mindquantum.algorithm.nisq.Max2SATAnsatz
- class mindquantum.algorithm.nisq.Max2SATAnsatz(clauses, depth=1)[source]
The Max-2-SAT ansatz.
For more detail, please refer to Reachability Deficits in Quantum Approximate Optimization.
\[U(\beta, \gamma) = e^{-\beta_pH_b}e^{-\gamma_pH_c} \cdots e^{-\beta_0H_b}e^{-\gamma_0H_c}H^{\otimes n}\]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
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*beta_0) ┠────■─────────────────────────■───┨ RX(alpha_0) ┠─── ┗━━━┛ ┗━━━━━━━━━━━━━━━━┛ ┃ ┃ ┗━━━━━━━━━━━━━┛ ┏━━━┓ ┏━━━━━━━━━━━━━━━━━┓ ┏━┻━┓ ┏━━━━━━━━━━━━━━━━━┓ ┏━┻━┓ ┏━━━━━━━━━━━━━┓ q2: ──┨ H ┠─┨ RZ(-1/2*beta_0) ┠─┨╺╋╸┠─┨ RZ(-1/2*beta_0) ┠─┨╺╋╸┠─┨ RX(alpha_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)[source]
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)[source]
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.