qat.opt.MWIS
- class qat.opt.MWIS(graph, weights=None)
The class allows for the representation of a Maximum Weighted Independent Set (MWIS) problem in the Rydberg framework, by providing a systematic way to embed any graph into a unit disk graph and realizing a one-to-one matching with a Rydberg atom system. The embedding procedure is called the crossing lattice. The Rydberg Hamiltonian writes,
\[H = \sum_v \frac{\Omega_v}{2}\sigma_v^x - \sum_v \Delta_v n_v + \sum_{v, w}U_{vw}n_v n_w\]where \(\Omega_v\) is the rabi frequency, \(\Delta_v\) the detuning and \(U_{vw}\) the elements of the coupling matrix between atoms. It is quite close to the energy minimization representation of a MWIS problem.
\[H = -\sum_{v \in V} \delta_v n_v + \sum_{(u, v) \in E} U_{uv} n_u n_v\]where \(V\) is the set of vertices of the graph, \(E\) the set of edges and \(\delta_v\) the node weights. In such a form, we can derive an Ising formulation of any MWIS problem, which is why this class inherits from the
Ising
object. It can also be translated to aQUBO
object viato_qubo()
.This class generates a new type of job different from the classes Ising and QUBO called
'ryd'
jobs.- Parameters
graph (nx.Graph) – input graph from which we will find the MWIS.
weights (dict) – dictionary of the weights of each note. No weights by default.
- graph
weighted graph attribute
- Type
nx.Graph
- aqo_job(tmax=None, mixing=None, **kwargs)
Generates an Adiabatic Quantum Optimization (AQO) job performing a linear interpolation between an initial mixing Hamiltonian and the problem’s Hamiltonian.
- classmethod decode_rydberg(job, result)
Returns the MWIS simulation result of the input graph.
- static decode_rydberg_meta_data(meta_data: dict, result)
Returns the MWIS simulation result of the input graph.
- dump(fname)
Dumps the ising in a binary file (.circ)
- Parameters
fname (str) – the file name
- classmethod from_thrift(tobject)
Builds an Ising object out of a thrift Ising object. Does so in place.
- get_best_parameters()
This method returns a dictionary with the best found parameters (after benchmarking) for simulated quantum annealing (SQA) of the respective Ising problem. SQA is available in QLM, but the temperature parameters temp_max and temp_min could also be used for simulated annealing (SA), available in myQLM.
The method should be called from one of the child problem classes (e.g. MaxCut, NumberPartitioning, etc.) and not directly from the parent Ising class as this will raise an exception.
- get_j_h_and_offset()
This method returns the \(J\) coupling matrix, the magnetic field \(h\) and Ising energy offset, which define the Ising object.
- Returns
3-element tuple containing
- J (2D numpy array) - a symmetric array with zero diagonal elements for the
coupling between each two spins - it represents the \(J\) matrix from the Hamiltonian of the problem
- h (1D numpy array) - an array with the magnetic field acting on each of the
spins, coming from the Hamiltonian of the problem
- offset_i (double) - the value of the Ising offset energy in the respective
Hamiltonian
- get_observable(obs_type)
Returns an ising- or a terms-type of
Observable
from theIsing
problem. If a ‘terms’ Observable is chosen, the Ising problem will first be translated to aCombinatorialProblem
.- Parameters
obs_type (string) –
The type of
Observable
to be returned:'ising'
or'terms'
.'ising'
observables can be used to create aSchedule
(by also proving gamma_t ifSQAQPU
in the full Qaptiva appliance will be used) and consecutively produce aJob
to be sent for Simulated Quantum Annealing.'terms'
observables can be used for gate-based quantum computations with aCircuit
or analog quantum computations, also with aSchedule
.
- Returns
an Ising Observable or an Observable with terms representing the problem
- Return type
- property j_coupling_matrix
The J-coupling of the Ising Hamiltonian as a symmetric numpy 2D array with zero diagonal elements.
- classmethod load(fname)
Loads an ising from a binary file.
