Efficient Entanglement Purification Circuit Design for Dual-Species Atom Arrays

TL;DR

This work tackles robust entanglement purification in noisy quantum channels by generalizing two-way EPPs to arbitrary stabilizer codes and implementing them on dual-species Rydberg atom arrays using a DACOS framework. The authors develop a circuit-compilation approach grounded in stabilizer tableaux to realize encoding unitaries $U_{enc}$ for any stabilizer code under global control, enabling ancilla-free EPPs and scalable purification workflows. They validate the framework with $1$- and $2$-round EPPs based on codes such as $[[4,2,2]]$, $[[5,1,3]]$, and $[[7,1,3]]$, and analyze fidelity improvements and distillation rates under circuit-level noise, as well as optimize the depth of CZ sequences. The DACOS-based approach promises near-term, high-fidelity entanglement distribution and provides a practical path toward fault-tolerant quantum networking on dual-species neutral-atom hardware, with broad applicability to stabilizer-code based purification and quantum communication tasks.

Abstract

Entanglement purification protocols (EPPs) are essential for generating high-fidelity entangled states in noisy quantum systems, enabling robust quantum networking and computation. Building on the circuit of the foundational recurrence protocol, we generalize two-way EPPs to arbitrary stabilizer codes. Through analytical derivations and noisy circuit simulations incorporating circuit-level noise, we demonstrate enhanced purification performance, with fidelity improvements and finite distillation rates for distillable input states. We propose efficient circuit designs for EPPs tailored to dual-species Rydberg atom arrays, leveraging species-specific laser control and interspecies Rydberg interactions. Introducing a low-overhead operation set, the dual-species atom convenient operation set, we facilitate straightforward compilation of EPP circuits without the need for ancillary atoms or complex atom rearrangements. Our framework provides practical guidance for near-term implementations on dual-species platforms, advancing towards scalable entanglement distribution in neutral atom systems and paving the way for fault-tolerant quantum technologies.

Figures (10)

• Figure 1: This figure illustrates the correspondence between the circuits of QECC and EPP. (a) A typical quantum circuit depicting the encoding and decoding processes for a QECC. (b, c) Circuits for one-way and two-way EPP, respectively. The white box without a label denotes local quantum operations conditioned on classical communication (indicated by purple lines and arrows). The circuits in (b) and (c) are derived by folding the circuit in (a), with minor modifications. The yellow V-shaped polyline represents a noisy initial Bell state $\Phi_+$.
• Figure 2: Panel (a) shows an array of Rydberg atoms comprising two species. The positions of the atoms can be manipulated using optical tweezers. All atoms are staying in the same working zone, so that the internal qubit state is controlled via a global laser field. (b) The interaction between two qubits is mediated by the Rydberg blockade mechanism. Here, $\ket{0}$ and $\ket{1}$ represent two nearly degenerate ground states (e.g., hyperfine clock state), while $\ket{r}$ is a highly excited Rydberg state optically coupled to $\ket{1}$ by an external laser drive. Under Rydberg blockade, both atoms cannot be simultaneously excited to the $\ket{rr}$ state if they are initially prepared in $\ket{11}$. This scheme is also applicable to interactions between atoms of different species, where the energy spectra are distinct.
• Figure 3: This figure uses different colors to distinguish qubits of different species of atoms (red for Rb and blue for Cs). (a) The original $2\to 1$ 2-EPP circuit bennett_1996_PRL. (b) The $[[4,2,2]]$ 2-EPP protocol that purifies 2 pairs of entangled states from 4 pairs of noisy entangled inputs. Using an LC equivalent $[[n,n-2,2]]$ QECC, the panel (c) generalizes the unitary in the panel (a), which purifies $n-2$ pairs of entangled Rb atoms with a constant amount of Cs atoms.
• Figure 4: The figure illustrates the expectation values of the fidelity $F(\psi_0, \rho_{\text{out}})$, the success probabilities, and the values of non-zero correlators for the $[[4,2,2]]$ 2-EPP (panels (a,c,e,f)) and $[[6,4,2]]$ 2-EPP (panels (b,d,g,h)). Each panel considers different levels of noise characterized by the parameter $q$. For panels (e,f,g,h), the values of $q$ are $0.01$, $0.03$, $0.005$, and $0.0015$.
• Figure 5: Panel (a) displays the asymptotic rate of distilled entanglement under the input $\lim_{N\to\infty}\hat{\rho}(p)^{\otimes N}$. The dashed line is an upper bound for the distillation rate. The black solid line represents the celebrated hashing bound regarding $\mathcal{E}^{(1)}_p$. The dashed black line represents the Rains bound $R(p)$ for $\hat{\rho}(p)$. $D_R$ and $D_M$ are the rates given by the recurrence-hashing method and Macchiavello method bennett_1996_PRL. The green solid line labels the rates $D_{[[4]]}$ based on $[[4,2,2]]$. The inset shows $D_{[[4]]}$ vanishes before $p\approx 0.5$. The colored solid lines in panel (b) display the relationship between $p$ and the output fidelity of a single pair $f_{\text{out},\text{red}}$ under different 2-EPPs.