core.converters.qaoa

core.converters.qaoa#

This module implements the Quantum Approximate Optimization Algorithm (QAOA) converter for the Qamomile framework [Farhi et al., 2014]. The parameterized state \(|\vec{\beta},\vec{\gamma}\rangle\) of \(p\)-layer QAOA is defined as:

\[|\vec{\beta},\vec{\gamma}\rangle = U(\vec{\beta},\vec{\gamma})|0\rangle^{\otimes n} = e^{-i\beta_{p-1} H_M}e^{-i\gamma_{p-1} H_P} \cdots e^{-i\beta_0 H_M}e^{-i\gamma_0 H_P} H^{\otimes n}|0\rangle^{\otimes n}\]

where \(H_P\) is the cost Hamiltonian, \(H_M\) is the mixer Hamiltonian and \(\gamma_l\) and \(\beta_l\) are the variational parameters. The 2 \(p\) variational parameters are optimized classically to minimize the expectation value \(\langle \vec{\beta},\vec{\gamma}|H_P|\vec{\beta},\vec{\gamma}\rangle\).

This module provides functionality to convert optimization problems which written by jijmodeling into QAOA circuits (\(U(\vec{\beta},\vec{\gamma})\)), construct cost Hamiltonians (\(H_P\)), and decode quantum computation results.

The QAOAConverter class extends the QuantumConverter base class, specializing in QAOA-specific operations such as ansatz circuit generation and result decoding.

Key Features: - Generation of QAOA ansatz circuits - Construction of cost Hamiltonians for QAOA - Decoding of quantum computation results into classical optimization solutions

Note: This module requires jijmodeling and jijmodeling_transpiler for problem representation.

[FGG14]

Edward Farhi, Jeffrey Goldstone, and Sam Gutmann. A quantum approximate optimization algorithm. 2014. URL: https://arxiv.org/abs/1411.4028, arXiv:1411.4028.

Classes#

QAOAConverter

QAOA (Quantum Approximate Optimization Algorithm) converter class.

Module Contents#

class QAOAConverter(compiled_instance, relax_method: jijmodeling_transpiler.core.pubo.RelaxationMethod = jmt.pubo.RelaxationMethod.AugmentedLagrangian, normalize_model: bool = False, normalize_ising: Literal['abs_max', 'rms'] | None = None)#

Bases: qamomile.core.converters.converter.QuantumConverter

QAOA (Quantum Approximate Optimization Algorithm) converter class.

This class provides methods to convert optimization problems into QAOA circuits, construct cost Hamiltonians, and decode quantum computation results.

Examples:

from qamomile.core.qaoa.qaoa import QAOAConverter

# Initialize with a compiled optimization problem instance
qaoa_converter = QAOAConverter(compiled_instance)

# Generate QAOA circuit and cost Hamiltonian
p = 2  # Number of QAOA layers
qaoa_circuit = qaoa_converter.get_ansatz_circuit(p)
cost_hamiltonian = qaoa_converter.get_cost_hamiltonian()

Initialize the QuantumConverter.

This method initializes the converter with the compiled instance of the optimization problem

Parameters:

  • compiled_instance – The compiled instance of the optimization problem.

  • relax_method (jmt.pubo.RelaxationMethod) – The relaxation method for PUBO conversion. Defaults to AugmentedLagrangian.

  • normalize_model (bool) – The objective function and the constraints are normalized using the maximum absolute value of the coefficients contained in each. Defaults to False

  • normalize_ising (Literal["abs_max", "rms"] | None) – The normalization method for the Ising Hamiltonian. Available options: - “abs_max”: Normalize by absolute maximum value - “rms”: Normalize by root mean square Defaults to None.

get_cost_ansatz(gamma: qamomile.core.circuit.Parameter, name: str = 'Cost') → qamomile.core.circuit.QuantumCircuit#

Generate the cost ansatz circuit (\(e^{-\gamma H_P}\)) for QAOA. This function is mainly used when you have designed your own mixer Hamiltonian and only need the cost Hamiltonian.

Parameters:

  • gamma (qm_c.Parameter) – The gamma parameter for the cost ansatz.

  • name (str, optional) – Name of the circuit. Defaults to “Cost”.

Returns:

The cost ansatz circuit.

Return type:

qm_c.QuantumCircuit

get_qaoa_ansatz(p: int, initial_hadamard: bool = True) → qamomile.core.circuit.QuantumCircuit#

Generate the complete QAOA ansatz circuit.

Parameters:

  • p (int) – Number of QAOA layers.

  • initial_hadamard (bool, optional) – Whether to apply initial Hadamard gates. Defaults to True.

Returns:

The complete QAOA ansatz circuit.

Return type:

qm_c.QuantumCircuit

get_cost_hamiltonian() → qamomile.core.operator.Hamiltonian#

Construct the cost Hamiltonian for QAOA.

Returns:

The cost Hamiltonian.

Return type:

qm_o.Hamiltonian