Quick start

This page cools one qubit with DBAC in a few lines, then explains what each line did. It assumes dbac is installed.

Cool a qubit

import numpy as np
from dbac.utils import rx_sweep
from dbac.dbqite import QITE_dme_select_M
from dbac.gci import GCI

psi = rx_sweep([0.5])[0]                  # a qubit halfway between |0> and |1>
step = QITE_dme_select_M(M=1)             # a DBAC step with one DME step
results = GCI(step, psi, None, [np.pi / 4, np.pi / 4]).execute_gci()

for k, F in enumerate(results[-1]):
    print(f"after {k} DBAC steps: fidelity with |0> = {F:.3f}")

after 0 DBAC steps: fidelity with |0> = 0.500
after 1 DBAC steps: fidelity with |0> = 0.750
after 2 DBAC steps: fidelity with |0> = 0.875

The qubit started with a 50% overlap with the ground state \(|0\rangle\). Two DBAC steps raised that to 87.5%, without measuring the qubit or knowing its state.

What just happened

rx_sweep([0.5]) built the initial state \(\cos\theta|0\rangle - i\sin\theta|1\rangle\) with \(\theta = 0.5 \cdot \pi/2\). It takes a list because it is usually used to sweep many angles at once. → States and conventions

QITE_dme_select_M(M=1) created a step function: one round of cooling. A step rotates a copy of the state and uses it as a quantum instruction, applied to the qubit through density matrix exponentiation (DME) with \(M\) steps. → One DBAC step, Density matrix exponentiation

GCI(step, psi, None, [s1, s2]) ran the step twice, with durations \(s_1 = s_2 = \pi/4\), each time on the output of the previous step. execute_gci() returned a tuple of results; results[-1] holds the fidelity after each step. → Running the recursion

Try changing

  • more DME steps: QITE_dme_select_M(M=2) uses two instruction copies per step and cools more;

  • more DBAC steps: a longer schedule [np.pi / 4] * 4 keeps cooling, with diminishing returns;

  • a hotter state: rx_sweep([0.9]) starts closer to \(|1\rangle\). Note that \(|1\rangle\) itself (rx_sweep([1])) cannot be cooled at all: it is an excited eigenstate.

for M in (1, 2):
    results = GCI(QITE_dme_select_M(M), psi, None, [np.pi / 4] * 4).execute_gci()
    print(f"M = {M}:", np.round(results[-1], 3))

M = 1: [0.5   0.75  0.875 0.891 0.891]
M = 2: [0.5   0.802 0.917 0.925 0.926]

Next steps

  • The front page shows the same calculation for the paper’s three hardware circuits, next to the measured data.

  • The guide, starting with States and conventions, explains each module in depth.

  • Reproducing the figures lists the scripts that regenerate every figure of the paper.