ket.qulib.ham

Hamiltonian library.

Functions ket.qulib.ham

falqon_a(hp, hd)	FALQON A operator.
falqon_b(hp, hd)	FALQON B operator.
falqon_c(hp, hd)	FALQON C operator.
falqon_get_beta_fo(hp, hd)	Get FALQON first-order beta parameter.
falqon_get_beta_so(delta_t, hp, hd)	Get FALQON second-order beta parameter.
maxcut(edges, qubits)	Max-Cut Hamiltonian.
qubo(model, qubits)	Convert a QUBO model to a Hamiltonian.
x_mixer(qubits)	X-Mixer Hamiltonian.
xy_mixer(qubits[, edges])	XY-Mixer Hamiltonian.

falqon_a(hp: Hamiltonian, hd: Hamiltonian) → Hamiltonian

FALQON A operator.

\[A = i[H_d, H_p]\]

See https://arxiv.org/abs/2103.08619.

Parameters:

• hp – Problem Hamiltonian.

• hd – Driver Hamiltonian.

falqon_b(hp: Hamiltonian, hd: Hamiltonian) → Hamiltonian

FALQON B operator.

\[B = [ [H_d, H_p], H_d ]\]

See https://arxiv.org/abs/2407.17810.

Parameters:

• hp – Problem Hamiltonian.

• hd – Driver Hamiltonian.

falqon_c(hp: Hamiltonian, hd: Hamiltonian) → Hamiltonian

FALQON C operator.

\[C = [ [H_d, H_p], H_p ]\]

See https://arxiv.org/abs/2407.17810.

Parameters:

• hp – Problem Hamiltonian.

• hd – Driver Hamiltonian.

falqon_get_beta_fo(hp: Hamiltonian, hd: Hamiltonian) → float

Get FALQON first-order beta parameter.

See https://arxiv.org/abs/2103.08619.

This function computes the expectation value, triggering the circuit execution.

Parameters:

• hp – Problem Hamiltonian.

• hd – Driver Hamiltonian.

falqon_get_beta_so(delta_t, hp: Hamiltonian, hd: Hamiltonian) → float

Get FALQON second-order beta parameter.

See https://arxiv.org/abs/2407.17810.

This function computes the expectation values, triggering the circuit execution.

Parameters:

• delta_t – Time step.

• hp – Problem Hamiltonian.

• hd – Driver Hamiltonian.

maxcut(edges: list[tuple[int, int]], qubits: Quant) → Hamiltonian

Max-Cut Hamiltonian.

\[\sum_{a, b\,\in\, \mathcal{E}}\frac{1}{2}(1-Z_a Z_b)\]

Parameters:

• edges – List of edges in the graph.

• qubits – Qubits representing the graph nodes.

qubo(model, qubits: Quant) → Hamiltonian

Convert a QUBO model to a Hamiltonian.

Converts a QUBO model from the pyQUBO library to a Hamiltonian observable.

Parameters:

• model – QUBO model.

• qubits – Qubits representing the variables in the model.

x_mixer(qubits: Quant) → Hamiltonian

X-Mixer Hamiltonian.

\[\sum_j X_j\]

Parameters:

qubits – Qubits to apply the mixer.

xy_mixer(qubits, edges: list[tuple[int, int]] | None = None) → Hamiltonian

XY-Mixer Hamiltonian.

\[\frac{1}{2}\sum_{a, b\,\in\, \mathcal{E}} X_a X_b + Y_a Y_b\]

If edges is None, a ring topology is assumed.

Parameters:

• qubits – Qubits to apply the mixer.

• edges – List of edges in the graph.