- Parameters
fname (str) – the file name
- Returns
an ising object
- Return type
- property magnetic_field_h
The magnetic field h of the Ising Hamiltonian as a numpy 1D array
- qaoa_job(depth, cnots=True, strategy='coloring', to_circ_args=None, **kwargs)
Generates a QAOA Ansatz Job for gate-based computations using the cost observable returned by the abstract method
get_observable
.Warning
When setting the cnots option to False, the circuit might make use of generalized many-qubits Z rotations. In that case, you might want to instantiate your variational plugins using a gate set that contains definition of these gates. If not, some matrices in the circuit structure will be missing and some QPUs may not be able to handle the circuit.
The following piece of code should allow you to link the correct gate set to a variational plugin:
from qat.plugins import ScipyMinimizePlugin from qat.vsolve.ansatz import get_qaoa_gate_set # This plugin will no be able to bind variables inside a # job generated with cnot set to False! my_plugin = ScipyMinimizePlugin() # This plugin can now be used with job generated with the # cnots option sets to False! my_plugin = ScipyMinimizePlugin(gate_set=get_qaoa_gate_set())
- Parameters
depth (int) – the depth of the Ansatz
strategy (str) – the strategy to adopt to generate the circuit. Possible strategies are “default” or “coloring”. The “coloring” strategy uses a greedy coloring heuristics to try to optimize the overall depth of the Ansatz. Default is “default” which synthesize the circuit without optimizing the term ordering.
cnots (optional, bool) – If set to True the Ansatz will only use CNOT gates. If set to False, some abstract gates will be used to generate collective pauli rotations, resulting in a lower gate count. Defaults to True.
**kwargs – optional arguments that will be transfered to the job’s constructor (e.g nbshots, etc).
- Returns
a Qaptiva job, ready to run
- Return type
- ryd_job(optimize=True, time_budget_sec=3, tmax=10, **kwargs)
Returns a ryd-type job for the MWIS problem.
- Parameters
optimize (bool) – if True, the node overhead will be reduced.
time_budget_sec (float) – time budget allocated for the core part of the optimization function.
tmax (float) – time duration of the adiabatic simulation.
- Returns
a ryd-type job
- Return type
- sqa_job(gamma_t=None, tmax=1.0, **kwargs)
Returns a sqa-type of Job for the problem - ready to run on a QPU for simulated annealing (SA) or simulated quantum annealing (SQA). The second one comes in the full Qaptiva. The optional
gamma_t
argument is only used for SQA.- Parameters
tmax (float, optional) – time duration of the annealing. Default is 1.
gamma_t (
ArithExpression
, optional) – a function specifying the time dependence of Gamma. It should be produced using the variable ‘t’ created by the classVariable
.
- Returns
a ready to run sqa-type of Job for the problem
- Return type
Note
For the supported NP problems, some well performing max and min Gamma (for a linearly decreasing gamma_t) have been found and could be accessed via the method
get_best_parameters
of the respective problem class.
- to_bqm()
Transforms an Ising problem to DWave’s Binary Quadratic Model from the library
dimod
.- Returns
a BinaryQuadraticModel object
- Return type
BinaryQuadraticModel
- to_combinatorial_problem()
Translates the Ising problem into a CombinatorialProblem.
- Returns
a combinatorial problem instance
- Return type
- to_job(job_type, *args, **kwargs)
A general method allowing the creation of an aqo-, qaoa- or sqa-type of Job from a problem description - ready to run on the respective QPU.
'aqo'
is for Adiabatic Quantum Optimization (with analog QPUs). Internally, methodaqo_job()
is used to generate the job.'qaoa'
is for using the Quantum Approximate Optimization Algorithm (with gate-based QPUs). Internally, methodqaoa_job()
is used to generate the job.'sqa'
is for Simulated Quantum Annealing to be used with SQAQPU in Qaptiva, also being able to be run withSimulatedAnnealing
(SA) for myQLM. Internally, methodsqa_job()
is used to generate the job.'ryd'
is for Rydberg. Internally, methodryd_job()
is used to generate the job.
- Parameters
job_type (string) – The type of job to be returned:
'aqo'
,'qaoa'
,'sqa'
, or'ryd'
.*args – additional arguments passed to
aqo_job()
,qaoa_job()
,sqa_job()
, orryd_job()
.**kwargs – additional keyword arguments passed to
aqo_job()
,qaoa_job()
,sqa_job()
, orryd_job()
.
- Returns
a ready to run Job for the respective type of problem
- Return type