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arXiv:2610.39067

Individually Addressed Logical Pauli Measurements by QLDPC Surgery on a Trapped Ion Quantum Computer

Surabhi Luthra, Alex Owens

quant-phSubmitted Oct 28, 2026• Announced Oct 30, 2026• 0 citations
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Abstract

Quantum low-density parity check (QLDPC) codes may lead to order-of-magnitude reductions in the qubit overhead required for fault-tolerant quantum computation. Achieving this improved overhead requires logical operations that selectively address individual logical qubits encoded within multi-qubit code blocks. Recently proposed architectures achieve this through QLDPC surgery, in which non-destructive Pauli measurements are performed using ancillary ''gadget'' systems transiently entangled with the code block, generalising lattice surgery. Here we implement QLDPC surgery on a [[10,2,3]] generalised bicycle code using Quantinuum's H2-2 trapped ion processor. A single-round surgery measurement using seven gadget qubits measures the $\bar{X}_1$ operator with a 0.72 [0.32, 1.41]% (95% credible interval) error rate and agrees with subsequent transversal measurement with 1.03 [0.60, 1.65]% error. Decoding across three rounds of syndrome extraction suppresses the gadget measurement error, reducing the error rate to below 0.26%. The syndrome after surgery confirms return to the code space and the unaddressed ''spectator'' qubit is preserved with error 0.21 [0.04, 0.67]% during the three-round measurement. We further demonstrate composition of conjugate basis gadgets by sequentially measuring $\bar{X}_1$ then $\bar{Z}_2$, reusing the gadget qubits, and obtain a 1.12 [0.60, 1.94]% error in the $\bar{Z}_2$ measurement. These results constitute a hardware validation of the generalised surgery primitive underlying Pauli-based computing for QLDPC architectures.

