From 7a279173f267f8ba36f672aacd32b4090116879b Mon Sep 17 00:00:00 2001 From: Balint Pato Date: Tue, 20 Jul 2021 15:38:42 -0400 Subject: [PATCH] Floquet notebook missed review nits (#4341) Nits in the floquet notebook: * electron -> fermionic particle * quirk circuit has the excitation in the middle qubit This is to address @mrwojtek's nits in https://github.com/quantumlib/Cirq/pull/4335/files/46ef155fc6170b636c8843225d3f06bf213cd00c#r673355517. --- docs/tutorials/google/floquet_calibration_example.ipynb | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/docs/tutorials/google/floquet_calibration_example.ipynb b/docs/tutorials/google/floquet_calibration_example.ipynb index b5b7d2386f8..af63befb50c 100644 --- a/docs/tutorials/google/floquet_calibration_example.ipynb +++ b/docs/tutorials/google/floquet_calibration_example.ipynb @@ -212,13 +212,13 @@ "id": "a0Nrd1pkVWzo" }, "source": [ - "We run Floquet calibration on a circuit which models the evolution of a single electron on 5 sites, realizing the Hamiltonian: \n", + "We run Floquet calibration on a circuit which models the evolution of a single fermionic particle on 5 sites, realizing the Hamiltonian: \n", "\n", "$$\n", "H=\\sum_{m=0}^{L-1} J(\\sigma_{m}^{+} \\sigma_{m+1}^{-} + \\sigma_{m}^{+} \\sigma_{m+1}^{-}),\n", "$$\n", "\n", - "where $\\sigma_{m}^{+}$ ($\\sigma_{m}^{-}$) are the raising (lowering) operators, and the single term describes the kinetic energy related to hopping from one site to the other. This [quirk circuit](https://algassert.com/quirk#circuit={%22cols%22:[[%22X%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22]],%22gates%22:[{%22id%22:%22~qcjg%22,%22name%22:%22sqrtISWAP%22,%22matrix%22:%22{{1,0,0,0},{0,%E2%88%9A%C2%BD,%E2%88%9A%C2%BDi,0},{0,%E2%88%9A%C2%BDi,%E2%88%9A%C2%BD,0},{0,0,0,1}}%22}]}) shows the evolution of the charge density.\n", + "where $\\sigma_{m}^{+}$ ($\\sigma_{m}^{-}$) are the raising (lowering) operators, and the single term describes the kinetic energy related to hopping from one site to the other. This [quirk circuit](https://algassert.com/quirk#circuit={%22cols%22:[[1,1,%22X%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22],[%22~qcjg%22,1,%22~qcjg%22],[1,%22~qcjg%22,1,%22~qcjg%22],[%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22,%22Chance%22]],%22gates%22:[{%22id%22:%22~qcjg%22,%22name%22:%22sqrtISWAP%22,%22matrix%22:%22{{1,0,0,0},{0,%E2%88%9A%C2%BD,%E2%88%9A%C2%BDi,0},{0,%E2%88%9A%C2%BDi,%E2%88%9A%C2%BD,0},{0,0,0,1}}%22}]}) shows the evolution of the charge density.\n", "\n", "\n", "This simulation can be looked at as a highly simplified version of the paper from our group, [Observation of separated dynamics of charge and spin in the Fermi-Hubbard model](https://arxiv.org/pdf/2010.07965). We model only a single fermion in the non-interacting case (with $U=0$). For a single particle, the parasitic controlled phase does not impact the evolution, and we can use a single chain that one can think about it as being in either up or down spin states. The parameter $\\theta$ for $K(\\theta)$ is fixed to $\\pi/4$. To smooth out the inhomogeneities of the quantum chip, we are using the technique of _averaging over multiple qubit configurations_ from this paper. The difference is that we pick a line that we segment and run the same circuit in parallel on each segment corresponding to a different qubit configuration. We measure the charge density at each site index (qubit) by averaging the Z densities (see Fig 2.a for comparison). \n",