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

This paper presents the first hardware validation of QLDPC surgery on Quantinuum's H2-2 trapped ion processor, demonstrating high-fidelity, individually addressed logical Pauli measurements on a [[10,2,3]] code that preserve spectator qubits and suppress errors through syndrome decoding, thereby confirming the feasibility of efficient fault-tolerant operations for QLDPC architectures.

Original authors: Surabhi Luthra, Alex Owens

Published 2026-10-30

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Surabhi Luthra, Alex Owens

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The quest to build a useful quantum computer faces a fundamental hurdle: the fragility of the information it holds. Quantum bits, or qubits, are easily disturbed by their environment, causing errors that can ruin a calculation. To overcome this, scientists use error-correcting codes, which spread a single piece of logical information across many physical qubits. If one physical qubit fails, the others can preserve the truth. However, the most common and reliable codes require hundreds or even thousands of physical qubits to protect just one logical qubit, a massive overhead that makes practical machines seem distant. A newer class of codes, known as quantum low-density parity-check codes, promises to shrink this requirement dramatically by packing multiple logical qubits into a single block of physical hardware. But to use these efficient codes, researchers must solve a difficult problem: how to measure and manipulate individual logical qubits within that block without destroying the information stored in the others or breaking the delicate error-correction structure.

A team of researchers has now demonstrated a solution to this problem on a real quantum computer. Using a trapped-ion processor, they successfully performed a technique called "QLDPC surgery" to measure one logical qubit while leaving a second, neighboring logical qubit untouched. This achievement validates a critical building block for the next generation of quantum computing, proving that it is possible to selectively address specific information within a dense, efficient code without collapsing the entire system. The work confirms that these advanced codes can be operated on in a way that preserves their integrity, a necessary step toward building machines that can solve complex scientific problems.

The researchers worked with a specific arrangement of ten physical qubits that encoded two logical qubits. To measure the first logical qubit, they introduced a temporary helper system, known as a gadget, consisting of seven additional qubits. Think of this gadget as a specialized probe that briefly connects to the main block of data. The team entangled this probe with the ten data qubits in a precise pattern, allowing them to read out the state of the first logical qubit without touching the second. This process is non-destructive; unlike traditional measurements that would collapse the quantum state and erase the information, this surgery extracts the answer while keeping the system intact and ready for further operations.

In their first set of experiments, the team performed this measurement in a single round. They prepared the logical qubits in known states and measured the first one using the gadget. The results showed that the gadget correctly identified the state of the targeted qubit with an error rate of less than one percent. Crucially, when they immediately measured the second, untargeted qubit directly, it remained in its original state, proving that the surgery had not disturbed the "spectator" qubit. The gadget acted like a precise surgical tool, operating on one part of the system while leaving the rest undisturbed. The researchers also verified that the system returned to its correct error-correcting state after the gadget was removed, confirming that the delicate structure of the code was preserved.

To make the process more robust against errors, the team repeated the measurement process three times in succession, a technique that allows the system to detect and correct mistakes that might occur during the reading process. By decoding the results from these three rounds, they suppressed the error rate significantly, pushing it below 0.26 percent. This demonstrated that the method is fault-tolerant, meaning it can handle the inevitable noise of a real machine without failing. Furthermore, they showed that the same seven helper qubits could be reused immediately after the first measurement to perform a second surgery on the second logical qubit. They measured the first qubit, then used the same hardware to measure the second, successfully retrieving information from both without needing to reset the entire machine or add new components.

The study provides concrete evidence that the theoretical advantages of these efficient codes can be realized in hardware. The researchers found that the error rates observed in their experiments matched predictions based on the known performance of the quantum processor, giving them high confidence in the results. They also identified that the primary source of error in the single-round measurement came from the act of reading the helper qubits themselves, a problem that was effectively solved by the three-round repetition. The ability to measure one logical qubit, preserve the other, and then reuse the same hardware for a second measurement is a foundational requirement for a computing model known as Pauli-based computing, which relies on a sequence of such measurements to perform complex calculations.

This work represents a significant step forward in the practical application of quantum error correction. By demonstrating that these complex codes can be manipulated with high precision and low overhead on a real device, the researchers have removed a major theoretical barrier. The success of the surgery protocol suggests that future quantum computers can be built with far fewer physical resources than previously thought necessary, bringing the era of fault-tolerant quantum computing closer to reality. The ability to selectively address and preserve information within a dense code block is no longer just a mathematical possibility; it has been proven to work in the laboratory.

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

Problem Statement
Fault-tolerant quantum computation (FTQC) based on surface codes typically requires hundreds to thousands of physical qubits per logical qubit, creating a significant overhead for near-term applications. Quantum Low-Density Parity Check (QLDPC) codes offer a pathway to reduce this overhead by encoding multiple logical qubits within a single code block while maintaining bounded-weight parity checks. However, realizing the potential of QLDPC codes requires a method for selectively addressing individual logical qubits within these multi-qubit blocks without destroying the encoded state or the code space. While "lattice surgery" has been demonstrated for single-qubit blocks, extending this to individually address logical qubits in multi-qubit QLDPC blocks via "QLDPC surgery" had not been realized in hardware prior to this work.

