We propose hardware-efficient schemes for implementing logical h and s gates transversally on the rotated surface code with reconfigurable neutral atom arrays. Our protocol for logical s gates utilizes the time dynamics of the data and ancilla qubits during syndrome extraction (SE). In particular, we move beyond traditional schemes where transversal logical gates take place between two SE rounds and instead embed our fold-transversal logical operation within a single SE round, leveraging the fact that data and ancilla qubits can be morphed into an unrotated surface code state halfway through an SE round. Under circuit noise, we observe that the performance of our s gate protocol is comparable to that of the quantum memory. For logical h gates, we first develop a simple strategy to rotate code patches efficiently with two sets of 2D acousto-optic deflectors (2D-AOD). We also propose a new transversal h gate protocol, based on the same principle as our s gate protocol, to remove the need for an additional set of 2D-AOD. Together with transversal logical cnot gates, our protocols complete a transversal logical Clifford gate set on the rotated surface code and allow for efficient implementation on neutral atom array platforms.
Neutral-atom quantum computers offer arbitrary connectivity enabled by atom transport. Some logical operations can then be simplified or reduced entirely to geometric rearrangements of the atoms. Minimizing the duration of these movements is therefore essential for high logical throughput. We introduce new primitives to shear, rotate and reflect 2D arrays of atoms in a static lattice using sweeps of a single dynamic crossed acousto-optic deflector (AOD) pair. Using (nega-)binary and geometric decompositions, we achieve an AOD stroke count scaling logarithmically in the linear size of the array. In one example, we use the Paeth decomposition to implement a
90∘ rotation for a transversal Hadamard gate in a rotated surface code of distance
d in
3⌊log2(d−1)⌋+4 AOD strokes and
O(d1/3) constant-jerk time, against
O(d2) strokes and
O(d7/3) time for atom-by-atom rearrangement.
A technique for realizing a universal set of fault-tolerant quantum operations is the code switching method, which leverages two quantum codes with complementary sets of transversal gates. To date, the application of this technique has been largely limited to families of color codes supporting a logical
T gate. No analogous code switching protocols exist for many other prominent families, such as rotated surface codes, or for finer
Z-rotation gates. In this work, we first utilize the doubling technique as a unified framework to construct a class of quantum color codes encoding a single logical qubit with an arbitrarily large minimum distance, enabling the transversal realization of arbitrary small logical
Z-rotation gates. We investigate the structural properties of this code family, demonstrating that they improve upon the parameters of state-of-the-art triorthogonal codes, achieve lower qubit overhead compared to certain known color codes, and admit single-shot decoding of
Z-syndromes via meta-checks. Furthermore, we show that this framework extends beyond color codes; specifically, it enables the generation of
r-orthogonal quantum codes,
r≥2, that inherit the local geometry of rotated surface codes. We then provide an overhead optimization protocol alongside several candidate codes tailored for realizing logical
Z-rotation gates within rotated surface codes. Finally, we extend the fault-tolerant code switching protocol based on transversal CNOT gates to incorporate fault-tolerant realization of
Z-rotation gates at any level of the Clifford hierarchy for geometries compatible with rotated surface codes. We present the first demonstration of fault-tolerant magic state preparation by means of code switching within a distance-three rotated surface code using a total footprint of only 45 physical qubits, and evaluate its performance through a simulation.
We give a fault tolerant construction for error correction and computation using two punctured quantum Reed-Muller (PQRM) codes. In particular, we consider the
[[127,1,15]] self-dual doubly-even code that has transversal Clifford gates (CNOT, H, S) and the triply-even
[[127,1,7]] code that has transversal T and CNOT gates. We show that code switching between these codes can be accomplished using Steane error correction. For fault-tolerant ancilla preparation we utilize the low-depth hypercube encoding circuit along with different code automorphism permutations in different ancilla blocks, while decoding is handled by the high-performance classical successive cancellation list decoder. In this way, every logical operation in this universal gate set is amenable to extended rectangle analysis. The CNOT exRec has a failure rate approaching
10−9 at
10−3 circuit-level depolarizing noise. Furthermore, we map the PQRM codes to a 2D layout suitable for implementation in arrays of trapped atoms and try to reduce the circuit depth of parallel atom movements in state preparation. The resulting protocol is strictly fault-tolerant for the
[[127,1,7]] code and practically fault-tolerant for the
[[127,1,15]] code. Moreover, each patch requires a permutation consisting of
7 sub-hypercube swaps only. These are swaps of rectangular grids in our 2D hypercube layout and can be naturally created with acousto-optic deflectors (AODs). Lastly, we show for the family of
[[22r,(r2r),2r]] QRM codes that the entire logical Clifford group can be achieved using only permutations, transversal gates, and fold-transversal gates.
Qubit shuttling has become an indispensable ingredient for scaling leading quantum computing platforms, including semiconductor spin, neutral-atom, and trapped-ion qubits, enabling both crosstalk reduction and tighter integration of control hardware. Cai et al. (2023) proposed a scalable architecture that employs short-range shuttling to realize effective three-dimensional connectivity on a strictly two-dimensional device. Building on recent advances in quantum error correction, we show that this architecture enables the native implementation of folded surface codes on 2D hardware, reducing the runtime of all single-qubit logical Clifford gates and logical CNOTs within subsets of qubits from
O(d) in conventional surface code lattice surgery to constant time. We present explicit protocols for these operations and demonstrate that access to a transversal
S gate reduces the spacetime volume of 8T-to-CCZ magic-state distillation by more than an order of magnitude compared with standard 2D lattice surgery approaches. Finally, we introduce a new "virtual-stack" layout that more efficiently exploits the quasi-three-dimensional structure of the architecture, enabling efficient multilayer routing on these two-dimensional devices.
Fault-tolerant quantum computation requires logical operations that manipulate encoded information while preserving quantum error-correction protection. In planar surface-code architectures, code deformation and lattice surgery provide a local, measurement-based route to such operations. Here we experimentally realize key elements of patch-based surface-code logical processing on a 107-qubit superconducting quantum processor. We first implement a reusable primitive layer comprising merge and split, patch expansion and shrinkage, and deformations mediated by domain walls and twist defects. We then compose these primitives to realize logical state routing, the logical controlled-NOT gate, and the single-qubit Hadamard and phase gates, which together form a Clifford-generating set. All operations are implemented on distance-three rotated surface-code patches with multi-round syndrome extraction and neural-network decoding, without post-selection. Our results advance superconducting surface-code experiments from protected logical memory to active, patch-based fault-tolerant logical operations.