Основные понятия
Almost all quantum states, including highly entangled ones, can be certified from only O(n^2) single-qubit measurements, where n is the number of qubits.
Аннотация
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:
- Machine learning tomography of quantum states: The shadow overlap provides a theoretically backed yet practically feasible procedure for learning a machine learning model of a quantum state or certifying the fidelity of an already trained model.
- Near-term benchmarking of quantum devices: The shadow overlap offers a flexible method for benchmarking noisy quantum devices, closely mirroring the fidelity.
- Optimizing quantum circuits for state preparation: The shadow overlap exhibits favorable properties for training quantum circuits, avoiding the barren plateau phenomenon faced by fidelity-based training.
Статистика
The content does not provide specific numerical data or statistics to support the claims. The focus is on the theoretical analysis and high-level applications of the shadow overlap certification procedure.
Цитаты
There are no direct quotes from the content that are particularly striking or support the key logics.