完成实作阶段后，目标是做到什么

What this practicum is designed to teach

能力边界：这是一条进阶实作路线，不保证仅凭阅读就达到独立研究水平。Day 1–8 教学材料和本地演示已完成；真实 QPU 作业需用户自行安装 Qiskit、管理服务商账户/凭据、选择真实后端并承担费用/排队限制，本网站不会上传凭据或声称代为运行硬件。

Scope: This advanced path is not a guarantee of research-level independence. Day 1–8 teaching material and local demos are complete. Real QPU jobs require users to install Qiskit, manage provider accounts/credentials, choose a real backend, and account for cost and queue limits; this site neither collects credentials nor claims to run hardware jobs.

实作路线图：先造工具，再做算法

Practicum roadmap: build the tool, then the algorithms

第 1 天实验｜亲手运行一个 statevector

Day 1 lab | Run a statevector circuit yourself

模拟器用长度为 2ⁿ 的复数向量保存 n 个量子比特的振幅。下方使用两比特电路：先施加 H，再施加 CNOT，就会得到 Bell 态；你可以逐个加门，查看振幅、概率并做固定种子采样。

A simulator stores amplitudes for n qubits in a complex vector of length 2ⁿ. Use the two-qubit circuit below: apply H, then CNOT, to prepare a Bell state. Add gates one at a time and inspect amplitudes, probabilities, and seeded samples.

第 2 天实验｜线路 IR、受控旋转与测量位序

Day 2 lab | Circuit IR, controlled rotations, and bit order

线路中间表示（IR）把“要执行哪些门、按什么顺序执行”保存成数据，再从 |00⟩ 重放。测量映射则明确指定经典位 cᵢ 记录哪个量子位；下面可构建门序列、检查 IR，并对照两种位序下的测量结果。

A circuit intermediate representation (IR) stores which gates to execute and in what order, then replays them from |00⟩. A measurement map explicitly defines which qubit is recorded in each classical bit cᵢ. Build a gate sequence, inspect its IR, and compare outcomes under two bit orders.

位序要点：映射数组第 i 项表示 cᵢ ← q[mapping[i]]。因此 [0,1] 时 c0 取 q0、c1 取 q1；结果字符串按 c1c0 显示。Bell 态对换位序后仍是 00/11；用 X(q0) 制备 |01⟩ 才能直观看到映射改成 [1,0] 后显示为 |10⟩。

Bit-order rule: Entry i of the map means cᵢ ← q[mapping[i]]. With [0,1], c0 reads q0 and c1 reads q1; outcome strings display c1c0. A Bell state remains 00/11 when the map is reversed. Prepare |01⟩ with X(q0) to see it displayed as |10⟩ under [1,0].

练习与自动性质检查

Exercises and automated properties

1. 依次添加 H(q0)、CNOT(q0,q1)，检查 IR 顺序与 Bell 态概率；清空后添加 X(q0)，切换测量映射，观察 |01⟩ 与 |10⟩ 的标签变化。
2. 先加 X(q0)，将 CRy 角度设为 π，再添加 CRy(q0,q1)；控制位为 1 时，目标位应从 0 旋转到 1，得到 |11⟩。
3. 运行自动化性质测试：对固定种子生成的 80 组随机小线路，逐条检查范数为 1、映射概率和为 1、shots 总数守恒且采样可复现。

1. Add H(q0), then CNOT(q0,q1). Inspect the IR order and Bell probabilities. Clear the circuit, add X(q0), switch the measurement map, and observe the |01⟩ to |10⟩ label change.
2. Add X(q0), set CRy's angle to π, then add CRy(q0,q1). With the control set, the target rotates from 0 to 1, producing |11⟩.
3. Run the property tests: 80 seeded random small circuits are checked for unit norm, mapped probabilities summing to one, conserved shot totals, and reproducible sampling.

第 3 天实验｜Deutsch–Jozsa 与 Grover 搜索

Day 3 lab | Deutsch–Jozsa and Grover search

两个算法都用黑盒 oracle 学习查询复杂度，但问题不同：Deutsch–Jozsa 在“常量或平衡”的 promise 下分类函数；Grover 为未排序搜索放大目标态振幅。下方运行的是可检查门序列的 2 输入位 / 4 项小型理想 statevector 实验，不是硬件运行，也不代表量子计算对所有任务都有指数加速。

Both algorithms illustrate oracle query complexity, but solve different problems: Deutsch–Jozsa classifies a function under a constant-or-balanced promise; Grover amplifies the marked state in an unstructured search. These are small ideal statevector experiments (two input bits / four items), not hardware runs or evidence that quantum computing gives exponential speedups for every task.

