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.
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Optimal ancilla-free Clifford+T approximation of z-rotations
Canonical reference. 78% of citing Pith papers cite this work as background.
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Background
78% of classified citations
abstract
We consider the problem of approximating arbitrary single-qubit z-rotations by ancilla-free Clifford+T circuits, up to given epsilon. We present a fast new probabilistic algorithm for solving this problem optimally, i.e., for finding the shortest possible circuit whatsoever for the given problem instance. The algorithm requires a factoring oracle (such as a quantum computer). Even in the absence of a factoring oracle, the algorithm is still near-optimal under a mild number-theoretic hypothesis. In this case, the algorithm finds a solution of T-count m + O(log(log(1/epsilon))), where m is the T-count of the second-to-optimal solution. In the typical case, this yields circuit approximations of T-count 3log_2(1/epsilon) + O(log(log(1/epsilon))). Our algorithm is efficient in practice, and provably efficient under the above-mentioned number-theoretic hypothesis, in the sense that its expected runtime is O(polylog(1/epsilon)).
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representative citing papers
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.
A microarchitecture-aware compiler for lattice surgery that exploits C-Phase commutativity to enable concurrent multi-target operations and dynamic event-driven scheduling, cutting execution time by up to 59.7 times versus standard baselines.
A deterministic recursive quantum circuit prepares antisymmetric states for η fermions in N orbitals with O(η²√N) T-gates and O(√N) dirty ancillas, outperforming sorting methods for η ≲ √N.
Stochastic magic-state production in fault-tolerant quantum computing inflates execution time but reduces peak resource demand, allowing stochastic-aware factory allocation to cut space-time volume by up to 27% and factories by up to 30% versus deterministic optima.
No-go theorems prove hierarchy level and state-independent sequences cannot maximize operational magic in early FTQC, requiring state-aware differentiable optimization and nonlinear phases for scalable magic generation.
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 generative QMLC framework tokenizes GST data, embeds it via curriculum-trained set-vision transformers into a context-aware latent space, and uses diffusion models to synthesize circuits conditioned on desired measurement distributions.
INJEQT reduces synthillation error by up to 22x, wall-clock time by 13x, and space-time cost by 7.2x in extractor FTQC architectures via auxiliary Rz synthesis and pre-fetching.
Syn@fac optimization reduces estimated circuit failure probability by a factor of 9 on average across non-Clifford benchmarks for bivariate bicycle code modular FTQC architectures, with additional gains from transvection deferral and Clifford insertion.
A teleportation-based parallelization architecture for neutral-atom quantum error correction delivers up to 3x speedup over extractor methods at fixed space cost and enables simulated quantum advantage at 11,495 atoms and 15-hour runtime.
A trapped-ion architecture based on LDPC codes and cat-state factories achieves 110 logical qubits and one million T gates per day using 2514 physical qubits, with estimates for Heisenberg model simulation on 100 sites in one month using 10000 qubits.
O3LS reduces space overhead by up to 46.7% and time overhead by up to 36% in lattice surgery while suppressing logical error rates by up to an order of magnitude compared with prior layout and scheduling approaches.
Delta_max outperforms T-depth as a predictor of slowdown under magic-state constraints and supplies a tight lower bound on makespan with zero violations across 4,904 test instances.
Orbifold lattices incur m^4 Trotter overhead, m^2 contamination, and mandatory mass extrapolation, rendering them 10^4 to 10^10 times costlier than alternatives for a 10^3 calculation.
The paper derives explicit finite-d break-even synthesis costs for qudit vs. qubit encodings of diagonal quadratic operators in product-formula and LCU simulations, identifying low-d regions where qudits yield savings.
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.
A two-level decoder scheduling framework reduces classical processing requirements for quantum error correction by 10-40% on fault-tolerant benchmarks by managing bursty workloads as shared resources.
AL-QHD benchmarks on nonconvex test functions and ACOPF power problems show useful accuracy at fixed qubit cost but require roughly 10^8 T gates for realistic instances.
citing papers explorer
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Efficient and high-performance routing of lattice-surgery paths on three-dimensional lattice
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.
-
Design automation and space-time reduction for surface-code logical operations using a SAT-based EDA kernel compatible with general encodings
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: growing T states as cheap as CNOT gates
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.
-
C-Phase-Aware Compilation for Efficient Fault-Tolerant Quantum Execution
A microarchitecture-aware compiler for lattice surgery that exploits C-Phase commutativity to enable concurrent multi-target operations and dynamic event-driven scheduling, cutting execution time by up to 59.7 times versus standard baselines.
