Robust GHZ State Preparation via Majority-Voted Boundary Measurements

TL;DR

Group-Majority-Voting (Group-MV) addresses robust GHZ state preparation on arbitrary single-device topologies by partitioning the qubit graph into groups, preparing local GHZ states in parallel, and fusing them with majority-voted boundary measurements to mitigate mid-circuit readout errors. The method reduces local preparation depth to $O(\log K)$ and uses topology-aware partitioning to enable fusion across arbitrary coupling maps. Simulations on Heavy-hex and Grid topologies with $N=30$ to $60$ qubits show Group-MV with $L=3$ achieving up to 2.4x higher entanglement-witness scores than Line Dynamic and closely tracking the unitary baseline within $3\%$, with fidelity validation via stabilizer sampling supporting these gains. The approach scales to very large systems and maps naturally to chiplet-based or heterogeneous architectures, offering a practical route to large-scale GHZ entanglement on NISQ devices.

Abstract

Preparing high-fidelity Greenberger-Horne-Zeilinger (GHZ) states on noisy quantum hardware remains challenging due to cumulative gate errors and decoherence. We introduce Group-Majority-Voting (Group-MV), a dynamic-circuit protocol that partitions arbitrary coupling graphs, prepares local GHZ states in parallel, and fuses them via majority-voted mid-circuit measurements. The majority vote over redundant boundary links mitigates measurement errors that would otherwise propagate through classical feedforward. We evaluate Group-MV on simulated Heavy-hex and Grid topologies for 30 through 60 qubits under a realistic noise regime. Group-MV generalizes to arbitrary GHZ sizes on arbitrary coupling topologies, achieving 2.4x higher fidelity than the Line Dynamic method while tracking the unitary baseline within 3%.

Figures (2)

• Figure 1: Overview of the Group-MV method.(a) A square lattice quantum processor (illustrated using a grid topology for reference), with a highlighted region indicating the partitioned area. (b) Two adjacent groups, $G_A$ (green) and $G_B$ (blue), each prepared in a local GHZ state. Red edges indicate the boundary links used for majority-vote correction. (c) Dynamic circuit for fusing $\ket{\mathrm{GHZ}_A}$ and $\ket{\mathrm{GHZ}_B}$ into $\ket{\mathrm{GHZ}_{A\cup B}}$. CNOTs (red) entangle boundary qubits across groups. Mid-circuit measurements on link qubits in $G_B$ feed a classical majority-vote block, which conditionally applies $X$ gates to non-measured qubits in $G_B$. Measured qubits are reset to $\ket{0}$ and re-entangled via CNOTs from their partners in $G_A$, restoring full participation in the merged GHZ state.
• Figure 2: Graph partitioning and entanglement scaling across topologies.(a--c) Example partitions for Heavy-hex, Grid, and Ring coupling graphs with $N{=}40$ qubits, group size $K{=}20$, and requested boundary redundancy $L{=}3$. Green and blue nodes indicate alternating groups; red edges mark boundary links used for majority-vote fusion. Circled numbers (, ) indicate correspondence with the $N{=}40$ results in (e) and (f), respectively. In (c), the Ring topology cannot support $L{=}3$ due to limited connectivity; our algorithm gracefully degrades to the highest $L$ supported by the architecture. (d) Large-scale Heavy Hex example with $N{=}1000$ qubits, $K{=}125$, and $L{=}3$, demonstrating scalability to larger system sizes. For this higher-scale example, the algorithm leverages variable group sizes to support scaling across very large topologies. This partition-and-fuse structure also maps naturally to chiplet-based and heterogeneous quantum architectures, where dense local regions are connected by sparse inter-chip links. (e--f) Estimated GHZ entanglement witness $\mathcal{W}_N$ for varying qubit counts on Heavy-hex (e) and Grid (f) topologies. Unitary is shown in blue. Line Dynamic baumer_efficient_2024 (orange) degrades rapidly with increasing $N$. Group-MV with $L{=}1$ (green) and $L{=}3$ (pink) demonstrate improved scaling, with higher redundancy ($L{=}3$) closely tracking the unitary.