The survey taxonomy

Quantum states

Single-qubit encodings show probability or amplitude magnitude, relative phase, and sometimes mixed-state purity. Multi-qubit state vectors grow exponentially with qubit count, motivating four scaling strategies.

Information Reduction

Select partial state information or project it into fewer dimensions, trading completeness for compact summaries.

Per-Qubit Composition

Arrange single-qubit views as small multiples. This scales linearly but omits joint relationships such as entanglement.

Relational Reformulation

Expose chosen relationships among qubits or basis states, including adjacency, correlations, or entangling structure.

Hierarchical Organization

Group basis terms or recursively subdivide the computational basis into treemap-like or fractal layouts.

These strategies trade completeness, scalability, and interpretability according to which state properties an analysis must preserve.

State transitions

Gate-driven evolution and inferred error propagation add changes to compare.

Temporal Composition

Arrange state snapshots across gate steps or overlay them on a circuit.

Flow Reformulation

Represent state changes as flows or links, exposing splitting, merging, or inferred error propagation.

Difference Encoding

Directly encode changes between adjacent states, reducing comparison effort.

Circuit structures

More qubits and gates require readable ordering and dependencies.

Structural Abstraction

Group gates, repeated patterns, or modules while retaining the circuit-diagram layout.

Dependency Reformulation

Use dependency graphs to expose ordering, parallelism, and critical paths.