qml.qnn.iqp_expval¶

iqp_expval(ops, weights, pattern, num_wires, n_samples, key, spin_sym=False, sparse=False, indep_estimates=False, max_batch_ops=None, max_batch_samples=None)[source]¶

Estimates the expectation values of a batch of Pauli-Z type operators for a parameterized IQP circuit.

The expectation values are estimated using a randomized method (Monte Carlo method) whose precision is controlled by the number of samples (n_samples), with larger values giving higher precision.

Parameters:

ops (list) – Array specifying the operator/s for which to estimate the expectation values.
weights (list) – The parameters of the IQP gates.
pattern (list[list[list[int]]]) – Specification of the trainable gates. Each element of pattern corresponds to a unique trainable parameter. Each sublist specifies the generators to which that parameter applies. Generators are specified by listing the qubits on which an X operator acts. For example, the pattern [[[0]], [[1]], [[2]], [[3]]] specifies a circuit with single qubit rotations on the first four qubits, each with its own trainable parameter. The pattern [[[0],[1]], [[2],[3]]] corresponds to a circuit with two trainable parameters with generators \(X_0+X_1\) and \(X_2+X_3\) respectively. A circuit with a single trainable gate with generator \(X_0\otimes X_1\) corresponds to the pattern [[[0,1]]].
num_wires (int) – Number of wires in the circuit.
n_samples (int) – Number of samples used to estimate the IQP expectation values. Higher values result in higher precision.
key (Array) – Jax key to control the randomness of the process.
spin_sym (bool, optional) – If True, the circuit is equivalent to one where the initial state \(\frac{1}{\sqrt(2)}(|00\dots0> + |11\dots1>)\) is used in place of \(|00\dots0>\). This defines a circuit whose output distribution is invariant to flipping all bits.
indep_estimates (bool) – Whether to use independent estimates of the operators in a batch. If True, correlation among the estimated expectation values can be avoided, although at the cost of larger runtime.
max_batch_ops (int) – Specifies the maximum size of sub-batches of ops that are used to estimate the expectation values (to control memory usage). If None, a single batch is used. Can only be used if ops is a jnp.array.
max_batch_samples (int) – Specifies the maximum size of sub-batches of samples that are used to estimate the expectation values of ops (to control memory usage). If None, a single batch is used.

Returns:

List of Vectors. The expected value of each operator and its corresponding standard deviation.

Return type:

list

Example:

To estimate the expectation value of a Pauli Z tensor, we represent the operator as a binary string (bitstring) that specifies on which qubit a Pauli Z operator acts. For example, in a three-qubit circuit, the operator \(Z_0 Z_2\) will be represented as \([1, 0, 1]\). Similarly, the expectation values for a group of operators can be evaluated by specifiying a sequence of bitstrings.

As an example, let’s estimate the expectation values for the operators \(Z_1\), \(Z_0\), and \(Z_0 Z_1\) for a two-qubit circuit, using 1000 samples for the Monte Carlo estimation:

from pennylane.qnn import iqp_expval
import jax

num_wires = 2
ops = np.array([[0, 1], [1, 0], [1, 1]]) # binary array representing ops Z1, Z0, Z0Z1
n_samples = 1000
key = jax.random.PRNGKey(42)

weights = np.ones(len(pattern))
pattern = [[[0]], [[1]], [[0, 1]]] # binary array representing gates X0, X1, X0X1

expvals, stds = iqp_expval(ops, weights, pattern, num_wires, n_samples, key)

>>> print(expvals, stds)
[0.18971464 0.14175898 0.17152457] [0.02615426 0.02614059 0.02615943]

qml.qnn.iqp_expval¶

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