Measurement

  • Prepare a state, choose a Pauli observable, and sample its measurement circuit.

  • Use the library estimators to calculate expectation values and standard errors.

Direct Pauli measurements

  • make_direct_measure_pauli_simple constructs basis changes and full-register measurement for a Pauli string, including products such as \(X_0Z_1\).

  • estimate_pauli_observable_expectation_from_bitstrings converts the measured bitstrings into the relevant parity and combines weighted terms.

  • See the direct measurement notebook for a complete circuit.

Hadamard-test measurements

  • make_hadamard_test_pauli measures a Pauli expectation through an ancilla.

  • estimate_expectation_from_binary_samples handles its binary readout.

  • For a sum of terms, use estimate_pauli_observable_expectation_from_binary_samples with a separate sample collection for each term.

  • See the Hadamard-test notebook.

Expectation values and uncertainty

For a binary Pauli measurement, False represents \(+1\) and True represents \(-1\). The estimator returns the sample mean and its estimated standard error:

\[ \widehat{\langle P\rangle}=\frac{N_+-N_-}{N}, \qquad \mathrm{SE}=\sqrt{\frac{1-\widehat{\langle P\rangle}^2}{N}}. \]
from guppyalgos.primitives.measurement import estimate_expectation_from_binary_samples

estimate = estimate_expectation_from_binary_samples({False: 750, True: 250})
print(f"Expectation: {estimate.expectation:.3f}")
print(f"Standard error: {estimate.standard_error:.3f}")

Expectation: 0.500
Standard error: 0.027

For a real observable \(H=\sum_j c_jP_j\), the observable estimators combine independently sampled terms:

\[ \widehat{\langle H\rangle}=\sum_j c_j\widehat{\langle P_j\rangle}, \qquad \mathrm{SE}(H)^2=\sum_j c_j^2\mathrm{SE}(P_j)^2. \]

  • Sample each term in its corresponding basis; computational-basis shots alone do not estimate arbitrary X or Y observables.

  • This uncertainty calculation assumes independent term samples. Grouped measurements require covariance terms.

  • The Trotter demo uses these routines to plot measured dynamics with error bars.

See all measurement notebooks.