Quantifying Error-Correction Overhead for
Long-Time QENM Simulations

Comprehensive resource analysis for fault-tolerant quantum elastic network model simulations on surface-code quantum hardware.

23 - 43
Logical Qubits
d = 13 - 35
Code Distance Range
64,047
Break-Even Atoms (0.1 ps)
75.7x
Max Graphene Speedup

Key Findings

Exponential Space Advantage Confirmed

O(log N) qubits

Even 10,000 atoms need only 43 logical qubits, confirming QENM's dramatic space compression.

Substantial Physical Overhead

1,158:1 to 10^12:1

Physical-to-logical qubit ratios range widely depending on circuit depth and target fidelity.

Error Rate is Critical Lever

10x gives 100x savings

A 10x improvement in physical error rate yields over 100x reduction in qubit requirements.

Graphene Advantage at Scale

500+ nm sheets

Quantum speedup emerges for graphene sheets above 500 nm, reaching 75.7x at 1,000 nm.

Interactive Analysis

Physical Qubit Requirements vs System Size

Physical-to-Logical Overhead Ratio

Quantum Speedup Factor vs System Size

Runtime Comparison (t = 10 ps)

Graphene: Qubit Requirements

Graphene: Speedup Factor

Code Distance vs Physical Error Rate

Physical Qubits vs Error Rate

Logical Qubit Scaling

Circuit Depth vs System Size (t = 10 ps)

Resource Estimates

Atoms Time (ps) Logical Qubits Code Distance Physical Qubits Overhead Ratio T-Gates Runtime (s)

Graphene Case Study (t = 10 ps)

Side (nm) Atoms Logical Qubits Code Distance Physical Qubits Quantum Time (s) Classical Time (s) Speedup