Feature: Inspect quantum circuit state at intermediate positions

[NicKIT01]

User Story

As a user of QuaK, I want to inspect the quantum state at arbitrary positions inside a circuit, so that I can debug and understand how gates affect the state before the final measurement.

Scope

The first version should introduce visual inspection elements that can be placed at selected positions in the circuit timeline. These inspection elements should not modify the circuit semantics unless explicitly configured as measurement probes.

Supported inspection types

• Amplitude view
• Probability / "chance of being ON" view
• Bloch sphere view
• Virtual full circuit measurement simulation at an intermediate circuit position
• (Density Matrix)

The inspection system should operate on the simulated state at a selected circuit position and be independent of the final measurement results currently displayed by the simulator.

Acceptance criteria

• Users can place an inspection marker between circuit columns.
• The simulator can evaluate the circuit state up to the selected marker.
• The UI displays amplitudes, probabilities, or Bloch sphere information depending on the selected inspection type.
• The probability view shows measurement probabilities for selected qubits.
• The amplitude view shows amplitude magnitude, phase, and derived probability where available.
• The Bloch sphere view works for single-qubit states.
• If a qubit is entangled or cannot be represented as a pure single-qubit state, the Bloch view shows a clear “mixed / entangled state” message instead of misleading data.
• Users can run a virtual measurement/simulation at the selected position for debugging the current exact state.
• Virtual measurements/simulations do not permanently change the circuit unless the user explicitly inserts a real measurement gate.
• Final simulation results continue to work as they do today.
• The feature is compatible with single-qubit mid circuit measurements written to classical bits.
• Multiple inspection markers can exist within the same circuit.
• Inspection data updates when the circuit changes.

Notes
This feature is inspired by Quirk-style inspection displays. The goal is not to copy Quirk completely, but to provide practical debugging views inside the existing circuit editor and simulation result workflow.