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LEAN Programming Language 1 contributor · 0 readers

1

Lean Programming Language

1.1

The tactic rfl means reflexivity

Oracle in Quantum Computing — Detailed Explanation 1 contributor · 0 readers

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Oracle in Quantum Computing — Detailed Explanation

1.1

\[ U_f^2 = I \]

1.2

\[ O\left(\sqrt{\frac{N}{M}}\right) \]

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AI explanation: \[ O\left(\sqrt{\frac{N}{M}}\right) \]

1.4

AI explanation: \[ O(\sqrt{N}) \]

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Two Flavors of the Equation

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Untitled document

Scrodinger Equation 1 contributor · 0 readers

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The **Schrödinger equation** is the fundamental governing equation of non-relativistic quantum mechanics. It plays the same role in the quantum world that Newton’s second law ($...

1.1

wavefunction

1.1.1

$$P(\mathbf{r}, t) = |\Psi(\mathbf{r}, t)|^2 = \Psi^*(\mathbf{r}, t)\Psi(\mathbf{r}, t)$$

1.1.1.1

$\Psi^*(\mathbf{r}, t)\Psi(\mathbf{r}, t)$:

1.1.1.2

$$|\Psi|^2 = \Psi^* \Psi = (a - bi)(a + bi) = a^2 + abi - abi - b^2i^2$$

1.1.1.2.1

$$|\Psi|^2 = \Psi^* \Psi = (a - bi)(a + bi) = a^2 + abi - abi - b^2i^2$$

1.2

($\sqrt{-1}$)

Quantum clock synchronization (QCS) 1 contributor · 0 readers

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Quantum Clock Synchronization from First Principles

1.1

Replacing a Theoretical Probability by an Empirical Estimate

1.1.1

Replacing a Theoretical Probability by an Empirical Estimate

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Quantum Einstein Synchronization

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Quantum Eddington Slow-Clock Transport

3.1

What It Means for a Qubit to Tick

3.1.1

AI explanation: $e^{-i\omega t}$

3.1.1.1

\[ U(t)=e^{-iHt/\hbar}. \]

3.1.1.1.1

\[ e^{-iHt/\hbar} = I-\frac{iHt}{\hbar} +\frac{1}{2!}\left(-\frac{iHt}{\hbar}\right)^2 +\frac{1}{3!}\left(-\frac{iHt}{\hbar}\right)^3+\cdots. \]