JijSQASampler

Simulated Quantum Annealing (SQA) is one of the quantum-inspired algorithms that simulates quantum annealing. In this method, instead of performing quantum annealing for $H(s) = sH_p-\Gamma(1-s)\sum_i \sigma_i^x$, we use the simulated annealing method on the Hamiltonian as follows:

$$\tilde{H} = \frac{s}{L}H_p - \frac{1}{2\beta}\log \coth\left(\frac{\Gamma(1-s)\beta}{L}\sum_i\sum_{l=1}^L\sigma^z_{ik}\sigma^z_{ik+1}\right)$$

where $L$ is a quantity called the Trotter number, $\Gamma$ is the strength of the transverse magnetic field, and $\beta$ is the inverse temperature. Theoretically, this method gives results corresponding to quantum annealing when $L$ is sufficiently large. $s$ varies in the range $[0,1]$ according to $s^4(35-84s+70s^2-20s^3)$ which is proposed in [S. Morita and H. Nishimori, “Mathematical foundation of quantum annealing”. J. Math. Phys. 1 December 2008; 49 (12): 125210.].

In SQA, replicas are created by Trotter decomposition, as shown in the illustration below. Interactions between these replicas emulate quantum effects. Therefore, for many replicas (if $L$ is large), the behavior of SQA is expected to be close to the original quantum annealing, but it should be noted that the computational cost of the simulation is as large as the number of replicas.

Currently, JijSQASampler is provided with the intention of research use for comparison with quantum annealers. Therefore, the SQA parameters, such as beta, gamma and trotter, are not well-tuned for the purpose of the optimization problem. If you wish to use Sampler to perform optimization calculations, please consider using other Samplers.

Usage

Use the two classes provided by the jijzept and run the method sample_model in the JijSQASampler class:

• JijSQASampler: a class to sample by the SQA method.
• JijSQAParameters: a class to set parameters specifically for the SQA sampler.

from jijzept import JijSQASampler, JijSQAParameters

sampler = JijSQASampler(config="./config.toml")
parameters = JijSQAParameters(
    beta=5,
    gamma=1,
    trotter=5,
)

response = sampler.sample_model(
    problem=problem,
    feed_dict=instance_data,
    parameters=parameters,
    search = True,
    max_wait_time=300,
)

What does JijZept automatically tune?

By setting the search argument of the sample_model method to True, the weight coefficients for converting the mathematical model to Quadratic Unconstrained Binary Optimization (QUBO) are automatically adjusted.

Parameters

JijSQAParameters

name	type	default	description
num_reads	Optional[int]	None	The number of samples. If None, 1 will be set.
num_sweeps	Optional[int]	None	The number of Monte-Carlo steps. If None, 1000 will be set.
beta	Optional[float]	None	Inverse tempareture. If None, this will be set automatically.
gamma	Optional[float]	None	Strangth of transverse field. If None, this will be set automatically.
trotter	Optional[int]	None	The number of Trotter. If None, this will be set automatically.
sparse	Optional[bool]	None	If True, only non-zero matrix elements are stored, which will save memory. If None, False will be set.
needs_sqaure_constraints	Optional[dict[str, bool]]	None	This dictionary object determines whether to square the constraint condition while incorporating it into the QUBO/HUBO penalty term. Here, the constraint's name is used as the key. If the value is set to True, the corresponding constraint is squared upon its addition to the QUBO/HUBO penalty term. If None, the value is set to True for linear constraints and to False for non-linear ones.
relax_as_penalties	Optional[dict[str, bool]]	None	This dictionary object is designed to regulate the incorporation of constraint conditions into the QUBO/HUBO penalty term, with the constraint's name functioning as the key. The respective constraint is added to the QUBO/HUBO penalty term if the key's value is True. If the value is False, the constraint is excluded from the penalty term, though it remains subject to evaluation to verify if it meets the constraint conditions. If None, all constraint conditions have this value set to True.

JijSQASampler.sample_model

name	type	default	description
parameters	Optional[JijSQAParameters]	None	Parameters for JijSQASampler.
search	bool	False	If True, the parameter search will be carried out, which tries to find better values of multipliers for penalty terms.
num_search	int	15	The number of parameter search iteration. This option works if search is True.
algorithm	Optional[Literal["v096", "v097-2", "v098"]]	None	Algorithm for parameter search. The valid strings for algorithm are "v096", "v097-2", "v098", users can specify the method used to the parameter search. If None, "v098" will be set.
max_wait_time	Optional[Union[int, float]]	None	The number of timeout [sec] for post request. If None, 60 (one minute) will be set. Please note that this argument is for the JijZept timeout and not for configuring solver settings, such as solving time.
sync	bool	True	If True, synchronous mode is enabled.
queue_name	Optional[str]	None	Queue name

Note

Currently, JijSQASampler is provided with the intention of research use for comparison with quantum annealers. Therefore, the SQA parameters, such as beta and gamma, are not well-tuned for the purpose of the optimization problem. If you wish to use Sampler to perform optimization calculations, please consider using other Samplers.