A. Deutsch–Jozsa：先检查 promise，再看干涉

A. Deutsch–Jozsa: verify the promise, then inspect interference

函数 oracle 实现 |x,y⟩ → |x, y XOR f(x)⟩。辅助位先制备为 |−⟩，让函数值变成相位；末尾对输入位做 H。若 f 为常量，测得输入 00；若 f 平衡，00 的概率为零。这个“1 次量子 oracle 查询 vs 最坏 3 次经典确定性查询”只针对两输入位且保证属于 promise 集的查询模型。

The function oracle implements |x,y⟩ → |x, y XOR f(x)⟩. Preparing the ancilla in |−⟩ turns function values into phases; Hadamards on the input bits reveal the result. A constant function yields input 00, while a balanced function gives it zero probability. “One quantum oracle query vs at most three deterministic classical queries” applies only to this two-input-bit promise problem.

B. Grover：目标振幅放大与迭代过冲

B. Grover: amplify the target and observe overshooting

四个候选态中标记一个，初态均匀叠加。每轮由 phase oracle 和 diffuser 组成；目标概率理论上为 sin²((2k+1)θ)，其中 sin²θ=1/4。此 N=4 示例 k=1 恰好达到 100%；k=0 仅 25%，继续到 k=2 又降至 25%，展示离散迭代的过冲。一般搜索需按目标数量选择轮数，不能把本例的一轮当作通用规则。

Mark one of four candidates in a uniform superposition. Each round applies a phase oracle and diffuser; the theoretical success probability is sin²((2k+1)θ), where sin²θ=1/4. Here k=1 happens to reach 100%; k=0 gives 25%, and another round (k=2) drops back to 25%, illustrating discrete-iteration overshoot. General searches must choose iterations based on the number of marked items—one round is not a universal rule.

实验边界：oracle 已编译成当前模拟器支持的 H/X/CNOT 门，显示的线路门数不包含噪声、硬件路由或编译开销；此处“查询次数”按 oracle 使用次数计，不等同于基础门数。全部计算在浏览器本地完成，采样是固定种子伪随机模拟。

Scope: Oracles are decomposed into H/X/CNOT gates supported by this simulator. Displayed gate counts exclude noise, hardware routing, and compilation overhead. “Query count” counts oracle uses, not elementary gates. All computation runs locally in the browser, and sampling uses a seeded pseudorandom generator.

练习与验收

Exercises and checks

1. 逐个切换 5 个 DJ oracle，检查每个真值表是不是常量或平衡；常量应只测得 00，平衡应完全排除 00。
2. 把 Grover 迭代设为 0、1、2，观察目标概率 25% → 100% → 25%，再更换目标态确认位序约定无关。
3. 改变 shots 与 seed：理论概率不变，样本计数总和应等于 shots；相同参数应可复现。
4. 解释为何 DJ 的查询分离依赖 promise，以及为何 Grover 继续迭代会过冲；对一般 N 用 sin²θ=M/N 推导合适的轮数。

1. Try all five DJ oracles and inspect their truth tables. Constant functions should yield only 00; balanced functions must exclude 00.
2. Set Grover iterations to 0, 1, and 2. Observe target probabilities of 25% → 100% → 25%, then change the marked state to check bit ordering.
3. Change shots and seed: ideal probabilities stay fixed, counts sum to shots, and identical parameters reproduce the same samples.
4. Explain why the Deutsch–Jozsa query separation depends on its promise and why Grover can overshoot; derive a suitable iteration count for general N from sin²θ=M/N.

第 4 天实验｜QFT、相位估计与 N=15 周期寻找

Day 4 lab | QFT, phase estimation, and N=15 period finding

QFT 把基态索引编码为相位斜坡；逆 QFT 把相位转回可测频率。本实验使用 q0 为最低有效位、最多 5 个量子位，直接构造受控相位门序列，并以正逆变换回到输入态作为校验。所有结果都是浏览器本地的理想 statevector 模拟。

The QFT encodes a basis index as a phase ramp; the inverse QFT turns phase back into measurable frequency. This lab constructs controlled-phase gate sequences using q0 as the least-significant bit, up to five qubits, and checks the transform by applying QFT followed by its inverse. Results are ideal statevector simulations in your browser.

