Tensor-based quantum phase difference estimation for large-scale demonstration
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Abstract
Significance Quantum phase estimation (QPE) is a foundational algorithm for quantum chemistry, cryptanalysis, and solving linear equations, due to the potential of exponential acceleration for classical algorithms. Despite its importance, QPE has been limited to a few qubits on real devices due to high gate costs, reinforcing the belief that large-scale QPE requires error-corrected quantum computers. We challenge this by introducing a scalable, noise-robust algorithm tailored for quantum chemistry. The demonstration is given in (quasi) one-dimensional (1D) systems, specifically 1D Hubbard models and molecular systems up to 33 qubits, and the broader applicability of the proposed techniques beyond 1D remains to be demonstrated. These results allow QPE executions of a scale near the classical limit for full configuration interactions.