Surface Code Stabilizer Readout

• Surface Code Stabilizer Readout is a method that extracts local parity constraints from a surface code via ancilla qubits, preserving the encoded logical state.
• It utilizes repeated, non-demolition syndrome extraction cycles with techniques like CNOT-based and optimized CZZ gates to enhance error detection across superconducting and spin-qubit systems.
• Optimized protocols, including multi-qubit parity mapping and measurement-free architectures, demonstrate improved logical error thresholds and reduced operational depth.

Searching arXiv for recent and foundational papers on surface-code stabilizer readout to ground the article in current literature. arXiv search query: surface code stabilizer readout superconducting repeated syndrome extraction CZZ parity measurement Surface code stabilizer readout is the procedure by which the local parity constraints of a surface code are extracted without directly measuring, and therefore destroying, the encoded logical state. In the standard formulation, the code space is the common $+1$ eigenspace of local $X$-type and $Z$-type stabilizers, and readout is performed by coupling dedicated ancilla or syndrome qubits to neighboring data qubits, measuring only the ancillas, and repeating the process over many cycles to build a spacetime syndrome history for decoding. Across minimal superconducting demonstrations, distance-three logical processors, compiled spin-qubit and neutral-atom schedules, and measurement-free variants, the same core requirements recur: locality, repeated non-demolition extraction of stabilizer eigenvalues, and control of correlated faults introduced by the readout circuit itself (Córcoles et al., 2014, Wang et al., 4 Jun 2026, Beverland et al., 2024).

1. Stabilizer structure and syndrome logic

In a rotated or planar surface code, the logical qubit is encoded in the simultaneous $+1$ eigenspace of local parity checks. One standard rotated-patch notation writes

$$A_f = \prod_{j\in\partial f} X_j, \qquad B_f = \prod_{j\in\partial f} Z_j,$$

with logical strings such as

$$Z_L = \prod_{j \in \text{TOP}} Z_j, \qquad X_L = \prod_{j\in \text{LEFT}} X_j.$$

A distance-three superconducting realization gives an explicit $Z$-stabilizer example,

$$S_{\mathrm{Z}1}=Z_{\mathrm{D}0}Z_{\mathrm{D}1}Z_{\mathrm{D}3}Z_{\mathrm{D}4},$$

and logical operators

$$X_{\mathrm{L1}}=X_{\mathrm{D}6}X_{\mathrm{D}7}X_{\mathrm{D}8}, \qquad Z_{\mathrm{L1}}=Z_{\mathrm{D}0}Z_{\mathrm{D}3}Z_{\mathrm{D}6},$$

with analogous expressions for a second logical patch (Wang et al., 4 Jun 2026, Márton et al., 2024).

The minimal syndrome logic is already visible in the $2\times 2$ superconducting tile that realizes

$X$0

The encoded Bell state

$X$1

is a simultaneous $X$2 eigenstate of both checks. A single-qubit Pauli error anticommutes with one or both stabilizers and flips the corresponding syndrome bits according to

$X$3

For a general single-qubit coherent error

$X$4

the syndrome probabilities are

$X$5

This establishes the basic principle that arbitrary single-qubit errors can be projected into stabilizer syndrome sectors without direct logical-state measurement (Córcoles et al., 2014).

Once cycles are repeated, the object of interest is no longer a single syndrome snapshot but the parity change between rounds. In unrotated-code circuit analyses, detectors are defined by

$X$6

so decoding operates on changes in stabilizer outcomes over space and time rather than on a single round in isolation (Old et al., 10 Jun 2025).

2. Ancilla-mediated readout and early superconducting demonstrations

Ancilla-based surface-code readout measures stabilizers indirectly. In the four-qubit superconducting tile, two code qubits $X$7 are coupled to two syndrome qubits $X$8 arranged as a square. The $X$9-syndrome qubit $Z$0 is initialized in $Z$1, the $Z$2-syndrome qubit $Z$3 in $Z$4, parity information is mapped onto them through CNOT-equivalent gates synthesized from the echoed cross-resonance primitive

$Z$5

and $Z$6 is Hadamard-rotated before computational-basis measurement. Because the syndrome qubits begin in known eigenstates and only acquire parity information, the readout is QND with respect to the stabilizers. Conditioned on the no-error syndrome outcome $Z$7, tomography returns the original Bell state with fidelity

$Z$8

For the other syndrome outcomes, the conditioned code states are the corresponding Bell states,

$Z$9

The same experiment reports two-qubit gate fidelities between about $+1$0 and $+1$1, single-qubit gate fidelities above $+1$2, single-shot assignment fidelities above $+1$3 for all four readout channels, conditional Bell-state fidelities in the range $+1$4–$+1$5, and syndrome contrasts around $+1$6 in continuous-rotation experiments (Córcoles et al., 2014).

