<p>You're correct that the <a href="https://github.com/microsoft/Quantum/tree/master/samples/chemistry/GetGateCount" rel="nofollow noreferrer"><code>GetGateCount</code> sample</a> was used to generate the plots in that figure.
The <a href="https://github.com/microsoft/Quantum/blob/master/samples/chemistry/GetGateCount/Operation.qs" rel="nofollow noreferrer"><code>Operations.qs</code> source file</a> in that sample shows the details of what each different plot represents; in particular, the Trotter, Qubitization and Optimized Qubitization results are for a single step of each algorithm. As you note, the number of steps required depends on the relevant chemical accuracy.</p>

<p>Though that's not a level of detail that we went into for that post, the follow-up <a href="https://arxiv.org/abs/1904.01131v1" rel="nofollow noreferrer">arXiv paper</a> goes into a lot more detail about that kind of comparison. All the source code used to generate that paper has been attached at <a href="https://arxiv.org/src/1904.01131v1/anc" rel="nofollow noreferrer">https://arxiv.org/src/1904.01131v1/anc</a>, along with a Dockerfile that can be used to reproduce the exact software environment.</p>

<p>With respect to your other question, the resources estimator's  count reports the number <code>T</code> operation calls required excluding used to decompose <code>R</code> calls. Thus, the optimized qubitization method trades off some <code>T</code> calls for a dramatic saving in the number of rotations that must be decomposed.</p>
Information needed to reproduce T-Costs for quantum chemistry as provided in the simulating nature article
<p>The article I was referring to in the title is: <a href="https://cloudblogs.microsoft.com/quantum/2018/12/04/simulating-nature-with-the-new-microsoft-quantum-development-kit-chemistry-library/" rel="nofollow noreferrer">https://cloudblogs.microsoft.com/quantum/2018/12/04/simulating-nature-with-the-new-microsoft-quantum-development-kit-chemistry-library/</a>  which provides resource estimates for certain metrics for different molecules with Trotterisation, Qubitization, and Optimized Qubitization.</p>

<p>I would like to reproduce some of this data, and I have been using the example program "GetGateCount" to do so. Trotterisation seems to have a problem with T-costs, see my question here for more: <a href="https://stackoverflow.com/questions/60619381/resource-estimation-for-trotterisation-always-outputs-a-0-t-gate-cost">Resource estimation for Trotterisation always outputs a 0 T-gate cost?</a></p>

<p>My question here is what information do I need to reproduce the same values as provided in the article? I am using robust phase estimation (is this what was used for the article?), in which the run time is very dependent on the bits of precision. To approximately get the same T-cost as in the article for qubitization, I found 3 bits of precision worked best, (but this leads to a large uncertainty on the phase  and energy? as described in: <a href="https://docs.microsoft.com/en-us/qsharp/api/qsharp/microsoft.quantum.characterization.robustphaseestimation" rel="nofollow noreferrer">https://docs.microsoft.com/en-us/qsharp/api/qsharp/microsoft.quantum.characterization.robustphaseestimation</a>). For comparison, I calculated that chemical accuracy for molecular hydrogen would require approx 13 bits of precision with robust phase estimation.</p>

<p>Another related question is regarding the difference between Qubitization and Optimized Qubitization. The article explains that Optimized should have a minimized T-cost, and the graph provided shows this to be the case across the molecules investigated. Contrary to this, I find, using the same example program "GetGateCount", that the Qubitization oracle is consistently "resource estimated" to have a lower T-cost as compared to the Optimized Qubitization oracle. This does not seem to be dependent on the additional parameter for Optimized, "targetError", as it causes only a minimal change to the T-cost when varied across a wide range. </p>

<p>An example of my results for energy estimation on LiH (not just a single application of the oracle) is included below:</p>

<pre><code>Gate Count results on ..\IntegralData\yaml\LiHdata\integrals_lih_sto-3g_0.800.nw.out.yaml
by Trotter with 12 spin-orbitals. It took 4335 ms.
Gate count statistics:

    # T:0,
    # Rotations:90756,
    # CNOT:559872,

Gate Count results on ..\IntegralData\yaml\LiHdata\integrals_lih_sto-3g_0.800.nw.out.yaml
by Qubitization with 12 spin-orbitals. It took 14012 ms.
Gate count statistics:

    # T:191376,
    # Rotations:315252,
    # CNOT:1241136,

Gate Count results on ..\IntegralData\yaml\LiHdata\integrals_lih_sto-3g_0.800.nw.out.yaml
by Optimized Qubitization with 12 spin-orbitals. It took 44345 ms.
Gate count statistics:

    # T:711360,
    # Rotations:1620,
    # CNOT:2118168
</code></pre>

<p>See Trotter with 0 cost, and the higher T cost of Optimized as compared to non-optimized. </p>

<p>Any help would be appreciated greatly!</p>