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# Glossary

- **Heisenber principle**:

$$\braket{\psi | M_1 M_2 |\psi } \neq \braket{\psi | M_1 |\psi } \braket{\psi | M_2 |\psi } $$

- **Strong Turing-Church Hypotesis**: all model of computation are plynomially equivalent.

- **Exponential Time Hypothesis**: is believed that classical algorithm for NP problems can run in time $2^{\delta N}$ for a constant $0 < $\delta \leq 1$.

- **Strong Exponential Time Hypothesis**: some believes that $\delta=1$.

- https://en.wikipedia.org/wiki/Tsirelson%27s_bound

<!-- - **PCP Theorem **: A language is in NP iif it has witness that can be verified probabilistically using only $O(\log n)$ bits of randomness and a constant number of queries to bits of the witness. -->

- **Collinearity**:

- **Clifford group**:

- **First order quantization**

- **Second order quantization**

- **Unbiased estimator**: An estimator $\widehat{\theta} = \mathcal{E}[f(X)]$ for a parameter $\theta$ is said to be unbiased if $\widehat{\theta}- \theta= 0$

- **Consistent estimator**:

- **Efficient estimator**:

<!-- - **[QMA - Quantum Merlin-Arthur]()**. Is a complexity class for decision problem. A language is in QMA if in polynomial time a verifier $V$ : -->

<!-- - $\forall x \in L$ there exists a quantum state over a polynomial number of qubits $\ket{\psi}$ -->

<!-- - $\forall x \notin L$ there exist a quantum state (the $\ket{\psi}$ plays the same role as the whitness in NP problems) -->

<!-- Max-d-CUT problem is QMA complete. -->

<!-- Merlin is the prover: all-powerful and untrusted who gives the poor Arthur a solution (witness) to Merlin: a honest verifier with limited computational power. It plays the same role of NP for classical computers because if Merlin has to send a witness to Arthur of a NP complete problem, we know such witness will always exists, and that Arthur should be able to check in polynomial time that the witness is correct. {% cite jordanis2018merlin %} -->

<!-- - **Online algorithm**: -->

<!-- - **Streaming algorithm**: -->

<!-- It seems to me that there is a slight difference between online and streaming algorithm, where the straming algorithm can defer action over time, and the stress is on the limited amount of memory they have, online algorithms are required to take an action as soon as the input is entered.-->

- **Irreducible repreesntation**: [here](https://math.stackexchange.com/questions/38958/what-is-the-meaning-of-an-irreducible-representation)**:

<!-- - [Jordan-weigner representation](): -->

<!-- - [Boson sampling](https://www.nature.com/articles/nature23458): -->

<!-- - [Linear Optics](wikipedia): -->