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mindquantum.algorithm.nisq.Max2SATAnsatz

class mindquantum.algorithm.nisq.Max2SATAnsatz(clauses, depth=1)

The Max-2-SAT ansatz.

For more detail, please refer to Reachability Deficits in Quantum Approximate Optimization.

$$U(\beta ,\gamma )=e^{-i{\beta }_p{H}_b}{e}^{-i\frac{{\gamma }_p}{2}{H}_c}\cdots e^{-i{\beta }_0{H}_b}{e}^{-i\frac{{\gamma }_0}{2}{H}_c}{H}^{\otimes n}$$

Where,

$$H_b=\sum _{i\in n}{X}_i,H_c=\sum _{l\in m}P(l)$$

Here $n$ is the number of Boolean variables and $m$ is the number of total clauses and $P(l)$ is rank-one projector.

Parameters

• clauses (list[tuple[int]]) – The Max-2-SAT structure. Every element of list is a clause represented by a tuple with length two. The element of tuple must be non-zero integer. For example, (2, -3) stands for clause $x_2\vee \mathrm{\neg }{x}_3$.

• depth (int) – The depth of Max-2-SAT ansatz. Default: 1.

Examples

>>> import numpy as np
>>> from mindquantum.algorithm.nisq import Max2SATAnsatz
>>> clauses = [(2, -3)]
>>> max2sat = Max2SATAnsatz(clauses, 1)
>>> max2sat.circuit
      ┏━━━┓ ┏━━━━━━━━━━━━━━━━━┓                                   ┏━━━━━━━━━━━━┓
q1: ──┨ H ┠─┨ RZ(1/2*gamma_0) ┠────■──────────────────────────■───┨ RX(beta_0) ┠───
      ┗━━━┛ ┗━━━━━━━━━━━━━━━━━┛    ┃                          ┃   ┗━━━━━━━━━━━━┛
      ┏━━━┓ ┏━━━━━━━━━━━━━━━━━━┓ ┏━┻━┓ ┏━━━━━━━━━━━━━━━━━━┓ ┏━┻━┓ ┏━━━━━━━━━━━━┓
q2: ──┨ H ┠─┨ RZ(-1/2*gamma_0) ┠─┨╺╋╸┠─┨ RZ(-1/2*gamma_0) ┠─┨╺╋╸┠─┨ RX(beta_0) ┠───
      ┗━━━┛ ┗━━━━━━━━━━━━━━━━━━┛ ┗━━━┛ ┗━━━━━━━━━━━━━━━━━━┛ ┗━━━┛ ┗━━━━━━━━━━━━┛
>>> max2sat.hamiltonian
1/4 [] +
1/4 [Z1] +
-1/4 [Z1 Z2] +
-1/4 [Z2]
>>> sats = max2sat.get_sat(4, np.array([4, 1]))
>>> sats
['001', '000', '011', '010']
>>> for i in sats:
...     print(f'sat value: {max2sat.get_sat_value(i)}')
sat value: 1
sat value: 0
sat value: 2
sat value: 1

get_sat(max_n, weight)

Get the strings of this max-2-sat problem.

Parameters

• max_n (int) – how many strings you want.

• weight (Union[ParameterResolver, dict, numpy.ndarray, list, numbers.Number]) – parameter value for Max-2-SAT ansatz.

Returns

list, a list of strings.

get_sat_value(string)

Get the sat values for given strings.

The string is a str that satisfies all the clauses of the given max-2-sat problem.

Parameters

string (str) – a string of the max-2-sat problem considered.

Returns

int, sat_value under the given string.

property hamiltonian

Get the hamiltonian of this max-2-sat problem.

Returns

QubitOperator, hamiltonian of this max-2-sat problem.