Classical codes plus SAT search yield no-go theorems limiting error detection in sub-8-qubit distillation and new minimal-qubit protocols for T-to-T (distances 4-5 on 10-11 qubits) and T-to-CCZ (distances 3-4 on 9-10 qubits).
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Low overhead quantum computation using lattice surgery
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When calculating the overhead of a quantum algorithm made fault-tolerant using the surface code, many previous works have used defects and braids for logical qubit storage and state distillation. In this work, we show that lattice surgery reduces the storage overhead by over a factor of 4, and the distillation overhead by nearly a factor of 5, making it possible to run algorithms with $10^8$ T gates using only $3.7\times 10^5$ physical qubits capable of executing gates with error $p\sim 10^{-3}$. These numbers strongly suggest that defects and braids in the surface code should be deprecated in favor of lattice surgery.
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representative citing papers
LightStim automates DEM construction for QEC protocols via a record-augmented Pauli tableau tracker, validated across memory, logical operations, distillation, and a novel cross-code lattice surgery design.
Double-slice routing provides bounded-depth spacetime routing for lattice surgery with termination guarantees, cutting compilation cost by up to 2.4x versus single-slice baselines and 7.5x with mapping optimizations on Hamiltonian simulation workloads.
Clifford+T synthesis for small-angle rotations reduces T-cost to ~O(θ²/δ) and makes Trotterization cost constant in the small-step limit.
Fermion lattices can be simulated on same-size qubit lattices with O(1) interaction overhead by dynamically reorienting the Jordan-Wigner transformation.
AI pre-decoders achieve O(1 μs) per round decoding runtimes on GPUs for surface codes while improving logical error rates over global decoding alone and enabling data-driven noise weight estimation.
KOVAL-Q uses SAT solving to optimize and verify surface-code logical operations with general encodings, finding d-cycle CNOTs and 2d-cycle rotations that reduce FTQC application runtime by about 10 percent.
Magic state cultivation prepares high-fidelity T states with an order of magnitude fewer qubit-rounds than prior distillation methods by gradually growing them within a surface code under depolarizing noise.
Lattice-surgery scheduling is mapped to 3D path embedding and solved with look-ahead Dijkstra projection, yielding 3.8x lower execution time on quantum phase estimation benchmarks versus greedy scheduling.
A symmetry-leveraging framework for fault-tolerant ancilla preparation in quantum BCH codes yields lower spatial overhead and logical error rates than standard distillation in simulations up to 127 qubits.
The biplanar architecture maps Fermi-Hubbard spin sectors to two planes, eliminating swaps and cutting each Trotter step depth to 4t_synth + 90 logical timesteps versus 6t_synth + 354 in single-plane methods, yielding an estimated 2-hour runtime for L=8 with 1.35 million physical qubits under a 1% 1
Triage is an adaptive parallel window decoding scheduler that reduces average logical error rates by 52.6% compared to standard temporal parallelism while keeping stalls low under scarce classical resources.
FTPrimitiveBench is a new benchmark suite for testing surface-code logical primitives under Pauli-biased, measurement-biased, and spatially non-uniform noise models, revealing that noise structure interacts distinctly with each primitive and decoder.
A defect-adaptive lattice surgery technique reconstructs joint logical parities on irregular surface-code patches via GF(2) binary synthesis from seam measurements and pre-merge constraints, yielding executable rules or failure certificates while preserving effective distance.
A tree-encoded fusion scheme and MemTree compiler suppress fusion erasure errors in photonic MBQC, achieving large execution-time reductions over prior compilers with real-hardware validation.
The paper introduces concrete code deformation procedures for dense surface code packing, proposes hook-error-avoiding CNOT scheduling for syndrome extraction, and reports Monte Carlo simulations showing lower logical error rates than standard surface codes at large distances and low physical error,
A resource estimation framework for distributed fault-tolerant quantum computers based on lattice surgery identifies feasible hardware configurations for eight applications across thousands of setups, showing that architecture design must be guided by resource analysis for scalability.
Quantum sieving for SVP in dimension 400 needs ~10^13 physical qubits and ~10^31 years under optimistic assumptions, offering no practical speedup over classical methods.
A pipelined framework with speculation for logical operations in fault-tolerant quantum computation reduces total pipeline steps by 20-40% on benchmarks by overlapping control, execution, and decoding stages.
GeneCS compiler reduces ancillary qubits and checks by over 85% on average for single- and cross-code logical operations on stabilizer codes while preserving error rates and scaling to over 10,000 qubits.
Catalyst towers reduce runtime and spacetime volume for continuous rotations in surface codes at small and medium distances in phase oracle and variational state preparation circuits for option pricing.
Simulations show non-local CNOT achieves up to 10x lower logical error than teleportation and distributed qLDPC needs d≈11 at p=10^{-4} or d≈29 at p=10^{-3} (with p_ebit=10p) for <10^{-12} error.
Quantum amplitude estimation algorithm for credit risk economic capital with qubit and runtime estimates on assumed future hardware.
NMR spectral simulations in zero/ultralow fields for small molecules and proteins are identified as promising applications for fault-tolerant quantum computation via qubitized dynamics circuits.
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