Core Concepts

This section introduces the fundamental building blocks of sparse-state quantum simulation in PySparQ. Understanding these concepts is a prerequisite for using the Register Level Programming paradigm.

• The System Class
  • Core Concepts
  • Static Variables: Global Register Tracking
  • Instance Members
  • Register Storage Principles
  • Query Methods
  • Accessing Register Values in Basis States
  • Comparison and Sorting
  • Best Practices
  • API Reference
• The SparseState Class
  • Sparse Representation Principles
  • Uniqueness Rule
  • Basic Usage
  • State Evolution Example
  • State Printing Modes
  • Clearing Near-Zero Amplitudes
  • Merging Duplicate Basis States
  • Iterator Support
  • API Reference
• Register Management
  • The Nature of Registers
  • Adding Registers: AddRegister
  • Removing Registers: RemoveRegister
  • Splitting Registers: SplitRegister
  • Combining Registers: CombineRegister
  • PartialTrace: Measurement
  • Register Stack Operations: Push / Pop
  • Summary: Register Operations and the Quantum State
  • API Reference
• Register Types
  • The StateStorageType Enum
  • Type Details
  • The StateStorage Class
  • Type Constraints in Operators
  • Type Selection Guide
• Operators
  • The Two-Phase Model
  • Construction Parameters
  • Applying Operators
  • Operator Categories
  • Concept: Operators vs. Flow-Control Classes

Core Abstractions

PySparQ is built on three core abstractions:

1. System — a single computational basis state, containing one complex amplitude amplitude and the values of all registers registers

2. SparseState — a sparse quantum state managing a std::vector<System>, storing only basis states with non-zero amplitudes

3. Registers — named quantum variables with typed storage, using uint64_t as the storage unit, allowing multi-register encodings of the form |a⟩|b⟩|c⟩

Core Data Relationships

• The default constructor of SparseState creates a |0...0⟩ initial state (internally containing a single System whose register values are all 0 and whose amplitude is 1)

• The register-value combination of each System instance must be unique within a SparseState — if a duplicate appears, quantum interference has occurred, and the two amplitudes should be added and de-duplicated

• The operational level of quantum programming rises from qubits up to quantum registers; almost all operations take registers as their unit

Unlike traditional full state-vector simulators, which store \(2^n\) amplitudes, PySparQ stores only the non-zero basis states, so quantum algorithms with a finite number of superposed states can be simulated with polynomial resources.