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Fix floquet quirk url #4347

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merged 2 commits into from
Jul 26, 2021
Merged

Fix floquet quirk url #4347

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3accf4c
fix quirk url
balopat Jul 22, 2021
a6fb0be
Merge branch 'master' into fix_floquet_calibration_example_quirk_url
CirqBot Jul 26, 2021
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2 changes: 1 addition & 1 deletion docs/tutorials/google/floquet_calibration_example.ipynb
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Original file line number Diff line number Diff line change
Expand Up @@ -218,7 +218,7 @@
"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:[[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",
"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=%7B%22cols%22%3A%5B%5B1%2C1%2C%22X%22%5D%2C%5B%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%5D%2C%5B%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B1%2C%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%5D%2C%5B%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B1%2C%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%5D%2C%5B%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B1%2C%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%5D%2C%5B%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B1%2C%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%5D%2C%5B%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B1%2C%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%5D%2C%5B%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B1%2C%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%5D%2C%5B%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B1%2C%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%5D%2C%5B%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B1%2C%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%5D%2C%5B%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B1%2C%22~qcjg%22%2C1%2C%22~qcjg%22%5D%2C%5B%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%2C%22Chance%22%5D%5D%2C%22gates%22%3A%5B%7B%22id%22%3A%22~qcjg%22%2C%22name%22%3A%22sqrtISWAP%22%2C%22matrix%22%3A%22%7B%7B1%2C0%2C0%2C0%7D%2C%7B0%2C%E2%88%9A%C2%BD%2C%E2%88%9A%C2%BDi%2C0%7D%2C%7B0%2C%E2%88%9A%C2%BDi%2C%E2%88%9A%C2%BD%2C0%7D%2C%7B0%2C0%2C0%2C1%7D%7D%22%7D%5D%7D) 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",
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