A later seven-qubit superconducting implementation demonstrated repeated error detection on the smallest viable surface-code instance with four data qubits $+1$7 and three ancillas $+1$8. The measured stabilizers are

$+1$9

with logical operators

$$A_f = \prod_{j\in\partial f} X_j, \qquad B_f = \prod_{j\in\partial f} Z_j,$$0

The device uses a pipelined, sequential stabilizer-measurement scheme and low-crosstalk multiplexed ancilla readout, with ancilla readout inducing less than $$A_f = \prod_{j\in\partial f} X_j, \qquad B_f = \prod_{j\in\partial f} Z_j,$$1 phase error on any data qubit. After a single stabilizer cycle, the average logical fidelity across the four prepared logical cardinal states is $$A_f = \prod_{j\in\partial f} X_j, \qquad B_f = \prod_{j\in\partial f} Z_j,$$2. Under repeated cycles and postselection on trajectories with no detected error, the logical observables decay with fitted times

$$A_f = \prod_{j\in\partial f} X_j, \qquad B_f = \prod_{j\in\partial f} Z_j,$$3

exceeding the best constituent-qubit values

$$A_f = \prod_{j\in\partial f} X_j, \qquad B_f = \prod_{j\in\partial f} Z_j,$$4

The corresponding per-cycle error probabilities are

$$A_f = \prod_{j\in\partial f} X_j, \qquad B_f = \prod_{j\in\partial f} Z_j,$$5

This makes explicit the distinction between merely measuring parity once and sustaining repeated stabilizer extraction over multiple cycles (Andersen et al., 2019).

3. Repeated syndrome extraction, decoding, and lattice surgery

In the distance-three superconducting processor with lattice-surgery logical operations, surface-code stabilizer readout is implemented as repeated syndrome extraction cycles on two rotated patches, each containing $$A_f = \prod_{j\in\partial f} X_j, \qquad B_f = \prod_{j\in\partial f} Z_j,$$6 data qubits and $$A_f = \prod_{j\in\partial f} X_j, \qquad B_f = \prod_{j\in\partial f} Z_j,$$7 syndrome qubits. Each cycle comprises four layers of CZ gates followed by a round of measurements on the syndrome qubits. The syndrome history is then decoded classically, and the decoded history determines the reported logical memory, Bell-state fidelity, algorithmic accuracy, and logical gate fidelity. In the logical-memory benchmark, the logical qubits are initialized in $$A_f = \prod_{j\in\partial f} X_j, \qquad B_f = \prod_{j\in\partial f} Z_j,$$8 and preserved for $$A_f = \prod_{j\in\partial f} X_j, \qquad B_f = \prod_{j\in\partial f} Z_j,$$9 SECs, yielding per-cycle logical error rates

$$Z_L = \prod_{j \in \text{TOP}} Z_j, \qquad X_L = \prod_{j\in \text{LEFT}} X_j.$$0

after leakage events are rejected (Wang et al., 4 Jun 2026).

Lattice surgery in that processor is itself a reconfiguration of stabilizer readout. To measure the joint logical operator $$Z_L = \prod_{j \in \text{TOP}} Z_j, \qquad X_L = \prod_{j\in \text{LEFT}} X_j.$$1, two distance-three patches are merged into a $$Z_L = \prod_{j \in \text{TOP}} Z_j, \qquad X_L = \prod_{j\in \text{LEFT}} X_j.$$2 rotated surface code by inserting ancilla data qubits $$Z_L = \prod_{j \in \text{TOP}} Z_j, \qquad X_L = \prod_{j\in \text{LEFT}} X_j.$$3 and ancilla syndrome qubits $$Z_L = \prod_{j \in \text{TOP}} Z_j, \qquad X_L = \prod_{j\in \text{LEFT}} X_j.$$4. Boundary $$Z_L = \prod_{j \in \text{TOP}} Z_j, \qquad X_L = \prod_{j\in \text{LEFT}} X_j.$$5-stabilizers are extended from weight two to weight four, and the four ancilla syndrome qubits measure newly created boundary-crossing $$Z_L = \prod_{j \in \text{TOP}} Z_j, \qquad X_L = \prod_{j\in \text{LEFT}} X_j.$$6-stabilizers. The joint logical operator is then obtained from the stabilizer outcomes as

$$Z_L = \prod_{j \in \text{TOP}} Z_j, \qquad X_L = \prod_{j\in \text{LEFT}} X_j.$$7

