Visually representing entangled qubits (i.e., Bell state)

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SUMMARY

This discussion focuses on the visual representation of entangled qubits, specifically Bell states, in quantum computing. Elroy is developing a quantum computer emulator and is exploring various methods, including the Bloch sphere and Majorana sphere, for visualizing entangled states. Participants suggest using state tomography and grid-based approaches, where amplitude and phase are represented through 3D bar charts or grids. The conversation highlights the challenges of visualizing complex entangled states as the number of qubits increases.

PREREQUISITES
  • Understanding of quantum computing concepts, particularly qubits and entanglement.
  • Familiarity with the Bloch sphere and Majorana sphere for visualizing quantum states.
  • Knowledge of state tomography and its applications in quantum mechanics.
  • Experience with graphical representation techniques, such as 3D bar charts and grid visualizations.
NEXT STEPS
  • Research the implementation of the Majorana sphere for visualizing entangled states.
  • Explore state tomography methods for representing quantum states effectively.
  • Investigate grid-based visualization techniques in quantum computing, focusing on amplitude and phase representation.
  • Learn about advanced visualization tools for quantum circuits and entangled states, such as quantum computing simulators.
USEFUL FOR

Quantum computing enthusiasts, software developers working on quantum emulators, and researchers interested in visualizing complex quantum states will benefit from this discussion.

Elroy
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Hi All,

I'm in the beginning stages of writing a quantum computer emulator, primarily to get all the concepts down.

I've got an excellent Bloch sphere with a Bloch vector that I can duplicate as many times as I like. However, I'm now tackling entangled states. I'm struggling with identifying the best way to visually represent these states.

I've been studying the Majorana sphere, and it seems to have definite possibilities, with its Majorana points and Closest Product Points (possibly making disks or cones from the center of the sphere).

I'm just wondering if others have different ideas about the best way to represent these entangled states. I'd like to start with the Bell states (EPR pairs of qubits), but would eventually like to generalize my visual representations to any entangled state with any number of qubits and any level of entanglement.

Thanks in advance for the suggestions/opinions.

Elroy
 
Isn't the various ways of visually representing state tomography pretty much the standard method for this (often represented by 3D bar charts)?
 
I don't know any good ways to represent entangled states, that aren't the algebraic form like "|00> + |11>" or just a big grid of amplitude representations.

Google's quantum computing playground uses the grid approach; they have a field of boxes where height is amplitude and color is phase.

In my own stuff, like this toy circuit simulator, I also just use the grid of amplitudes. In my case I use circles with radius equal to the amplitude and a line on them pointing along the phase. Also I "fill up" the cell based on the squared amplitude, since that total is preserved by the operations. For example, if you have four qubits where A1 is entangled with B1 such that they always disagree and A2 is entangled with B2 such that they always agree then I show that as:

msvTZDs.png

Basically, entanglement ends up looking like diagonals.

Naturally this becomes a visual mess as you add more qubits. You'd need a 1024-by-1024 grid to show the state of 20 qubits this way.
 

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