QuTip

QuTip is designed with a focus on physics applications, and thus has a massive library of methods for that goal. The extra learning materials are available through the platforms for QuTip.

Getting Started

Below is a base example for creating and running the QuTip simulator which will create a Bell state (an entangled state of two qubits):

import numpy as np
from qutip import *

# Define the initial state (|00> state for two qubits)
initial_state = tensor(basis(2, 0), basis(2, 0))

# Define the Hadamard gate and CNOT gate
hadamard_gate = snot()  # Single qubit Hadamard gate
cnot_gate = cnot()      # CNOT gate

# Apply Hadamard gate to the first qubit
state_after_hadamard = tensor(hadamard_gate, qeye(2)) * initial_state

# Apply the CNOT gate to create entanglement
final_state = cnot_gate * state_after_hadamard

# Print the final state (Bell state)
print(final_state)

# Optionally, check the final state's density matrix
rho = final_state * final_state.dag()
print(rho)

Code Insights

Import the necessary dependencies.
Define a quantum state and build the quantum circuit.
Hints between the lines:
- The snot() is creating a single qubit Hadamard gate to create a superposition.
- The cnot() is the CNOT gate to entangle the qubits, resulting in a Bell state.
- The final_state.dag() gives the conjugate transpose and the qeye() is the identity operator.
Print out the results. The density matrix of the final state is to analyze the entanglement and see the mixed states.

Follow up on the GWDG Updates:

Qutip
- The version of Qutip provided by GWDG: 5.0.4

Key Features

QuTiP is a framework built in Python that is intended for the simulation and analysis of open quantum systems. Extensively utilized in quantum optics, quantum thermodynamics, and quantum control research, it provides a wide range of tools for simulating dissipative and decoherent quantum phenomena.

Open Quantum System Simulation: QuTiP is highly effective in simulating open quantum systems, which involve interactions with environments causing decoherence and dissipation, essential for studying practical quantum systems.
Quantum Control: QuTiP offers strong resources for creating and mimicking quantum control plans, which is perfect for creating methods to manage qubits with great accuracy.
Quantum Optics and Dynamics: QuTiP is widely utilized in quantum optics due to its native support for typical quantum systems like cavities, harmonic oscillators, and two-level atoms.
Hamiltonian Engineering: The Hamiltonian Engineering framework enables users to define and simulate time-dependent and custom Hamiltonians, allowing in-depth exploration of dynamic behaviors in quantum systems.

Supplementary Modules

Command	Description
`coherent(N,alpha)`	Coherent state, alpha = complex number (eigenvalue) for requested coherent state.
`maximally_mixed_dm(N)`	Maximally mixed density matrix, N = number of levels in Hilbert space.
`zero_ket(N)`	Empty ket vector, N = number of levels in Hilbert space.
`basis(N,#m)`,`fock(N,#m)`	Fock state ket vector, N = number of levels in Hilbert space, m = level containing excitation (0 if no m given).
`momentum(qobj)`	Momentum operator, qobj = Object to copy dimensions from.
`position(qobj)`	Position operator, qobj = Object to copy dimensions from.
`qeye(N)`	Identity, N = number of levels in Hilbert space.
`destroy(qobj)`	Lowering (destruction) operator, qobj = Object to copy dimensions from.
`create(qobj)`	Raising (creation) operator, qobj = Object to copy dimensions from.
`squeezing(q1, q2, sp)`	Squeezing operator (Generalized), q1,q2 = Quantum operators (Qobj) sp = squeezing parameter.
`Q.check_herm()`	Check Hermicity, check if quantum object is Hermitian.
`Q.dag()`	Dagger (adjoint), returns adjoint (dagger) of object.
`Q.diag()`	Returns the diagonal elements.
`Q.eigenenergies()`	Eigenenergies (values) of operator.
`Q.eigenstates()`	Returns eigenvalues and eigenvectors.
`Q.groundstate()`	Eigenval & eigket of Qobj groundstate.
`Q.inv()`	Matrix inverse of the Qobj.
`Q.norm()`	Returns L2 norm for states, trace norm for operators.
`Q.ptrace(sel)`	Partial trace returning components selected using ‘sel’ parameter.
`Q.proj()`	Form projector operator from given ket or bra vector.
`Q.transform(inpt)`	A basis transformation defined by matrix or list of kets ‘inpt’.

The fundemental explanations behind of these functions,operators and states and more can be found on the official QuTip webpage.