qalgora-Q Docs Hub量子文档 ✦ Ask AI✦ 问问文档
/

Constructing Operators

Spin operators are weighted sums of Pauli strings. They define the Hamiltonians and observables you measure.

Building spin operators

Start from the Pauli primitives spin.x(i), spin.y(i), spin.z(i), and the identity spin.i(i); combine them with +, -, * and scalar coefficients (real or complex). This runs on the reference build today.

from qalgora import spin

op = spin.z(0) + 0.5 * spin.x(1) - spin.y(0) * spin.y(1)
print(op)                       # human-readable Pauli sum
Term introspection — spec interface (规范接口·暂未实现)
Counting terms/qubits (op.get_term_count(), op.get_qubit_count()) and iterating individual Pauli terms (for term in op, term.to_string()) are documented specification interfaces; the open reference build does not implement them yet. The lines below are illustrative. 
# Spec interface — not yet in the reference build:
# print("terms:", op.get_term_count())
# print("qubits:", op.get_qubit_count())
# for term in op:                 # iterate the individual Pauli terms
#     print(term.get_coefficient(), str(term))

Pauli words & exponentiation

A pauli_word like "XYZ" names a Pauli string. exp_pauli applies exp(-iθP) directly — the elementary step of Trotterized time evolution.

exp_pauli — spec interface (规范接口·暂未实现)
exp_pauli and the pauli_word type are documented specification interfaces; the open reference build does not bundle them yet. The kernel below shows the intended usage. 
import qalgora

@qalgora.kernel
def trotter_step(q: qalgora.qview, words: list[qalgora.pauli_word],
                 coeffs: list[float], dt: float):
    for i in range(len(words)):
        exp_pauli(coeffs[i] * dt, q, words[i])   # exp(-i c dt P)  (spec interface)
Specification API — not in the open reference build yet
This example shows a qalgora-Q specification API (or a third-party library) that the open reference build does not bundle today. It documents the intended interface; to run code now, use the reference build’s supported core API.

Decomposing a Hamiltonian

Extract coefficients and Pauli words from any spin operator to drive a Trotter loop or hand to hardware:

Decomposition helpers — spec interface (规范接口·暂未实现)
Per-term coefficient and Pauli-word extraction (term.to_string(), term.get_coefficient()) is a documented specification interface; the open reference build does not implement it yet. 
# Spec interface — not yet in the reference build:
# words  = [str(term) for term in hamiltonian]            # e.g. "XYZ"
# coeffs = [term.get_coefficient() for term in hamiltonian]

Common Hamiltonians

  • Ising: -J Σ Z_i Z_{i+1} - h Σ X_i
  • Heisenberg: Σ (X_iX_j + Y_iY_j + Z_iZ_j)
  • Molecular: a Jordan–Wigner-mapped fermionic Hamiltonian (see OpenFermion interop)

构造算符

自旋算符是 Pauli 串的加权求和，用来描述要测量的哈密顿量和可观测量。

构建自旋算符

从 Pauli 原语 spin.x(i)、spin.y(i)、 spin.z(i) 和单位算符 spin.i(i) 出发，用 +、 -、* 配上实数或复数系数组合起来即可。这部分现在即可在参考实现上运行。

from qalgora import spin

op = spin.z(0) + 0.5 * spin.x(1) - spin.y(0) * spin.y(1)
print(op)                       # 人类可读的 Pauli 求和
项内省 — 规范接口·暂未实现
统计项数/比特数（op.get_term_count()、op.get_qubit_count()）以及遍历各个 Pauli 项（for term in op、term.to_string()）属于规范中的接口，开放参考实现目前尚未实现。下面几行仅用于说明。 
# 规范接口——参考实现暂未内置：
# print("terms:", op.get_term_count())
# print("qubits:", op.get_qubit_count())
# for term in op:                 # 遍历各个 Pauli 项
#     print(term.get_coefficient(), str(term))

Pauli 词与指数化

pauli_word（如 "XYZ"）用来表示一个 Pauli 串。exp_pauli 直接施加 exp(-iθP)——它是 Trotter 时间演化的基本步骤。

exp_pauli — 规范接口·暂未实现
exp_pauli 与 pauli_word 类型属于规范中的接口，开放参考实现目前尚未内置；下面的内核仅用于说明预期用法。 
import qalgora

@qalgora.kernel
def trotter_step(q: qalgora.qview, words: list[qalgora.pauli_word],
                 coeffs: list[float], dt: float):
    for i in range(len(words)):
        exp_pauli(coeffs[i] * dt, q, words[i])   # exp(-i c dt P)（规范接口）
规范接口 · 参考实现暂未包含
此示例展示的是 qalgora-Q 规范中的接口（或第三方库），开放参考实现目前尚未内置，仅用于说明预期用法；如需立即运行，请使用参考实现已支持的核心 API。

分解哈密顿量

从任意自旋算符里取出系数和 Pauli 词，用来驱动 Trotter 循环或喂给硬件：

分解辅助 — 规范接口·暂未实现
按项提取系数与 Pauli 词（term.to_string()、term.get_coefficient()）属于规范中的接口，开放参考实现目前尚未实现。 
# 规范接口——参考实现暂未内置：
# words  = [str(term) for term in hamiltonian]            # 例如 "XYZ"
# coeffs = [term.get_coefficient() for term in hamiltonian]

常见哈密顿量

  • Ising： -J Σ Z_i Z_{i+1} - h Σ X_i
  • Heisenberg： Σ (X_iX_j + Y_iY_j + Z_iZ_j)
  • 分子哈密顿量： 经 Jordan–Wigner 映射的费米子哈密顿量（参见 OpenFermion 互操作）