Gradients

QuantumFlow: Gradients of parameterized gates, and gradient descent optimizers

quantumflow.expectation_gradients(ket0: State, circ: Circuit, hermitian: Operation, dfunc: Callable[[float], float] | None = None) → Sequence[float]

Calculate the gradients of a function of expectation for a parameterized quantum circuit, using the middle-out algorithm.

Parameters:

• ket0 – An initial state.

• circ – A circuit that acts on the initial state.

• hermitian – A Hermitian Operation for which the expectation is evaluated

• dfunc – Derivative of func. Defaults to identity.

Returns:

The gradient with respect to the circuits parameters.

quantumflow.state_fidelity_gradients(ket0: State, ket1: State, circ: Circuit) → Sequence[float]

Calculate the gradients of state fidelity for a parameterized quantum circuit, using the middle-out algorithm.

Parameters:

• ket0 – An initial state.

• ket1 – A target state. We calculate the fidelity between this state and

• circuit. (the resultant of the) –

• circ – A circuit that acts on ket0.

Returns:

The gradients of state fidelity with respect to the circuits parameters.

quantumflow.state_angle_gradients(ket0: State, ket1: State, circ: Circuit) → Sequence[float]

Calculate the gradients of state angle for a parameterized quantum circuit, using the middle-out algorithm.

Parameters:

• ket0 – An initial state.

• ket1 – A target state. We calculate the fidelity between this state and the resultant of the circuit.

• circ – A circuit that acts on ket0.

Returns:

The gradients of the inter-state angle with respect to the circuits parameters.

quantumflow.parameter_shift_circuits(circ: Circuit, index: int) → Tuple[float, Circuit, Circuit]

Calculate the gradients of state angle for a parameterized quantum circuit, using the parameter-shift rule.

Returns the gate shift-constant, and two circuits, circ0, circ1. Gradients are proportional to the difference in expectation between the two circuits.

r, circ0, circ1 = qf.parameter_shift_circuits(circ, n)
fid0 = qf.state_fidelity(circ0.run(ket0), ket1)
fid1 = qf.state_fidelity(circ1.run(ket0), ket1)
grad = r*(fid1-fid0)

Parameters:

• circ – A quantum circuit with parameterized gates

• index – The index of the target gate in the quantum circuit

Returns:

r – The gate shift constant circ0: Circuit with parameter shift on target gate. circ1: Circuit with negative parameter shift on target gate.