THE QUBIT PARADOX: WHY MORE QUBITS ACTUALLY LOWER ERROR RATES?
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Fault Tolerance, Logical Qubits, Quantum Error Correction, urface Code, Threshold Theorem
Abstract
Physical qubits intuitively introduces greater cumulative noise and control complexity. This “Qubit Paradox” presents a fundamental barrier to scalability, suggesting that larger systems might become inherently less stable. This research aims to rigorously validate the threshold theorem, defining the precise boundary where topological protection overcomes physical noise accumulation. We utilized high-fidelity Monte Carlo simulations of Rotated Surface Codes, scaling from distance d=3 to d=9, under realistic circuit-level noise models including leakage and crosstalk. Decoding was executed using the Minimum Weight Perfect Matching (MWPM) algorithm to analyze logical failure rates across 109 error correction cycles. Results identify a critical physical error threshold of approximately 0.57%. Below this value, logical error rates exhibited exponential suppression via power-law decay, reducing by seven orders of magnitude at distance-9. Conversely, systems operating above this threshold demonstrated error amplification with increased scale. We conclude that the paradox resolves only when individual gate fidelity surpasses the threshold, mandating that hardware optimization must precede quantitative scaling. These findings establish a validated roadmap for the transition from the NISQ era to fault-tolerant architecture.
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Copyright (c) 2025 Miku Fujita, Ren Suzuki, Daiki Nishida
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