QSimulations

Python library for quantum systems and simulation

Overview

This module provides various tools and utilities for simulating quantum systems. It includes functions for handling common quantum operations, such as Pauli operators, outer products, commutators, and anti-commutators. Additionally, it provides a class qsimulations to manage and simulate time-dependent quantum systems with ancillary qubits and damping operators.

Articles

• Single-ancilla ground state preparation via Lindbladians
• Simulating Open Quantum Systems Using Hamiltonian Simulations

Simulations:

• TFIM_time_indep_multi_qubit_.ipynb: Time independent transverse-field Ising model
• TFIM_time_dependent_mult_qub.ipynb: Time dependent transverse-field Ising model
• Fermi_Hub_multi_qubit.ipynb: Fermi-Hubbard model

Functions

Utility Functions

Pauli_array

def Pauli_array(op, poz, size):

Generates a Pauli operator for a given position in a system.

• op (np.array): The Pauli operator (X, Y, Z).
• poz (int): Position of the operator in the system.
• size (int): Total size of the system.

outer_prod

def outer_prod(left_poz, right_poz, size):

Computes the outer product of two states.

• left_poz (int): Position of the 1 in the ket vector.
• right_poz (int): Position of the 1 in the bra vector.
• size (int): Size of the overall system.

commute

def commute(op1, op2):

Calculates the commutator of two operators.

• op1 (np.array): First operator.
• op2 (np.array): Second operator.

anti_commute

def anti_commute(op1, op2):

Calculates the anti-commutator of two operators.

• op1 (np.array): First operator.
• op2 (np.array): Second operator.

Taylor_approximation

def Taylor_approximtion(H_op, order, dt, initial_state):

Computes the Taylor approximation for a given Hamiltonian.

• H_op (Qobj): Hamiltonian to be approximated.
• order (int): Order of the approximation.
• dt (float): Time step.
• initial_state (Qobj): Initial state of the system.

Class: qsimulations

The qsimulations class provides a framework for setting up and running quantum simulations with ancillary qubits and damping operators.

Initialization

def __init__(self, H=0, systemSize=0, nrOfDampingOps=0, nrOFAncillas=0):

Initializes the simulation parameters.

• H (Qobj): Hamiltonian of the system.
• systemSize (int): Size of the quantum system.
• nrOfDampingOps (int): Number of damping operators.
• nrOFAncillas (int): Number of ancillary qubits.

Methods

set_H_op

def set_H_op(self, H_tmp):

Sets the Hamiltonian of the system.

• H_tmp (Qobj): New Hamiltonian.

set_system_size

def set_system_size(self, size):

Sets the size of the quantum system.

• size (int): New system size.

set_nr_of_damping_ops

def set_nr_of_damping_ops(self, nr):

Sets the number of damping operators.

• nr (int): Number of damping operators.

set_nr_of_ancillas

def set_nr_of_ancillas(self, nr):

Sets the number of ancillary qubits.

• nr (int): Number of ancillary qubits.

H_op

def H_op(self):

Returns the Hamiltonian of the system.

V_op

def V_op(self, i):

Returns the damping operator for a given index.

• i (int): Index of the damping operator.

H_op_derivative

def H_op_derivative(self):

Returns the time derivative of the Hamiltonian.

V_op_derivative

def V_op_derivative(self, i):

Returns the time derivative of a damping operator.

• i (int): Index of the damping operator.

sum_of_V_dag_V

def sum_of_V_dag_V(self):

Returns the summation of all damping operators.

H_tilde_first_order

def H_tilde_first_order(self, dt):

Calculates the first-order approximation of the Hamiltonian.

• dt (float): Time step.

H_tilde_second_order

def H_tilde_second_order(self, dt):

Calculates the second-order approximation of the Hamiltonian.

• dt (float): Time step.