Visualizing Quantum States

QIRT provides a powerful draw method to visualize quantum states in various formats. This method offers flexibility in how you want to represent and view your quantum states.

Basic Usage

To visualize a quantum state, simply call the draw method on a QuantumState object:

from QIRT import QuantumState

state = QuantumState.from_label((1/math.sqrt(2), "00"), (-1j/math.sqrt(2), "11"))
state.draw()

By default, this will produce a LaTeX representation of the state.

Customizing the Output

The draw method accepts several parameters to customize the visualization:

1. Output Format

You can specify the output format using the output parameter:

# LaTeX format (default)
state.draw(output="latex")

# Matrix format
state.draw(output="matrix")

2. Target Basis

You can visualize the state in different bases:

# Visualize in X-basis
state.draw(target_basis="x")

# Visualize in Y-basis
state.draw(target_basis="y")

# Mix of bases
state.draw(target_basis=["x", "z"])  # For a two-qubit state

3. Qubit Indexing

Control whether to show qubit indices:

# Hide qubit indices
state.draw(show_qubit_index=False)

4. Output Length

Control how many terms appear per line:

# 8 terms per line (2^3)
state.draw(output_length=3)

5. LaTeX Source

Get the LaTeX source code instead of rendering:

latex_source = state.draw(source=True)
print(latex_source)

Examples

Let's go through some examples to showcase these features:

1. Visualizing a Bell state

   bell_state = QuantumState.from_label((1/math.sqrt(2), "00"), (1/math.sqrt(2), "11"))
   bell_state.draw()
   

   >> Output: \(\frac{\sqrt{2}}{2}|\texttt{00}\rangle_{01} + \frac{\sqrt{2}}{2}|\texttt{11}\rangle_{01}\)

2. Matrix representation

   # This will display the state vector as a column matrix.
   bell_state.draw(output="matrix")
   

   >> Output:
   

3. Changing basis

   # This will show the Bell state represented in the X-basis.
   bell_state.draw(target_basis="x")
   

   >> Output: $ \frac{\sqrt{2}}{2}|\texttt{++}\rangle_{01} +\frac{\sqrt{2}}{2}|\texttt{--}\rangle_{01} $

4. Changing output length

   complex_state = QuantumState.from_label("000", "001", "010", "011", "100", "101", "110", "111")
   # This will display the state with (2^output_length) terms per line.
   complex_state.draw(output_length=1)
   

   >> Output: