The content presents a new technique for certifying the overlap between an n-qubit quantum state ρ synthesized in the lab and a target state |ψ⟩. The key idea is to define a "shadow overlap" ω that can be estimated using O(n^2) single-qubit Pauli measurements on ρ, and this shadow overlap provides a good surrogate for the fidelity ⟨ψ|ρ|ψ⟩.
The analysis establishes that for almost all n-qubit target states |ψ⟩, including highly entangled states with exponential circuit complexity, the relaxation time τ of a Markov chain related to the measurement distribution π(x) = |⟨x|ψ⟩|^2 is bounded by τ ≤ O(n^2). This allows the certification protocol to succeed with high probability using only O(n^2/ϵ) single-qubit measurements, where ϵ is the desired error tolerance.
The content also discusses several applications of the shadow overlap formalism, including:
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by Hsin-Yuan Hu... at arxiv.org 04-12-2024
https://arxiv.org/pdf/2404.07281.pdfDeeper Inquiries