mindquantum.algorithm.nisq.MaxCutAnsatz
- class mindquantum.algorithm.nisq.MaxCutAnsatz(graph, depth=1)[source]
The MaxCut ansatz.
For more detail, please refer to A Quantum Approximate Optimization Algorithm.
\[U(\beta, \gamma) = e^{-\beta_pH_b}e^{-\gamma_pH_c} \cdots e^{-\beta_0H_b}e^{-\gamma_0H_c}H^{\otimes n}\]Where,
\[H_b = \sum_{i\in n}X_{i}, H_c = \sum_{(i,j)\in C}Z_iZ_j\]Here \(n\) is the set of nodes and \(C\) is the set of edges of the graph.
- Parameters
graph (list[tuple[int]]) – The graph structure. Every element of graph is a edge that constructed by two nodes. For example, [(0, 1), (1, 2)] means the graph has three nodes which are 0 , 1 and 2 with one edge connect between node 0 and node 1 and another connect between node 1 and node 2.
depth (int) – The depth of max cut ansatz. Default:
1
.
Examples
>>> import numpy as np >>> from mindquantum.algorithm.nisq import MaxCutAnsatz >>> graph = [(0, 1), (1, 2), (0, 2)] >>> maxcut = MaxCutAnsatz(graph, 1) >>> maxcut.circuit ┏━━━┓ ┏━━━━━━━━━━━━━┓ ┏━━━━━━━━━━━━━┓ ┏━━━━━━━━━━━━━┓ q0: ──┨ H ┠─┨ ┠─────────────────● ┠─┨ RX(alpha_0) ┠─── ┗━━━┛ ┃ ┃ ┃ ┃ ┗━━━━━━━━━━━━━┛ ┏━━━┓ ┃ Rzz(beta_0) ┃ ┏━━━━━━━━━━━━━┓ ┃ ┃ ┏━━━━━━━━━━━━━┓ q1: ──┨ H ┠─┨ ┠─┨ ┠─┨ Rzz(beta_0) ┠─┨ RX(alpha_0) ┠─── ┗━━━┛ ┗━━━━━━━━━━━━━┛ ┃ ┃ ┃ ┃ ┗━━━━━━━━━━━━━┛ ┏━━━┓ ┃ Rzz(beta_0) ┃ ┃ ┃ ┏━━━━━━━━━━━━━┓ q2: ──┨ H ┠─────────────────┨ ┠─● ┠─┨ RX(alpha_0) ┠─── ┗━━━┛ ┗━━━━━━━━━━━━━┛ ┗━━━━━━━━━━━━━┛ ┗━━━━━━━━━━━━━┛ >>> >>> print(maxcut.hamiltonian) 3/2 [] + -1/2 [Z0 Z1] + -1/2 [Z0 Z2] + -1/2 [Z1 Z2] >>> partitions = maxcut.get_partition(5, np.array([4, 1])) >>> for i in partitions: ... print(f'partition: left: {i[0]}, right: {i[1]}, cut value: {maxcut.get_cut_value(i)}') partition: left: [2], right: [0, 1], cut value: 2 partition: left: [0, 1], right: [2], cut value: 2 partition: left: [0], right: [1, 2], cut value: 2 partition: left: [0, 1, 2], right: [], cut value: 0 partition: left: [], right: [0, 1, 2], cut value: 0
- get_cut_value(partition)[source]
Get the cut values for given partitions.
The partition is a list that contains two lists, each list contains the nodes of the given graph.
- Parameters
partition (list) – a partition of the graph considered.
- Returns
int, cut_value under the given partition.
- get_partition(max_n, weight)[source]
Get the partitions of this max-cut problem.
- Parameters
max_n (int) – how many partitions you want.
weight (Union[ParameterResolver, dict, numpy.ndarray, list, numbers.Number]) – parameter value for max-cut ansatz.
- Returns
list, a list of partitions.
- property hamiltonian
Get the hamiltonian of this max cut problem.
- Returns
QubitOperator, hamiltonian of this max cut problem.