Reproducing the figures¶

Every figure of the paper is produced by a script in scripts/, named after the figure. Run a script from the repository root and it writes its PDFs to figures/:

python scripts/figure_4.py

The notebooks in notebooks/ walk through the same calculations with explanations. They only save PDFs when SAVE_PLOTS = True in notebooks/config.py (off by default).

Tip

The scripts use the paper style, which renders labels with LaTeX. Without a LaTeX installation, see Installation.

Main text¶

Fig. 4: cooling on hardware¶

python scripts/figure_4.py

Energy of the data qubit after DBAC against the initialization angle, for the three hardware circuits A (\(k=1\), \(M=1\)), B (\(k=1\), \(M=2\)) and C (\(k=2\), \(M=1\)), with the measured data overlaid. Writes F4_Circuit_A_n_2.pdf, F4_Circuit_B_n_3.pdf and F4_Circuit_C_n_4.pdf.

The front page of this documentation is the narrated version of this script, including the circuit diagrams.

Supplementary material¶

Fig. S2: accuracy of DME¶

python scripts/sup_figure_S2.py

Distance between Trotterized DME and the exact evolution as the number of Trotter steps \(M\) grows, comparing the implementations in dbac.dme. Writes S2_DME_norm.pdf. → Density matrix exponentiation

Fig. S4: DBAC with ideal DME¶

python scripts/sup_figure_S4.py

DBAC in the limit \(M\to\infty\) (dbac.dbqite.ideal_DME), sweeping the recursion depth \(k = 1, \dots, 6\): final fidelity against initial fidelity, the hottest state that still reaches a target fidelity, and the optimized step durations. Writes S4_QITE_ideal_DME_merged.pdf. Notebook: notebooks/sup_figure_S4.ipynb. → Running the recursion

This script also owns the table of optimized durations notebooks/optimal_s_Mk.npy used by the other scripts (load_or_fit_optimal_s_Mk), and refits it if the file is missing.

Fig. S5: the recursion on the Bloch sphere¶

python scripts/sup_figure_S5.py

The states of the DBAC recursion drawn on the Bloch sphere, for three initial states that are close to, halfway from and far from \(|0\rangle\). Writes S5_bloch_good.pdf, S5_bloch_mid.pdf and S5_bloch_bad.pdf. The module also provides compare_pure_vs_mixed, which runs DBAC on depolarized inputs.

Fig. S6: choosing the step duration¶

python scripts/sup_figure_S6.py

Final fidelity after one DBAC step as a function of the initial angle and the step duration \(s\), for \(M=1\) and \(M=2\), with the optimal durations marked. Writes S6_M1k1_s_sweep.pdf and S6_M2k1_s_sweep.pdf. → One DBAC step

Other notebooks¶

notebook	what it shows
`notebooks/dme_ptm_plot.ipynb`	Pauli-transfer matrices of the \(ZZ\) interaction, the DME unitary and hardware circuits A and B
`notebooks/hbac.ipynb`	heat-bath algorithmic cooling on three qubits, for pure and depolarized inputs → HBAC baseline
`notebooks/draw_circuit.ipynb`	LaTeX (qcircuit) drawings of the DME, DBAC and HBAC circuits, made with qiskit