Measurement-Based Fault-Tolerant Quantum Computation on High-Connectivity Devices: A Resource-Efficient Approach toward Early FTQC

TL;DR

This work introduces a measurement-based, fault-tolerant quantum computing architecture optimized for high-connectivity platforms, leveraging Knill's error-correcting teleportation with pre-verified logical ancillas to bypass repeated syndrome measurements and heavy decoding. It instantiates two non-concatenated CSS codes—Steane for analog $R_Z(\theta)$ rotations and Golay for fully fault-tolerant $T$-gates via higher-order zero-level distillation—together with a zoned hardware layout that separates ancilla factories from the computation zone. Numerical simulations under circuit-level depolarizing noise show Steane-based operations achieve $O(p^2)$ scaling for Clifford gates and a practical megaquop regime ($\sim 10^6$ to $10^7$ $T$ gates) at $p=10^{-4}$, while Golay-based distillation yields $O(p^4)$ scaling with gigaquop-scale capabilities ($\sim 10^9$ $T$ gates) on devices with tens of thousands of qubits. The results suggest near-term high-connectivity hardware can perform large-scale, fault-tolerant quantum computations without relying on resource-intensive surface codes or deep concatenation, with clear pathways to practical application workloads such as quantum chemistry simulations and RSA-2048 factoring.

Abstract

We propose a measurement-based FTQC (MB-FTQC) architecture for high-connectivity platforms such as trapped ions and neutral atoms. The key idea is to use verified logical ancillas combined with Knill's error-correcting teleportation, eliminating repeated syndrome measurements and simplifying decoding to logical Pauli corrections, thus keeping classical overhead low. To align with near-term device scales, we present two implementations benchmarked under circuit-level depolarizing noise: (i) a Steane-code version that uses analog $R_Z(θ)$ rotations, akin to the STAR architecture [Akahoshi et al., PRX Quantum 5, 010337], aiming for the megaquop regime ($\sim 10^6$ $T$ gates) on devices with thousands of qubits; and (ii) a Golay-code version with higher-order zero-level magic-state distillation, targeting the gigaquop regime ($\sim 10^9$ $T$ gates) on devices with tens of thousands of qubits. At a physical error rate $p=10^{-4}$, the Steane path supports $5\times 10^{4}$ logical $R_Z(θ)$ rotations, corresponding to $\sim 2.4\times 10^{6}$ $T$ gates and enabling megaquop-scale computation. With about $2{,}240$ physical qubits, it achieves $\log_{2}\mathrm{QV}=64$. The Golay path supports more than $2\times 10^{9}$ $T$ gates, enabling gigaquop-scale computation. These results suggest that our architecture can deliver practical large-scale quantum computation on near-term high-connectivity hardware without relying on resource-intensive surface codes or complex code concatenation.

Figures (22)

• Figure 1: Overview of MB-FTQC architecture. (a) Clifford gates are executed by Knill's ECT gadget with pre-generated and verified logical ancillas; the gadget is single-shot and decoding is a Pauli-frame update (Sec. \ref{['subsec:logical-h-cz']}). (b) Two options are provided for non-Clifford gates: an analog $R_Z(\theta)$ using a $\lvert{+_\theta}\rangle_L$ factory (Sec. \ref{['subsec:method-analog-rot']}), or a $T$ gate enabled by a $\lvert T\rangle_L$ factory based on higher-order zero-level distillation (Sec. \ref{['subsec:MagicT']}). Prepared ancillas are applied with gate teleportation. (c) The architecture utilizes transversal entangling gates, logical one-bit teleportation (Sec. \ref{['sec:preliminaries']}), and entanglement purification for $\lvert0\rangle_L$ state preparation (Sec. \ref{['subsec:method_zero_prep']}).
• Figure 2: Full circuit for preparing the rotated Steane ancilla $\ket{+_\theta}_L$. (Top) A non-fault-tolerant encoding circuit using a single analog two-qubit rotation $R_{ZZ}(\theta)$. (Bottom) Post-selection with Steane's gadget that couples the prepared block to two fault-tolerant $\ket{0}_L$ ancillas and extracts both $Z$- and $X$-type syndromes; only runs with trivial syndromes are accepted.
• Figure 3: The higher-order zero-level distillation protocol. $PS$ stands for post-selection using Steane's gadget.
• Figure 4: The implementation of the Hadamard test used in the distillation protocol (Fig. \ref{['fig:golay-distillation']}). The first two qubits implement the control qubit in Fig. \ref{['fig:golay-distillation']}, and the rest represents a logical qubit encoded in the Golay code.
• Figure 5: Zoned architecture for MB-FTQC.