A. QFT / 逆 QFT：检查振幅与往返误差

A. QFT / inverse QFT: inspect amplitudes and round-trip error

B. 相位估计：精确网格与 off-grid 相位

B. Phase estimation: grid-aligned and off-grid phases

用 4 个估计位构造相位回踢，再施加逆 QFT。可输入相位 φ∈[0,1)：当 φ=k/16 时理论结果集中在 k；偏离 1/16 网格时概率会展宽。这里的本征相位是直接编码到估计寄存器的可控模型，不包含通用目标寄存器或真实模乘 oracle。

With four estimation qubits, encode phase kickback and apply the inverse QFT. Enter φ∈[0,1): when φ=k/16, the ideal result is concentrated at k; phases between grid points spread probability across outcomes. This directly encodes a known eigenphase in a controlled model—it does not implement a general target register or a modular-multiplication oracle.

C. Shor 骨架：N=15 的周期与经典因子后处理

C. Shor outline: N=15 period and classical factor post-processing

选择与 15 互素的底数 a，查看相位测量 y/16 的连分数分母候选；经典端验证 aʳ mod 15=1，再在 r 为偶数且 a^(r/2)≠−1 mod 15 时计算 gcd(a^(r/2)±1,15)。y=0、分母不可靠或因子条件失败都要重试。为控制范围，本演示用经典枚举得到参考周期，并将该周期的本征相位等权混合后送入 4 位 QPE；这不是完整可逆模指数电路，也不是 Shor 量子加速或 QPU 运行。非互素底数会由经典 gcd 预检直接给出因子。

Choose a base a coprime to 15 and inspect continued-fraction denominator candidates for measured y/16. Classical post-processing verifies aʳ mod 15=1, then computes gcd(a^(r/2)±1,15) only when r is even and a^(r/2) is not −1 mod 15. y=0, unreliable denominators, and failed factor conditions require retries. To keep this lab bounded, a classical enumeration supplies the reference period; an equal mixture of its eigenphases is passed through four-bit QPE. This is not a reversible modular-exponentiation circuit, a demonstration of Shor speedup, or a QPU run. A non-coprime base returns a factor through a classical gcd pre-check.

验收练习：验证 3 位 QFT 后接逆 QFT 回到 |x⟩；用 φ=5/16 检查只出现 y=5，用 φ=0.30 观察主峰向 y=5 附近展宽；运行 a=2 与 a=4 比较恢复 r=4、r=2 及因子 3、5；再用 a=3 解释 gcd 预检为何已足够。QPE 的 shot 采样与 Shor 模型均固定种子、完全本地执行。

Exercises: Verify that a three-qubit QFT followed by its inverse returns |x⟩. For φ=5/16, only y=5 should appear; for φ=0.30, inspect the broadened peak near y=5. Compare a=2 and a=4 to recover r=4 and r=2 and factors 3 and 5, then explain why the gcd pre-check suffices for a=3. QPE sampling and the Shor model are seeded, local simulations.

第 5 天实验｜噪声通道、三比特重复码與后选择

Day 5 lab | Noise channels, three-qubit repetition code, and post-selection

对三物理比特编码态逐次采样独立 X 翻转、Z 退相位、振幅弛豫与经典读出错误。可以切换 bit-flip 码（|000⟩/|111⟩）和 phase-flip 码（|+++⟩/|---⟩），看综合征如何定位单个可纠错误；比较未经处理的逻辑读出、综合征纠正和只保留零综合征的后选择。这里是独立噪声的 Monte Carlo 轨迹模型，不含门故障、泄漏、相关噪声或完整容错架构。

Sample independent X flips, Z dephasing, amplitude damping, and classical readout faults on a three-physical-qubit encoded state. Switch between the bit-flip code (|000⟩/|111⟩) and phase-flip code (|+++⟩/|---⟩), inspect how syndromes locate a single correctable error, and compare raw logical readout, syndrome correction, and post-selection that keeps only zero-syndrome shots. This Monte Carlo trajectory model omits gate faults, leakage, correlated noise, and full fault-tolerant architecture.

判读要点：综合征 s₀=q₀⊕q₁、s₁=q₁⊕q₂；01、11、10 分别指向 q₀、q₁、q₂ 单错。纠错是按综合征主动翻转相应物理位；后选择只丢弃非零综合征样本，会降低有效样本数但不能发现 000→111 这种零综合征逻辑错；读出错误也会污染综合征。重复码只能纠正所选基底中的单一 Pauli 翻转，另一类 Pauli 错误可能成为逻辑错误。

How to read it: s₀=q₀⊕q₁ and s₁=q₁⊕q₂; 01, 11, and 10 point to single-qubit errors on q₀, q₁, and q₂. Correction actively flips the indicated physical bit. Post-selection merely discards nonzero syndromes, reducing usable shots while missing zero-syndrome logical errors such as 000→111; readout faults also corrupt syndromes. A repetition code corrects one Pauli-flip type in its chosen basis; the complementary type can become a logical error.