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Quantum low-density parity check (QLDPC) codes may lead to order-of-magnitude reductions in the qubit overhead required for fault-tolerant quantum computation. Achieving this improved overhead requires logical operations that selectively address individual logical qubits encoded within multi-qubit code blocks. Recently proposed architectures achieve this through QLDPC surgery, in which non-destructive Pauli measurements are performed using ancillary ''gadget'' systems transiently entangled with the code block, generalising lattice surgery. Here we implement QLDPC surgery on a [[10,2,3]] generalised bicycle code using Quantinuum's H2-2 trapped ion processor. A single-round surgery measurement using seven gadget qubits measures the Xˉ1\bar{X}_1Xˉ1​ operator with a 0.72 [0.32, 1.41]% (95% credible interval) error rate and agrees with subsequent transversal measurement with 1.03 [0.60, 1.65]% error. Decoding across three rounds of syndrome extraction suppresses the gadget measurement error, reducing the error rate to below 0.26%. The syndrome after surgery confirms return to the code space and the unaddressed ''spectator'' qubit is preserved with error 0.21 [0.04, 0.67]% during the three-round measurement. We further demonstrate composition of conjugate basis gadgets by sequentially measuring Xˉ1\bar{X}_1Xˉ1​ then Zˉ2\bar{Z}_2Zˉ2​, reusing the gadget qubits, and obtain a 1.12 [0.60, 1.94]% error in the Zˉ2\bar{Z}_2Zˉ2​ measurement. These results constitute a hardware validation of the generalised surgery primitive underlying Pauli-based computing for QLDPC architectures.
Quantum low-density parity-check (QLDPC) codes are a leading candidate for achieving low-overhead fault-tolerant quantum computing. However, the time overhead of logical operations in QLDPC codes remains a key challenge. Code surgery, a space-efficient technique for fault-tolerant logical measurements, incurs this overhead through repeated rounds of syndrome measurement. We introduce lifted surgery, a method for fast and parallel surgery on Abelian group algebra codes that maintains the low physical overhead that makes QLDPC codes attractive. Lifted surgery preserves the symmetries of the underlying code, making searches for large instances tractable and offering a natural route towards efficient hardware implementations. We utilise block decompositions and techniques from commutative algebra to characterise lifted surgery, investigate well-behaved subfamilies, and construct explicit examples. In particular, we present quantum radial codes with parameters [[90,8,10]][[90, 8, 10]][[90,8,10]] and [[198,8,16]][[198, 8, 16 ]][[198,8,16]] for which surgery is fast, parallel, and addressable, allowing arbitrary sets of independent logical operators of the same Pauli type to be measured in a single round of syndrome extraction. We benchmark lifted surgery under circuit-level depolarising noise and, for the [[90,8,10]][[ 90, 8, 10 ]][[90,8,10]] code, find logical performance comparable to standard code surgery while requiring ten times fewer rounds of syndrome measurement. By combining speed and parallelism, lifted surgery offers a practical route towards low-overhead fault-tolerant quantum computing.
Quantum low-density parity check (QLDPC) codes can significantly reduce the overhead of quantum computing, provided the methods for performing logical operations do not require substantial space and time resources. A popular method for performing logical operations is by measuring logical Pauli operators. We present a simple, explicit construction for fixed gadgets that can measure arbitrary logical Pauli operators on QLDPC codes when dynamically connected to the code block. We apply this construction to a family of generalised bicycle codes with distances relevant to utility-scale quantum computation (10≤d≤2410\leq d \leq 2410≤d≤24) and show that it reduces the space overhead by at least an order of magnitude compared to corresponding surface code architectures, without increasing the time overhead.
Quantum code surgery offers a flexible, low-overhead framework for executing logical measurements within quantum error-correcting codes. It encompasses several fault-tolerant logical computation schemes, including parallel surgery, universal adapters and fast surgery, and serves as the key primitive in extractor architectures. The efficiency of these schemes crucially depends on constructing low-overhead ancilla systems for measuring arbitrary logical operators in general quantum Low-Density Parity-Check (qLDPC) codes. In this work, we introduce a method to construct an ancilla system of qubit size O(Wlog⁡W)O(W \log W)O(WlogW) to measure an arbitrary logical Pauli operator of weight WWW in any qLDPC stabilizer code. This new construction immediately reduces the asymptotic overhead across various quantum code surgery schemes.
Quantum low-density parity-check (qLDPC) codes offer a promising route to reducing the qubit overhead of fault tolerance, with recent ultra-high-rate constructions achieving encoding rates above one half. In this work, we develop fast and parallel logical computation methods for ultra-high-rate codes. We first utilize the group symmetries of the codes to partition the logical qubits into orbits, and then apply parallel surgery methods to implement group-invariant collections of logical Pauli-product measurements. These measurements are highly programmable, as we may arbitrarily couple logical orbits as long as each measurement is repeated across the whole orbit(s). To reduce the space and time overheads, we develop a technique called chain-map convolution, which uses the group structure to boost both the spatial and temporal distances of our protocol in a highly efficient manner. As case studies, we construct distance-preserving parallel measurement gadgets for the [[256, 68, 12]], [[576, 148, 18]] pair-partition codes, and a [[1152, 580, 12]] rate-1/21/21/2 code, with only around 2.5×2.5\times2.5× space overhead and 3-4 rounds of syndrome extraction each. The same methods also enable parallel injection of cultivated magic states into high-rate codes. Finally, we extend programmability through subgroup restrictions, revealing a tradeoff between logical control and the spacetime resources required for fault tolerance and highlighting the crucial role structured parallelism plays in reducing overhead. These results provide new methods for designing qLDPC logical operations with low spacetime overhead, opening a route toward more efficient fault-tolerant quantum architectures.
High-rate quantum low-density parity-check (qLDPC) codes encode many logical qubits with low physical-qubit overhead, but realizing efficient fault-tolerant computation on such dense encodings remains a major challenge. Generic, code-agnostic techniques such as code surgery and gate teleportation apply broadly, but are difficult to make modular, low-overhead, and fully certifiable on complex high-rate codes whose structure is left unexploited. Here we overcome these obstacles by co-designing the code together with its logical instruction set for a broad family of canonical lifted-product (LP) codes with cyclic symmetry. We show that these codes admit a canonical logical basis, in which conjugate logical operators are organized into rows and columns of cyclic orbits inherited directly from the underlying classical codes, analogous to the structure that makes hypergraph-product codes so tractable. This canonical basis enables universal logical processing using magic-state input and a constant number of reusable seed surgery gadgets---only two (resp. four) for a [[1122,148,≤20]][[1122,148,\leq 20]][[1122,148,≤20]] (resp. [[4350,1224,≤20]][[4350,1224,\leq 20]][[4350,1224,≤20]]) LP code. A fixed extractor smaller than half the data block also enables arbitrarily high-weight logical Pauli-product measurements (PPMs) while preserving the code's cyclic symmetry. These codes also enable rigorously fault-tolerant parallel logic, including PPMs across all logical qubits and magic-state injection from many surface codes into a full LP block. For example, a [[468,36,20]][[468,36,20]][[468,36,20]] (resp. [[952,112,17]][[952,112,17]][[952,112,17]]) code supports simultaneous measurements of arbitrary logically disjoint Pauli products with an ancilla overhead of roughly three (resp. four) times the data block size. These results advance the frontier of fault-tolerant quantum computation on ultra-high-rate quantum architectures.
Universal quantum computers are expected to generate arbitrary complex quantum states of logical qubits encoded in many physical qubits. This capability hinges on a fault-tolerantly implemented universal gate set, which no single quantum error-correction code admits transversally but which becomes accessible by joining complementary codes via lattice surgery. Here we report on the experimental generation and certification of logical genuine multipartite entanglement in a trapped-ion quantum processor using a transversally implemented universal logical gate set. The gate set is accessed via lattice surgery across two different codes and comprises a Hadamard gate on a four-qubit surface code and a doubly controlled Pauli-ZZZ (CCZ‾\overline{\mathrm{CCZ}}CCZ) gate on an eight-qubit 3D colour code. To showcase this lattice-surgery toolbox, we generate both stabiliser (Greenberger-Horne-Zeilinger) and non-stabiliser (∣CCZ‾⟩|\overline{\mathrm{CCZ}}\rangle∣CCZ⟩) states of three logical qubits and verify their genuine multipartite entanglement--a form of correlation beyond statistical mixtures of bipartite entanglement across any bipartition. We further use these cross-code primitives to demonstrate arbitrary rotations of single logical qubits via a CCZ‾\overline{\mathrm{CCZ}}CCZ-based resource gadget accessing the full universal gate set through lattice surgery. Together, these demonstrations showcase the core building blocks of an architecture for fault-tolerant quantum computation and its ability to generate complex logical quantum states.