After splitting, ancilla data are measured in the $$Z_L = \prod_{j \in \text{TOP}} Z_j, \qquad X_L = \prod_{j\in \text{LEFT}} X_j.$$8 basis, boundary stabilizers revert to their original support, and Pauli-frame updates are determined from intermediate syndrome and ancilla outcomes. In Bell-state generation, the raw expectation values

$$Z_L = \prod_{j \in \text{TOP}} Z_j, \qquad X_L = \prod_{j\in \text{LEFT}} X_j.$$9

give

$Z$0

while decoded values improve $Z$1 and $Z$2 to $Z$3 and $Z$4, with

$Z$5

Detected-error-free post-selection yields

$Z$6

The same syndrome infrastructure supports a logical Deutsch-Jozsa implementation and logical $Z$7 teleportation, the latter with detected-error-free post-selected average logical gate fidelity

$Z$8

The paper also notes that the logical $Z$9 measurement is non-fault-tolerant in the current implementation, so readout quality remains basis dependent (Wang et al., 4 Jun 2026).

At a more abstract level, such procedures can be treated as stabilizer channels: stabilizer circuits that map an input stabilizer code to an output stabilizer code while implementing a logical action. In a single code-deformation step with measured commuting Pauli set $$S_{\mathrm{Z}1}=Z_{\mathrm{D}0}Z_{\mathrm{D}1}Z_{\mathrm{D}3}Z_{\mathrm{D}4},$$0, the output stabilizer group is

$$S_{\mathrm{Z}1}=Z_{\mathrm{D}0}Z_{\mathrm{D}1}Z_{\mathrm{D}3}Z_{\mathrm{D}4},$$1

The associated fault analysis introduces a channel check matrix $$S_{\mathrm{Z}1}=Z_{\mathrm{D}0}Z_{\mathrm{D}1}Z_{\mathrm{D}3}Z_{\mathrm{D}4},$$2, a logical effect matrix $$S_{\mathrm{Z}1}=Z_{\mathrm{D}0}Z_{\mathrm{D}1}Z_{\mathrm{D}3}Z_{\mathrm{D}4},$$3, and fault distance

$$S_{\mathrm{Z}1}=Z_{\mathrm{D}0}Z_{\mathrm{D}1}Z_{\mathrm{D}3}Z_{\mathrm{D}4},$$4

equivalently the minimum weight in $$S_{\mathrm{Z}1}=Z_{\mathrm{D}0}Z_{\mathrm{D}1}Z_{\mathrm{D}3}Z_{\mathrm{D}4},$$5. This formalism is used to analyze both lattice-surgery $$S_{\mathrm{Z}1}=Z_{\mathrm{D}0}Z_{\mathrm{D}1}Z_{\mathrm{D}3}Z_{\mathrm{D}4},$$6 measurement and more intricate deformation-based operations such as logical Hadamard, including the effect of hook faults and time-local composition (Beverland et al., 2024).