第 6 天实验｜VQE、Pauli 测量与经典优化

Day 6 lab | VQE, Pauli measurements, and classical optimization

变分量子本征求解器（VQE）在参数化线路中制备 |ψ(θ,φ)⟩，分别估计 Hamiltonian 各 Pauli 项的期望值，再由经典优化器调整参数。这里使用两比特各向同性 Heisenberg 模型 H = ½(XX + YY + ZZ)：已知精确基态是单重态，能量 −1.5；本实验的小型 ansatz 可以到达该状态，方便检查测量和优化是否正确。

The variational quantum eigensolver (VQE) prepares |ψ(θ,φ)⟩ with a parameterized circuit, estimates each Pauli term in the Hamiltonian, and lets a classical optimizer update the parameters. This two-qubit isotropic Heisenberg model is H = ½(XX + YY + ZZ). Its known singlet ground state has energy −1.5; the compact ansatz here can reach it, making measurements and optimization easy to verify.

线路顺序为 X(q0) → Ry(q1, θ) → CNOT(q1→q0) → Rz(q1, φ)。q0 是最低有效位。θ=π/2、φ=π 时制备单重态（忽略全局相位）。每个 Pauli 项使用独立测量基底，每项采样 shots 次，所以总采样数为 3×shots。

The gate order is X(q0) → Ry(q1, θ) → CNOT(q1→q0) → Rz(q1, φ), with q0 as the least-significant bit. θ=π/2 and φ=π prepare the singlet up to global phase. Each Pauli term is measured in its own basis with the requested number of shots, so the total is 3×shots.

模型与优化边界：精确基态能量 −1.5 来自这个两比特 Hamiltonian 的解析谱，不是量子硬件测得。有限 shots 分别采样 XX、YY、ZZ，因此能量估计有统计误差。演示中的参数移步梯度由本地精确 statevector 期望计算，采样能量只作并列对照、没有反馈到参数更新；真实 VQE 会受有限 shots、噪声、ansatz 表达能力、优化器与设备编译影响。

Model and optimizer limits: The exact ground energy −1.5 comes from the analytic spectrum of this two-qubit Hamiltonian, not a quantum-hardware measurement. Finite shots independently sample XX, YY, and ZZ, so the energy estimate has statistical error. This demo computes parameter-shift gradients from exact local statevector expectations; shot estimates are shown for comparison but do not feed parameter updates. Real VQE is affected by finite shots, noise, ansatz expressibility, optimizer behavior, and device transpilation.

第 7 天实验｜QAOA 与三角形 Max-Cut

Day 7 lab | QAOA and triangle Max-Cut

最大割（Max-Cut）把图的顶点分到两组，目标是让尽可能多的边跨越两组。此处固定三节点三角形，三条边为 (0,1)、(1,2)、(0,2)。用 bᵢ∈{0,1} 表示分组，经典代价为 C(b)=Σ(bᵢ XOR bⱼ)，对应的量子代价 Hamiltonian 为 H_C=Σ(1−ZᵢZⱼ)/2；三角形无法二分，经典穷举最大割为 2 条边。

Max-Cut divides a graph's vertices into two sets and tries to maximize crossing edges. This fixed three-node triangle has edges (0,1), (1,2), and (0,2). With bᵢ∈{0,1} denoting the set, the classical cost is C(b)=Σ(bᵢ XOR bⱼ), with quantum cost Hamiltonian H_C=Σ(1−ZᵢZⱼ)/2. A triangle is not bipartite, so exhaustive classical search gives a maximum cut of two edges.

p=1 QAOA 先制备均匀叠加态，再交替施加代价演化 U_C(γ)=e^−iγH_C 与混合演化 U_B(β)=e^{−iβ(X₀+X₁+X₂)}，最后测量位串。模拟器把每条边的代价门分解为 CNOT—Rz(−γ)—CNOT（忽略全局相位），混合层对每位使用 Rx(2β)。显示位串按 q₂q₁q₀ 排列，q0 是最低有效位。

For p=1, QAOA starts in a uniform superposition, alternates cost evolution U_C(γ)=e^−iγH_C and mixer evolution U_B(β)=e^{−iβ(X₀+X₁+X₂)}, then measures a bitstring. Each edge cost is decomposed into CNOT—Rz(−γ)—CNOT (up to global phase); the mixer uses Rx(2β) on each qubit. Bitstrings display as q₂q₁q₀, with q0 the least-significant bit.

