Quantum computational advantage in simulating many-body spin dynamics

IQC Colloquium - Chae-Yeun Park, Xanadu

Understanding the dynamics of quantum many-body systems is one of the fundamental objectives of physics. The existence of an efficient quantum algorithm for simulating these dynamics with reasonable resource requirements suggests that this problem might be among the first practically relevant tasks quantum computers can tackle. Although an efficient classical algorithm for simulating such dynamics is not generally expected, the classical hardness of many-body dynamics has been rigorously proven only for certain commuting Hamiltonians. In this talk, I will show that computing the output distribution of quantum many-body dynamics is classically difficult, classified as #P-hard, also for a large class of non-commuting many-body spin Hamiltonians. Our proof leverages the robust polynomial estimation technique and the #P-hardness of computing the permanent of a matrix. By combining this with the anticoncentration conjecture of the output distribution, I will argue that sampling from the output distribution generated by the dynamics of a large class of spin Hamiltonians is classically infeasible. Our findings can significantly reduce the number of qubits required to demonstrate quantum advantage using analog quantum simulators.

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