4. Scalable control stacks and platform-specific readout mechanisms

A central problem in surface-code stabilizer readout is not only how to measure a single stabilizer, but how to do so at scale without exploding control complexity or crosstalk. A superconducting proposal based on fast-flux-tunable transmons addresses this with a repeating eight-qubit unit cell containing four data qubits $$S_{\mathrm{Z}1}=Z_{\mathrm{D}0}Z_{\mathrm{D}1}Z_{\mathrm{D}3}Z_{\mathrm{D}4},$$7 and four ancillas $$S_{\mathrm{Z}1}=Z_{\mathrm{D}0}Z_{\mathrm{D}1}Z_{\mathrm{D}3}Z_{\mathrm{D}4},$$8. The readout cycle is pipelined: while one stabilizer type undergoes coherent two-qubit interaction steps, the other is being measured. The cycle occupies slots $$S_{\mathrm{Z}1}=Z_{\mathrm{D}0}Z_{\mathrm{D}1}Z_{\mathrm{D}3}Z_{\mathrm{D}4},$$9 for $$X_{\mathrm{L1}}=X_{\mathrm{D}6}X_{\mathrm{D}7}X_{\mathrm{D}8}, \qquad Z_{\mathrm{L1}}=Z_{\mathrm{D}0}Z_{\mathrm{D}3}Z_{\mathrm{D}6},$$0-type operations and $$X_{\mathrm{L1}}=X_{\mathrm{D}6}X_{\mathrm{D}7}X_{\mathrm{D}8}, \qquad Z_{\mathrm{L1}}=Z_{\mathrm{D}0}Z_{\mathrm{D}3}Z_{\mathrm{D}6},$$1 for $$X_{\mathrm{L1}}=X_{\mathrm{D}6}X_{\mathrm{D}7}X_{\mathrm{D}8}, \qquad Z_{\mathrm{L1}}=Z_{\mathrm{D}0}Z_{\mathrm{D}3}Z_{\mathrm{D}6},$$2-type operations, with optional data operations in slots $$X_{\mathrm{L1}}=X_{\mathrm{D}6}X_{\mathrm{D}7}X_{\mathrm{D}8}, \qquad Z_{\mathrm{L1}}=Z_{\mathrm{D}0}Z_{\mathrm{D}3}Z_{\mathrm{D}6},$$3 and $$X_{\mathrm{L1}}=X_{\mathrm{D}6}X_{\mathrm{D}7}X_{\mathrm{D}8}, \qquad Z_{\mathrm{L1}}=Z_{\mathrm{D}0}Z_{\mathrm{D}3}Z_{\mathrm{D}6},$$4. The resulting pipelined unit-cell cycle has depth $$X_{\mathrm{L1}}=X_{\mathrm{D}6}X_{\mathrm{D}7}X_{\mathrm{D}8}, \qquad Z_{\mathrm{L1}}=Z_{\mathrm{D}0}Z_{\mathrm{D}3}Z_{\mathrm{D}6},$$5. For Surface-17, with single-qubit gate time $$X_{\mathrm{L1}}=X_{\mathrm{D}6}X_{\mathrm{D}7}X_{\mathrm{D}8}, \qquad Z_{\mathrm{L1}}=Z_{\mathrm{D}0}Z_{\mathrm{D}3}Z_{\mathrm{D}6},$$6, $$X_{\mathrm{L1}}=X_{\mathrm{D}6}X_{\mathrm{D}7}X_{\mathrm{D}8}, \qquad Z_{\mathrm{L1}}=Z_{\mathrm{D}0}Z_{\mathrm{D}3}Z_{\mathrm{D}6},$$7 time $$X_{\mathrm{L1}}=X_{\mathrm{D}6}X_{\mathrm{D}7}X_{\mathrm{D}8}, \qquad Z_{\mathrm{L1}}=Z_{\mathrm{D}0}Z_{\mathrm{D}3}Z_{\mathrm{D}6},$$8, and readout plus photon depletion $$X_{\mathrm{L1}}=X_{\mathrm{D}6}X_{\mathrm{D}7}X_{\mathrm{D}8}, \qquad Z_{\mathrm{L1}}=Z_{\mathrm{D}0}Z_{\mathrm{D}3}Z_{\mathrm{D}6},$$9, the full QEC cycle time is about $2\times 2$0. The same architecture uses only three fixed single-qubit gate frequencies and three primitive flux pulses for the entire repeating fabric, and it explicitly supports defect-based logical qubits and lattice surgery by masking ancilla Hadamards or flux-pulse primitives (Versluis et al., 2016).

In crossbar spin-qubit architectures, the stabilizer cycle must be compiled into native operations: ESR rotations, electron shuttling, exchange-based $2\times 2$1 gates, and Pauli readout via spin-to-charge conversion or PSB. The surface-code patch is mapped onto a $2\times 2$2 crossbar unit with alternating Larmor frequencies $2\times 2$3 and $2\times 2$4. The protocol defines explicit Z-cycle and X-cycle routing schedules, then converts them into abstract and physical gate-voltage pulse sequences. PSB readout pairs the measured ancilla with a neighboring reference qubit and infers spin parity from the charge outcome. For parallel operation, the total cycle time is

$2\times 2$5

and the refined idle-qubit crosstalk estimate is

$2\times 2$6

below the empirical threshold

$2\times 2$7

The paper therefore identifies an experimentally relevant below-threshold regime for compiled stabilizer extraction in a shared-control spin-qubit array (Pataki et al., 2024).

