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Paper 1
Quantum Lego Power-up: Designing Transversal Gates with Tensor Networks
ChunJun Cao, Brad Lackey
- Year
- 2026
- Journal
- arXiv preprint
- DOI
- arXiv:2603.03542
- arXiv
- 2603.03542
Transversal gates are the simplest form of fault-tolerant gates and are relatively easy to implement in practice. Yet designing codes that support useful transversal operations -- especially non-Clifford or addressable gates -- remains difficult within the stabilizer formalism or CSS constructions alone. We show that these limitations can be overcome using tensor-network frameworks such as the quantum lego formalism, where transversal gates naturally appear as global or localized symmetries. Within the quantum lego formalism, small codes carrying desirable symmetries can be "glued" into larger ones, with operator-flow rules guiding how logical symmetries are preserved. This approach enables the systematic construction of codes with addressable transversal single- and multi-qubit gates targeting specific logical qubits regardless of whether the gate is Clifford or not. As a proof of principle, we build new finite-rate code families that support strongly transversal $T$, $CCZ$, $SH$, and Gottesman's $K_3$ gates, structures that are challenging to realize with conventional methods. We further construct holographic and fractal-like codes that admit addressable transversal inter-, meso-, and intra-block $T$, $CS$, and $C^\ell Z$ gates. As a corollary, we demonstrate that the heterogeneous holographic Steane-Reed-Muller black hole code also supports fully addressable transversal inter- and intra-block $CZ$ gates, significantly lowering the overhead for universal fault-tolerant computation.
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Fast surgery for quantum LDPC codes
Nouédyn Baspin, Lucas Berent, Lawrence Z. Cohen
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2510.04521
- arXiv
- 2510.04521
Quantum LDPC codes promise significant reductions in physical qubit overhead compared with topological codes. However, many existing constructions for performing logical operations come with distance-dependent temporal overheads. We introduce a scheme for performing generalized surgery on quantum LDPC codes using a constant number of rounds of syndrome measurement. The merged code in our scheme is constructed by taking the total complex of the base code and a suitably chosen homomorphic chain complex. We demonstrate the applicability of our scheme on an example multi-cycle code and assess the performance under a phenomenological noise model, showing that fast surgery performs comparably to standard generalized surgery with multiple rounds. Our results pave the way towards fault-tolerant quantum computing with LDPC codes with both low spatial and temporal overheads.
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