实验边界：图、线路只有 3 个量子位，statevector 与全部 8 个切分都可经典穷举。参数优化按钮是在 CPU 上做二维均匀网格搜索，目标函数取精确理想 statevector 期望，shots 仅采样最后选出的线路；这不是量子硬件运行、不是有限-shot 反馈优化，也不是量子加速证据。网格分辨率会影响得到的参数精度。

Scope: The graph and circuit use only three qubits, so the statevector and all eight cuts are classically enumerable. The optimizer performs a uniform two-dimensional grid search on the CPU using the exact ideal statevector objective; shots sample only the selected final circuit. This is not a hardware run, shot-feedback optimization, or evidence of quantum speedup. Grid resolution limits parameter precision.

第 8 天实验｜Qiskit 构建、transpile 与可选 QPU

Day 8 lab | Qiskit circuits, transpilation, and optional QPU

Qiskit 工作流通常分为：构造 QuantumCircuit → 选择 backend/目标指令集 → transpile（门分解、布局、路由、优化）→ 在本地模拟器或真实 backend 上 run → 记录 backend 名称、shots、作业 ID 与结果。编译不是单纯“缩短门数”：受限耦合图会触发 SWAP 路由，优化级别和初始布局也会改变结果。下方线路拓扑动画是教学模型；后面列出可由用户在自己的 Qiskit 环境运行的 API 轮廓。

A typical Qiskit workflow is: build a QuantumCircuit → choose a backend/target instruction set → transpile (decompose, layout, route, optimize) → run on a local simulator or real backend → record backend, shots, job ID, and results. Transpilation is not simply gate-count reduction: limited coupling can require SWAP routing, and optimization level or initial layout can change the output. The topology demo below is pedagogical; a user-side Qiskit API outline follows.

用户侧 Qiskit 本地示例

User-side local Qiskit example

在独立 Python 环境安装兼容版本的 Qiskit（例如 python -m pip install qiskit qiskit-aer），保存以下脚本后运行。模拟器由本地安装提供，不会创建云作业；执行前请根据安装版本核对 import 和 API 文档。

Install compatible Qiskit packages in a separate Python environment (for example, python -m pip install qiskit qiskit-aer), save the script below, and run it locally. The simulator comes from the local install and creates no cloud job; check imports and APIs against the installed version before use.

from qiskit import QuantumCircuit, transpile
from qiskit_aer import AerSimulator

qc = QuantumCircuit(3, 3)
qc.h(0)
qc.cx(0, 1)
qc.cx(1, 2)
qc.measure([0, 1, 2], [0, 1, 2])

backend = AerSimulator()
compiled = transpile(qc, backend=backend, optimization_level=1, seed_transpiler=7)
result = backend.run(compiled, shots=1024, seed_simulator=2026).result()
print("depth", compiled.depth(), "ops", compiled.count_ops())
print(result.get_counts())

可选：由用户自行提交真实 QPU 作业

Optional: submit a real QPU job yourself

1. 依量子服务商官方文档创建账户，把凭据存入本机环境变量或官方凭据存储；不要把 token 写进网页、仓库或聊天内容。
2. 查看当前 Qiskit provider 插件的文档，确认账户初始化、后端名称、可用位数、原生门、耦合图和作业 API；不同服务商接口并不相同。
3. 先将同一 QuantumCircuit transpile 到所选 backend，记录 seed_transpiler、optimization_level、初始布局、输出深度、门数和 SWAP 数。
4. 调用该 provider 的公开 run / Sampler API 提交有限 shots；安全保存 job ID，完成后取回 counts，同时记录后端校准与作业时间。
5. 把实测分布与理想模拟、有限 shots 统计区间和本地噪声模型对照，区分采样波动、门/读出误差与漂移。

1. Create a provider account using its official docs and store credentials in a local environment variable or approved credential store—never in a webpage, repository, or chat.
2. Check the installed provider plugin's docs for account setup, backend names, qubit count, native gates, coupling map, and job API; providers differ.
3. Transpile the same QuantumCircuit to the chosen backend and record seed_transpiler, optimization_level, initial layout, depth, operation counts, and SWAP count.
4. Submit a bounded-shot job through that provider's documented run or Sampler API. Store the job ID securely, retrieve counts on completion, and record backend calibration and timestamp.
5. Compare hardware counts with ideal simulation, finite-shot uncertainty, and local noise models; distinguish sampling fluctuation from gate/readout error and drift.

