliNR}}\nolimits$: RSP, RSV, and RSI. On a monolithic architecture, all three would be executed on a single $3n+1$ qubit QPU. In the distributed architecture, RSP and RSV (RSP&V) would be executed on one QPU requiring $2n+1$ computational qubits and RSI would require remote gates. (b) Distributed $\mathop{\mathrm{CliNR}}\nolimits$ with $t=3$ (4 QPUs). The RSP&V stages which are expected to have a relatively large depth are executed in parallel. For simplicity, qubit rails are terminated when they are no longer used.
• Figure 3: Simulation results for the three different implementation, direct, monolithic $\mathop{\mathrm{CliNR}}\nolimits_{3,3}$ and distributed $\mathop{\mathrm{CliNR}}\nolimits_{3,3}$. (a) Logical error rate (left) and depth (right) as a function of $n$. (b) Logical error rate (left) and depth (right) as a function of entanglement generation time at $n=85$.

Theorems & Definitions (6)

• Proposition 1: monolithic CliNR depth
• proof
• Proposition 2: distributed CliNR depth
• proof
• Lemma 1
• proof