Quantum-classical crossover in fault-tolerant quantum dynamics simulation

• URL: http://arxiv.org/abs/2607.16116v1
• Date: Fri, 17 Jul 2026 16:54:25 GMT
• Title: Quantum-classical crossover in fault-tolerant quantum dynamics simulation
• Abstract summary: We introduce a scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations.<n>A benchmark against state-of-the-art tensor-network and variational Monte Carlo algorithms reveals a concrete crossover for mixed-field Ising dynamics.
• Score: 56.198154828333685
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: While quantum computers promise to solve classically intractable problems, identifying the point at which fault-tolerant quantum computation outperforms the best classical algorithms for practical applications remains an outstanding challenge. Here we establish a concrete quantum-classical crossover for quantum many-body dynamics under realistic hardware conditions. We introduce a scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations, suppressing the residual logical errors that limit existing partially fault-tolerant approaches. A benchmark against state-of-the-art tensor-network and variational Monte Carlo algorithms reveals a concrete crossover for mixed-field Ising dynamics at modest system sizes. For a physical error rate of $p=10^{-3}$, fault-tolerant simulation requires approximately 2 hours and $3.7 \times 10^5$ physical qubits for a 100-site 1D system, whereas tensor network approaches would require about 100 years. For 2D models, where rapid entanglement growth limits the classical evolution time, we project quantum runtimes within minutes. A physical error rate of $p=10^{-4}$ leads to at least an order of magnitude reduction in qubit count ($3.1 \times 10^4$ physical qubits) and runtime (minutes for 1D and seconds for 2D). The reduction in quantum runtime arises from our improved rotation-state injection and co-design of quantum error correction and observable-estimation protocols, which jointly suppress logical-error accumulation and reduce sampling overhead. Our results establish a scalable route towards practical quantum advantage and identify quantitative engineering targets for future fault-tolerant architectures.

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