真实硬件边界：本网页不包含 provider SDK、凭据输入或网络作业提交，也不显示虚构的 backend、校准值、job ID 或 QPU counts。拓扑路由结果只是固定简化规则的概念演示，并非 Qiskit transpile 输出；请勿把教学 SWAP 数当成真实编译结果。

Hardware boundary: This page includes no provider SDK, credential entry, or network job submission, and shows no fabricated backend, calibration, job ID, or QPU counts. The topology route is a conceptual demo using fixed simplified rules, not Qiskit's transpiler output; do not treat its SWAP count as a real compilation result.

核心实现：只更新目标位对应的振幅对

Core implementation: update amplitude pairs for one target bit

把基态编号 x 写成二进制，目标量子位 q 对应掩码 2^q。当该位为 0 时，和翻转该位后的基态组成一对；对这两个振幅应用 2×2 门矩阵即可，不需要建立庞大的 2ⁿ×2ⁿ 全局矩阵。

Write basis index x in binary; target qubit q corresponds to mask 2^q. Pair each basis state whose target bit is 0 with the state obtained by flipping that bit, then apply the 2×2 gate matrix. There is no need to construct a dense 2ⁿ×2ⁿ global matrix.

mask = 1 << target
for basis in 0 .. 2^n - 1:
    if basis & mask == 0:
        partner = basis | mask
        a0, a1 = state[basis], state[partner]
        state[basis]   = m00*a0 + m01*a1
        state[partner] = m10*a0 + m11*a1

规模边界：状态向量内存随 2ⁿ 指数增长。单个单比特门直接作用于 statevector 需要约 O(2ⁿ) 次更新；这适合学习和小规模验证，不意味着可在普通设备模拟任意大电路。

Scaling: statevector memory grows exponentially as 2ⁿ. Applying one single-qubit gate takes about O(2ⁿ) updates. This is useful for learning and small verification—not a way to simulate arbitrarily large circuits on a laptop.

动手任务与验收标准

Exercises and completion criteria

1. 依次运行 H(q0)，观察 |00⟩ 与 |01⟩ 各占一半；再加 CNOT(q0,q1)，确认 Bell 态只有 |00⟩、|11⟩ 两条结果。
2. 尝试 X、Z、Ry(π/2) 与反向 CNOT，观察“概率不变但相位改变”与“位序改变”的差异。
3. 运行两次相同线路和种子，比较采样计数；更换种子后计数可变，但 Bell 态的 |01⟩、|10⟩ 仍不应出现。
4. 打开对应源码与测试：解释索引约定、单门复杂度，并增加一个“门与其逆门相消”或“概率和为 1”的自动测试。

1. Apply H(q0): |00⟩ and |01⟩ should each have probability one half. Add CNOT(q0,q1): the Bell state should contain only |00⟩ and |11⟩ outcomes.
2. Try X, Z, Ry(π/2), and reversed CNOT. Compare phase changes that preserve probabilities with changes to bit ordering.
3. Run the same circuit and seed twice, then change the seed. Counts may change, but |01⟩ and |10⟩ must remain impossible for this Bell state.
4. Read the implementation and tests. Explain the indexing convention and single-gate complexity; add an inverse-gate or probability-sum test.

本页配套代码：量子线路模拟器、算法、QFT、噪声、VQE、QAOA 与周期后处理、Day 5 噪声实验、Day 6 VQE 实验、Day 7 QAOA 实验、Day 8 拓扑路由教学模型。在项目仓库中运行 node --test tests/quantum-simulator.test.cjs 执行模拟器与算法回归测试。算法实验限于小规模本地模型；真实 QPU 作业需用户自行安装 Qiskit、管理 provider 凭据并依其文档操作，本页不会代为提交。

Companion code: statevector simulator, algorithms, QFT, noise, VQE, QAOA, and period post-processing, Day 5 noise lab, Day 6 VQE lab, Day 7 QAOA lab, and Day 8 topology-routing teaching model. Run node --test tests/quantum-simulator.test.cjs for simulator and algorithm regressions. These are small local models. Real QPU jobs require a user-managed Qiskit install and provider credentials; this page does not submit them.