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量子计算
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量子计算
12
engines
Single-qubit gates · unitary evolution
Single-qubit gates · unitary evolution
X/Y/Z/H/S/T 2×2酉矩阵 · 布洛赫球旋转 · 振幅
Apply X, Y, Z, H, S or T to an editable state |ψ⟩ = α|0⟩ + β|1⟩
Born rule · measuring a superposition
Born rule · measuring a superposition
玻恩规则P=|α|² · 坍缩 · Z/X基测量
P(outcome) = |amplitude|² — deterministic probabilities, not a random draw
CNOT · entanglement & the Bell state
CNOT · entanglement & the Bell state
4×4矩阵 · 真值表 · |+0⟩→Bell纠缠
The controlled-NOT flips the target when the control is |1⟩ — and makes a Bell state
Grover's search · amplitude amplification
Grover's search · amplitude amplification
振幅放大 · oracle+扩散 · ~π/4·√N次
Oracle + diffusion rotate amplitude toward the marked item in ~(π/4)√N steps
Deutsch–Jozsa · constant vs balanced
Deutsch–Jozsa · constant vs balanced
单次查询判常/平衡 · 干涉坍缩全零⟺常函数
One quantum query decides whether f is constant or balanced
Phase kickback · controlled-U eigenphase
Phase kickback · controlled-U eigenphase
受控U把本征相位e^(iφ)踢到控制位 · QPE/Shor核心
A controlled-U kicks the eigenphase e^{iφ} onto a |+⟩ control qubit
Quantum Fourier Transform (QFT)
Quantum Fourier Transform (QFT)
ω^(jk)/√N矩阵 · 相位阶梯 · 受控相位门
The quantum DFT: unitary on N = 2ⁿ, entries ωʲᵏ/√N with ω = e^{2πi/N}
Shor's period finding
Shor's period finding
aˣ mod N周期r · gcd(a^(r/2)±1,N)分解
Find the period r of aˣ mod N, then factor N with gcd(a^{r/2} ± 1, N)
Quantum teleportation
Quantum teleportation
Bell对+Bell测量+2经典位 · Pauli校正还原|ψ⟩
Send an unknown qubit |ψ⟩ with a shared Bell pair + 2 classical bits
GHZ state & 3-qubit correlations
GHZ state & 3-qubit correlations
(|000⟩+|111⟩)/√2 · 三方关联 · 对比W态
H + two CNOTs make (|000⟩+|111⟩)/√2 — genuine tripartite entanglement
Superdense coding
Superdense coding
共享Bell对 · I/X/Z/ZX编2位 · 1量子位传输
Send 2 classical bits by transmitting only 1 qubit (shared Bell pair)
BB84 quantum key distribution
BB84 quantum key distribution
基筛选 · 窃听Eve引入~25%误码QBER · 密钥
Sift a shared secret key from matching bases; an eavesdropper leaves ~25% errors