A more radical platform-specific variant replaces ancilla-gate circuits by spectroscopy of native many-body stabilizers. In the proposed Majorana fermion surface code, a square-octagon lattice of Josephson-coupled topological superconductor islands realizes the commuting Hamiltonian

$2\times 2$8

where $2\times 2$9 is the product of four Majoranas around a square plaquette and $X$00 the product of eight Majoranas around an octagonal plaquette. Square stabilizers are generated by charging-energy-induced phase slips; octagon stabilizers arise from fourth-order ring exchange. Readout is performed by microwave spectroscopy: for square plaquettes by observing stabilizer-dependent excitation gaps, and for octagons by adiabatically turning on charging energy so that phase slips split the spectrum in a parity-dependent way, measuring the gap, and adiabatically returning to the original Hamiltonian. This is explicitly presented as single-step measurement of multi-body stabilizers rather than ancilla-based circuit extraction (Vijay et al., 2015).

5. Depth reduction, multi-qubit parity mapping, and alternative readout primitives

Several recent works focus on replacing the standard staircase of two-qubit gates by primitives that shorten the stabilizer circuit and reshape its error channel. A superconducting three-qubit $X$01 gate is designed to map the parity of two data qubits onto one measurement qubit in a single step. The ideal unitary is equivalent to applying CZ between the ancilla and each of the two data qubits simultaneously, and the paper describes a five-step protocol: prepare ancilla in $X$02, activate the $X$03 couplings, switch them off, apply a second Hadamard, and measure the ancilla. For surface-code readout, this reduces entangling depth to two timesteps per Pauli type instead of four. The optimized gate can be executed in $X$04 ns with fidelity $X$05, with

$X$06

In the rotated surface code, the threshold rises from about $X$07 for the standard CZ-based protocol to approximately $X$08 with the optimized effective Pauli model, and the logical error rate in the experimentally relevant regime $X$09 to $X$10 is reduced by up to about one order of magnitude. In the unrotated code, the threshold rises to approximately $X$11 and the geometry permits a strictly fault-tolerant CZZ schedule (Tasler et al., 10 Jun 2025).

A complementary analysis asks whether such multi-qubit gates can be strictly fault-tolerant at all. For unrotated surface codes, the answer is affirmative when one uses a single ancilla and native three-qubit $X$12 gates with suitable ordering. The protocol reduces a weight-$X$13 stabilizer measurement from $X$14 fault locations to approximately $X$15. In a distance-three example, a full stabilizer round uses $X$16 entangling time steps with CZ, but only $X$17 with $X$18. The asymptotic fault-location count ratio satisfies

$X$19

so the $X$20 protocol has about $X$21 fewer fault locations. Under belief-matching decoding with idling noise $X$22, the threshold increases from

$X$23

to

$X$24

The same study reports that in the optimistic regime $X$25, the unrotated $X$26 protocol can yield logical error rates up to $X$27 lower in the $X$28 to $X$29 physical-error range with idling noise included, and still outperforms the $X$30-based protocol for $X$31 when $X$32 (Old et al., 10 Jun 2025).

Other alternatives compile stabilizer readout into lower-level parity measurements. On the Cairo pentagonal tiling, a four-body stabilizer is reconstructed from five two-body pair measurements rather than six, and a full round needs six time steps rather than ten. Monte Carlo simulations then raise the threshold of the pair-measurement surface code from about $X$33 to about $X$34, and improve the teraquop footprint at $X$35 physical gate error rate from about $X$36 qubits to about $X$37 qubits. The same paper notes, however, that bidirectional hook errors cut the effective distance in half and likely make the construction worse below about $X$38 physical gate error rate (Gidney, 2022).

Single-shot analog parity mapping has also been proposed. In a dispersive-shift-based superconducting architecture, an ancilla is driven at frequencies resonant only for selected parity sectors because of engineered $X$39 shifts. For the simulated four-qubit system, two ancilla drives at

$X$40

produce a process fidelity of $X$41 with gate time $X$42 ns. The paper presents this as a replacement for a multi-CNOT stabilizer circuit by a single-shot parity-selective ancilla drive (Baker, 2023).