Methodology
The authors implemented QLDPC surgery on Quantinuum's H2-2 trapped ion processor, which features all-to-all connectivity and mid-circuit measurement. The experiment utilized a $[[10,2,3]]$ Generalised Bicycle (GB) code, which encodes two logical qubits into ten physical data qubits.

The core methodology involved constructing a non-destructive measurement "gadget" for a specific logical Pauli operator (e.g., $\bar{X}_1$ ). Following the construction in Ref. [19], the gadget consists of:

Gadget Qubits ( $\kappa$ ): Ancillary qubits appended to the code stabilizers overlapping with the target logical operator's support.
X-type Gadget Checks ( $\chi$ ): Checks supported on the data qubits of the logical operator and their associated gadget qubits. The product of these checks yields the logical operator.
Z-type Gauge Checks ( $\gamma$ ): Checks on the gadget qubits to fix degrees of freedom and maintain the code distance.

The experimental protocol involved three distinct circuit configurations:

XR1: A single round of syndrome extraction for the merged code-gadget system to measure $\bar{X}_1$ .
XR3: Three rounds of syndrome extraction for the same $\bar{X}_1$ measurement to demonstrate fault tolerance against measurement errors.
SEQ: A sequential measurement of $\bar{X}_1$ followed by $\bar{Z}_2$ using the same physical gadget qubits (re-initialized) to demonstrate composability and preservation of the "spectator" logical qubit.

The experiments included verification steps (trivial syndrome checks) and offline decoding using the Tesseract decoder acting on detector error models generated by Stim.

Key Contributions

First Hardware Demonstration: This work presents the first hardware realization of individually addressed logical Pauli measurements in a multi-qubit QLDPC code block using surgery.
Gadget Construction and Validation: The authors explicitly constructed and validated a 7-qubit gadget (3 gadget qubits, 4 check qubits) for the $[[10,2,3]]$ code, demonstrating that the product of gadget checks correctly extracts the logical eigenvalue.
Fault-Tolerance via Repetition: The study demonstrated that repeating the gadget syndrome extraction over $R=3$ rounds suppresses measurement errors, effectively increasing the circuit distance of the logical measurement from $d_c=1$ to $d_c=3$ .
Code Space Preservation: The authors verified that the surgery process is non-destructive, returning the system to the original code space and preserving the unaddressed "spectator" logical qubit.
Composability: The work demonstrated the sequential composition of conjugate basis gadgets ( $\bar{X}_1$ then $\bar{Z}_2$ ) using the same physical resources, a requirement for Pauli-based computing.

Results

Single-Round Performance: A single-round measurement of $\bar{X}_1$ achieved an error rate of 0.72% [0.32, 1.41]% relative to the intended logical preparation and 1.03% [0.60, 1.65]% relative to a subsequent destructive transversal measurement. The error budget analysis identified reset and measurement errors as the dominant contributors.
Fault-Tolerant Performance: By decoding over three rounds of syndrome extraction (XR3), the logical error rate was suppressed. For the $|++\rangle_L$ preparation, zero errors were observed in 957 verified shots, bounding the error rate below 0.26% (95% credible interval). This confirmed that the protocol successfully mitigates single measurement faults.
Spectator Preservation: The unaddressed logical qubit ( $\bar{X}_2$ ) was preserved with an error rate of 0.21% [0.04, 0.67]% during the three-round measurement.
Sequential Measurement: In the sequential circuit (SEQ), the second gadget measurement of $\bar{Z}_2$ (after $\bar{X}_1$ ) yielded an error rate of 1.12% [0.60, 1.94]%. The results confirmed that the conjugate basis information ( $\bar{Z}_2$ ) remained addressable while the measured basis ( $\bar{X}_1$ ) collapsed, validating the non-destructive nature of the surgery.
Code Space Return: Analysis of detector rates on deformed stabilizers showed that with fusion corrections, the system returned to the code space, with detector rates remaining low (<2.66%) compared to the ~50% randomization observed without fusion correction.

Significance and Claims
The paper claims to provide a hardware validation of the generalized surgery primitive underlying Pauli-based computing for QLDPC architectures. The authors state that these results constitute a foundational step toward scalable QLDPC architectures by demonstrating:

The ability to selectively address individual logical qubits within a multi-qubit block.
The non-destructive nature of the measurement, preserving the code space and spectator qubits.
The feasibility of composing these operations sequentially.

The authors note that while the current demonstration uses a minimal distance code ( $d=3$ ) and offline decoding, it establishes the necessary primitives for future implementations involving real-time decoding, higher-distance codes, and more complex Pauli-product measurements. The work does not claim to have solved all overhead issues or achieved break-even error correction for large-scale algorithms, but rather validates the specific mechanism required to enable such scalability in QLDPC systems.

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