-
Recursive algorithm for constructing antisymmetric fermionic states in first quantization mapping
A deterministic recursive quantum circuit prepares antisymmetric states for η fermions in N orbitals with O(η²√N) T-gates and O(√N) dirty ancillas, outperforming sorting methods for η ≲ √N.
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Price and Payoff: Non-Determinism in Fault Tolerant Quantum Computation
Stochastic magic-state production in fault-tolerant quantum computing inflates execution time but reduces peak resource demand, allowing stochastic-aware factory allocation to cut space-time volume by up to 27% and factories by up to 30% versus deterministic optima.
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Quantum Magic in early FTQC: From Diagonal Clifford Hierarchy No-Go Theorems to Architecture Design Blueprints
No-go theorems prove hierarchy level and state-independent sequences cannot maximize operational magic in early FTQC, requiring state-aware differentiable optimization and nonlinear phases for scalable magic generation.
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FTPrimitiveBench: A Benchmark Suite For Logical Computation Under Hardware-Motivated and Biased Noise Models
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.
-
From Characterization To Construction: Generative Quantum Circuit Synthesis from Gate Set Tomography Data
A generative QMLC framework tokenizes GST data, embeds it via curriculum-trained set-vision transformers into a context-aware latent space, and uses diffusion models to synthesize circuits conditioned on desired measurement distributions.
-
INJEQT: Improved Magic-State Injection Protocol for Fault-Tolerant Quantum Extractor Architectures
INJEQT reduces synthillation error by up to 22x, wall-clock time by 13x, and space-time cost by 7.2x in extractor FTQC architectures via auxiliary Rz synthesis and pre-fetching.
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Assessing System Capabilities and Bottlenecks of an Early Fault-Tolerant Bicycle Architecture
Syn@fac optimization reduces estimated circuit failure probability by a factor of 9 on average across non-Clifford benchmarks for bivariate bicycle code modular FTQC architectures, with additional gains from transvection deferral and Clifford insertion.
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Architecting Early Fault Tolerant Neutral Atoms Systems with Quantum Advantage
A teleportation-based parallelization architecture for neutral-atom quantum error correction delivers up to 3x speedup over extractor methods at fixed space cost and enables simulated quantum advantage at 11,495 atoms and 15-hour runtime.
-
Fault-Tolerant Quantum Computing with Trapped Ions: The Walking Cat Architecture
A trapped-ion architecture based on LDPC codes and cat-state factories achieves 110 logical qubits and one million T gates per day using 2514 physical qubits, with estimates for Heisenberg model simulation on 100 sites in one month using 10000 qubits.
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O3LS: Optimizing Lattice Surgery via Automatic Layout Searching and Loose Scheduling
O3LS reduces space overhead by up to 46.7% and time overhead by up to 36% in lattice surgery while suppressing logical error rates by up to an order of magnitude compared with prior layout and scheduling approaches.
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When T-Depth Misleads: Predicting Fault-Tolerant Quantum Execution Slowdown under Magic-State Delivery Constraints
Delta_max outperforms T-depth as a predictor of slowdown under magic-state constraints and supplies a tight lower bound on makespan with zero violations across 4,904 test instances.
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Ether of Orbifolds
Orbifold lattices incur m^4 Trotter overhead, m^2 contamination, and mandatory mass extrapolation, rendering them 10^4 to 10^10 times costlier than alternatives for a 10^3 calculation.
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Fault-Tolerant Resource Comparison of Qudit and Qubit Encodings for Diagonal Quadratic Operators
The paper derives explicit finite-d break-even synthesis costs for qudit vs. qubit encodings of diagonal quadratic operators in product-formula and LCU simulations, identifying low-d regions where qudits yield savings.
-
Space and Time Cost of Continuous Rotations in Surface Codes
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.
-
Managing Classical Processing Requirements for Quantum Error Correction
A two-level decoder scheduling framework reduces classical processing requirements for quantum error correction by 10-40% on fault-tolerant benchmarks by managing bursty workloads as shared resources.
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Benchmarking and Resource Analysis for Augmented-Lagrangian Quantum Hamiltonian Descent
AL-QHD benchmarks on nonconvex test functions and ACOPF power problems show useful accuracy at fixed qubit cost but require roughly 10^8 T gates for realistic instances.