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.

Core Abstractions¶

PySparQ is built on three core abstractions:

System — a single computational basis state, containing one complex amplitude amplitude and the values of all registers registers
SparseState — a sparse quantum state managing a std::vector<System>, storing only basis states with non-zero amplitudes
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.

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核心概念¶

本节介绍 PySparQ 稀疏态量子模拟的基础构建模块。理解这些概念是使用 Register Level Programming 范式的前提。

核心抽象¶

PySparQ 基于三个核心抽象构建：

System — 单个计算基态，包含一个复数振幅 amplitude 和所有寄存器的值 registers
SparseState — 托管 std::vector<System> 的稀疏量子态，仅存储振幅非零的基态
Registers — 具有类型存储的命名量子变量，以 uint64_t 为存储单位，允许 |a⟩|b⟩|c⟩ 式的多寄存器编码

核心数据关系¶

SparseState 的默认构造函数会创建一个 |0...0⟩ 的初态（内部包含一个所有寄存器值为 0、振幅为 1 的 System）
每个 System 实例中的寄存器值组合在 SparseState 中必须是唯一的——若出现重复，意味着发生了量子干涉，两个振幅应相加并去重
量子编程的操作层面从量子比特上升到了量子寄存器，几乎所有操作都以寄存器为单位

与传统全态矢量模拟器存储 \(2^n\) 个振幅不同，PySparQ 仅存储非零基态，使得叠加态数量有限的量子算法可以在多项式资源内模拟。