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As quantum computers improve, eventually we may have error-corrected devices that have very low error rate. However, many applications (Shor's algorithm, quantum chemistry) appear to require thousands of error-corrected qubits, if not more. Are there any promising examples in a lower qubit range of a few hundred fault-tolerant qubits, where it could truly be useful to society? The only concrete one I am aware of is Fermi-Hubbard model simulation, which might lie in this range.

shixian105
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In addition to the Fermi-Hubbard model, there are other many-body models whose simulation on a quantum computer with 100 high-quality qubits would provide novel insights for condensed matter physicists.

  • Simulation of the Heisenberg model

    The most up to date resource estimates give us 50 qubits with a $10^{-8}$ error rate for a classically intractable problem

  • Simulation of the 2D Transverse field ising model

    The most up to date resource estimates give us 100 qubits with a $10^{-5}$ error rate for a classically intractable problem

Reference: Table 2 of Quantum algorithms: A survey of applications and end-to-end complexities

Victory Omole
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