QAOA cost functions

As with VQE, we also provide two different cost functions for QAOA that derive from their VQE counterparts: one for the WavefunctionSimulator, and one for the QVM that can also be run on Rigetti’s QPU.

On the Wavefunction Simulator

class qaoa.cost_function.QAOACostFunctionOnWFSim(hamiltonian, params, sim=None, scalar_cost_function=True, nshots=0, enable_logging=False, initial_state=None, qubit_mapping=None)

A cost function that inherits from PrepareAndMeasureOnWFSim and implements the specifics of QAOA

Parameters

  • hamiltonian (PauliSum) – The cost hamiltonian

  • params (Type[AbstractParams]) – Form of the QAOA parameters (with n_steps and type fixed for this instance)

  • sim (Optional[WavefunctionSimulator]) – connection to the WavefunctionSimulator to run the simulation on Automatically creates one, if None is passed.

  • scalar_cost_function (bool) – If True: __call__ returns only the expectation value If False: __call__ returns a tuple (exp_val, std_dev) Defaults to True.

  • nshots (int) – Number of shots to assume to simulate the sampling noise. 0 corresponds to no sampling noise added and is the default.

  • log – List to keep log of function calls

  • initial_state (Optional[Program]) – A Program to run for state preparation. Defaults to applying a Hadamard on each qubit (all plust state).

  • qubit_mapping (Optional[Dict[QubitPlaceholder, Union[Qubit, int]]]) – A mapping to fix QubitPlaceholders to physical qubits. E.g. pyquil.quil.get_default_qubit_mapping(program) gives you on.

__call__(params, nshots=None)

Cost function that computes <psi|ham|psi> with psi prepared with prepare_ansatz(params).

Parameters

  • params – Parameters of the state preparation circuit.

  • nshots (Optional[int]) – Overrides nshots from __init__ if passed

Returns

Either only the cost or a tuple of the cost and the standard deviation estimate based on the samples.

Return type

float or tuple (cost, cost_stdev)

get_wavefunction(params)

Same as __call__ but returns the wavefunction instead of cost

Parameters

params (Union[list, ndarray]) – _Raw_(!) QAOA parameters for the state preparation. Can be obtained from Type[AbstractParams] objects via .raw()

Returns

The wavefunction prepared with raw QAOA parameters params

Return type

Wavefunction

On the QVM / QPU

class qaoa.cost_function.QAOACostFunctionOnQVM(hamiltonian, params, qvm, scalar_cost_function=True, nshots=1, base_numshots=100, enable_logging=False, initial_state=None, qubit_mapping=None)

A cost function that inherits from PrepareAndMeasureOnQVM and implements the specifics of QAOA

Parameters

  • hamiltonian (PauliSum) – The cost hamiltonian

  • params (Type[AbstractParams]) – Form of the QAOA parameters (with n_steps and type fixed for this instance)

  • qvm (Union[QuantumComputer, str]) – Connection the QC to run the program on OR a name string like expected by pyquil.api.get_qc

  • scalar_cost_function (bool) – If True: __call__ returns only the expectation value If False: __call__ returns a tuple (exp_val, std_dev) Defaults to True.

  • nshots (int) – Fixed multiple of base_numshots for each estimation of the expectation value. Defaults to 1

  • base_numshots (int) –

    numshots multiplier to compile into the binary. The argument nshots of

    __call__ is then a multplier of this.

  • log – List to keep log of function calls

  • qubit_mapping (Optional[Dict[QubitPlaceholder, Union[Qubit, int]]]) – A mapping to fix QubitPlaceholders to physical qubits. E.g. pyquil.quil.get_default_qubit_mapping(program) gives you on.

__call__(params, nshots=None)
Parameters

  • params (param) – the parameters to run the state preparation circuit with

  • nshots (param) – Overrides nshots in __init__ if passed

Returns

Either only the cost or a tuple of the cost and the standard deviation estimate based on the samples.

Return type

float or tuple (cost, cost_stdev)