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About this paper
Anurag Anshu, Shankar Balasubramanian, Jonas Haferkamp, Aram W. Harrow, Xinyu Tan
Researchers developed a family of depth-1 quantum expanders on n qubits and the special unitary group, which they then applied to construct 1D frustration-free Hamiltonians exhibiting volume-law entanglement with a \u0398(n^-2) gap, and to design streaming protocols for highly entangled states.
Key insights
- Constant-degree, constant-gap quantum expanders can be realized with extremely shallow, depth-1 quantum circuits using only Pauli and CNOT gates in a 1D local geometry.
- The conjectured S \u223d 1/\u0394^1/2 bound for 1D frustration-free Hamiltonians is tight, as systems can exhibit volume-law entanglement (\u0398(n)) with a polynomially small spectral gap (\u0398(n^-2)).
- The locality and expansion properties of depth-1 expanders enable the development of single-pass, resource-efficient streaming protocols for verifying highly entangled quantum states with constant memory.
Summary by alphaXiv.
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