Stats

In this section, we benchmark between backends to solve a partial differential equation using a Differential Quantum Circuit (DQC). The underlying ansatz is the hardware-efficient-ansatz. The underlying gradient-based Adam optimizer is run for \(15\) iterations. The example is taken from the pyqtorch and horqrux documentation. The circuits are defined over \(4, 6\) qubits \(R=5\) for avoiding long jobs time on Github.

Differential Quantum Circuit

Here are the median execution times for DQC. We compare optimizing with PyQTorch against optimizing with Horqrux and jitting.

fname = "stats_dqc.json"

if not os.path.isfile(fname):
    fname = "docs/stats_dqc.json"
with open(fname, 'r') as f:
    data_vqe = json.load(f)['benchmarks']


data_stats_vqe = [{'name': x['name']} | x['params'] | x['stats'] for x in data_vqe]

frame_vqe = pd.DataFrame(data_stats_vqe)
frame_vqe['n_qubits'] = frame_vqe['name'].apply(lambda x: int(re.findall('n:(.*)\\D:', x)[0]))
frame_vqe['name'] = frame_vqe['name'].apply(lambda x: re.findall('test_(.*)\\[', x)[0])
frame_vqe['fn_circuit'] = frame_vqe['benchmark_dqc_ansatz'].apply(str)
frame_vqe['fn_circuit'] = frame_vqe['fn_circuit'].apply(lambda x: re.findall('function (.*) at', x)[0])
frame_vqe['name'] = frame_vqe['name'].str.replace('dqc_', '')

nqubits = frame_vqe.n_qubits.unique()

Timings

Below we present the distribution of median times for each number of qubits.

for nq in nqubits:
    axes = frame_vqe[frame_vqe.n_qubits == nq].boxplot('median', by=['fn_circuit', 'name'])
    axes.set_title(f"Timing distributions - {nq} qubits")
    axes.set_xlabel('')
    axes.set_ylabel('Time (s)')
    plt.xticks(rotation=75)
    plt.suptitle('')
    plt.tight_layout()

Speed-ups

pyq_vqe = frame_vqe[frame_vqe.name == 'pyq'][['fn_circuit', 'median', 'n_qubits']]
horqrux_vqe = frame_vqe[frame_vqe.name == 'horqrux'][['fn_circuit', 'median', 'n_qubits']]
ratio_df = pd.merge(pyq_vqe, horqrux_vqe, on=['fn_circuit', 'n_qubits'], suffixes=['_pyq', '_horqrux'])
ratio_df['ratio'] = ratio_df['median_pyq'] / ratio_df['median_horqrux']


axes = ratio_df.boxplot('ratio', by=['fn_circuit', 'n_qubits'])
axes.set_title(f"Speedup distributions by circuit and qubit number without shots")
axes.set_xlabel('')
axes.set_ylabel('Speedup')
plt.xticks(rotation=75)
plt.suptitle('')