Neutral-atom surface-code readout exhibits a different optimization target. In Rydberg-mediated stabilizer measurement, the best protocol is not the one with the best physical two-qubit gate fidelity, but the one that prevents propagation of leakage caused by spontaneous emission from Rydberg states. A leaked excitation can spread through later gates, so under bad protocols only

$X$43

decay events may already cause a logical failure, instead of the usual

$X$44

The paper identifies a No-Hopping protocol in the data-ancilla blockade setting and a No-Phase protocol in the all-to-all blockade setting as the logically favorable choices, explicitly arguing that gate optimization for logical error suppression is more relevant than optimization for raw two-qubit fidelity alone (Jandura et al., 2024).

A recurring implication of these works is that “better stabilizer readout” is not synonymous with “higher unitary fidelity.” This suggests a more precise criterion: the residual faults must be those that least damage decoding, distance preservation, and leakage containment (Tasler et al., 10 Jun 2025, Jandura et al., 2024).

6. Noise, readout scheduling, and measurement-free directions

The performance of surface-code stabilizer readout depends strongly on how measurement noise is modeled across cycles. Under quasistatic phase damping, physical noise is described by

$X$45

with $X$46 fixed across all cycles within a shot and redrawn between shots. The phenomenological readout model flips a recorded stabilizer outcome with probability $X$47,

$X$48

To handle such readout errors, the decoder uses $X$49 consecutive cycles and 3D MWPM with spatial and temporal weights

$X$50

assuming the last measurement cycle is readout-error-free. In this setting, the reported surface-code threshold is

$X$51

for $X$52. Although the threshold is close to that of independent phase-flip noise plus readout errors, the logical error at threshold is about $X$53, compared with about $X$54 for independent phase flips. This indicates that temporally correlated coherent dephasing changes multi-cycle decoding behavior without destroying threshold behavior (Pataki et al., 2024).

Repeated stabilizer measurement is itself a resource that must be scheduled. In an idling rotated surface-code patch with circuit-level Pauli noise, amplitude damping, phase damping, gate errors, and readout errors, the logical failure rate is minimized at an optimal number $X$55 of syndrome rounds during a fixed memory interval $X$56. The leading-order estimate

$X$57

yields

$X$58

The reported qualitative trend is that the optimal number of rounds gets smaller for better qubits and larger for better gates or larger code sizes. The hardware interpretation is platform dependent: for superconducting qubits, with approximate parameters $X$59, $X$60, $X$61, $X$62, and cycle time $X$63 ns, the beneficial strategy is to perform the maximum feasible number of stabilizer measurement rounds; for neutral atoms, with $X$64 s, $X$65 s, $X$66, $X$67, and cycle time $X$68 ms, the optimum may involve substantially fewer rounds than the maximum allowed by wall-clock time (Márton et al., 2024).

A more radical response to the readout bottleneck is to remove mid-circuit measurement entirely. In a 3D stacked measurement-free architecture, three rotated surface-code patches are stacked vertically: a logical ancilla $X$69, a data block $X$70, and a logical ancilla $X$71. Standard measurement-based syndrome extraction and classical feed-forward are replaced by coherent parity mapping and coherent correction,

$X$72

Vertical couplers make inter-layer operations constant-depth $X$73 in code distance, avoiding the $X$74 SWAP overhead of planar measurement-free realizations while preserving local 2D stabilizer checks inside each layer. The paper states that the 3D architecture overcomes the readout error floor and achieves logical error rates orders of magnitude below both standard measurement-based surface codes and 2D measurement-free variants in regimes with slow, noisy measurements (Min et al., 20 Jan 2026).

Surface code stabilizer readout therefore spans a spectrum from minimal ancilla parity checks to repeated, decoded spacetime syndrome extraction; from native multi-body spectroscopy to deeply optimized three-qubit parity gates; and from conventional mid-circuit measurement to fully coherent feedback. The common thread is that the stabilizer record is not merely diagnostic. It is the operational interface between the local code constraints and the logical layer: it determines whether encoded information is preserved, whether lattice surgery yields the intended joint observable, and whether the full architecture remains distance preserving under realistic noise.