Efficient verification of anticoncentrated quantum states
Abstract I present a method for estimating the fidelity F(μ, τ) between a preparable quantum state μ and a classically specified pure target state $$\tau =\left|\tau \right\rangle \left\langle \tau \right|$$ τ = τ τ , using simple quantum circuits and on-the-fly classical calculation (or lookup) of...
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
Nature Portfolio
2021
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/767e2f03f98244aba338e0817676b0d4 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| Sumario: | Abstract I present a method for estimating the fidelity F(μ, τ) between a preparable quantum state μ and a classically specified pure target state $$\tau =\left|\tau \right\rangle \left\langle \tau \right|$$ τ = τ τ , using simple quantum circuits and on-the-fly classical calculation (or lookup) of selected amplitudes of $$\left|\tau \right\rangle$$ τ . The method is sample efficient for anticoncentrated states (including many states that are hard to simulate classically), with approximate cost 4ϵ −2(1 − F)d p coll where ϵ is the desired precision of the estimate, d is the dimension of the Hilbert space, and p coll is the collision probability of the target distribution. This scaling is exponentially better than that of any method based on classical sampling. I also present a more sophisticated version of the method that uses any efficiently preparable and well-characterized quantum state as an importance sampler to further reduce the number of copies of μ needed. Though some challenges remain, this work takes a significant step toward scalable verification of complex states produced by quantum processors. |
|---|