# Questions tagged [gottesman-knill]

Questions directed to the Gottemsman-Knill theorem, which states that quantum circuits consisting of elements from the Clifford group are classically efficient to simulate.

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### How powerful are boundedly many $T$-gates?

For a natural number $k$ (0 is a natural number), let $T_k$ be the collection of all languages that can be efficiently decided by quantum circuits consisting of Clifford gates and at most $k$ $T$-...
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### In quantum circuits, why does $UNU^\dagger$ act on states in the same way $N$ acts before the operation?

I understand that the Schrodinger picture changes the quantum states, while the Heisenberg picture changes the operators. In this paper The Heisenberg Representation of Quantum Computers, in equations ...
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### Twirling Quantum Channels: Pauli and Clifford Twirling

I am currently working through some papers related with approximations of more general quantum channels such as amplitude and phase damping channels to Pauli channels. The reason to do so is so that ...
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### Gottesman Knill theorem: why $O(n^2)$ classical operation to keep track of a Clifford gate

Starting from a state stabilized by Pauli matrices, and using only Clifford operations Gottesman Knill theorem ensures us that such algorithm can be classically simulated. Indeed, if I call my initial ...
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### Is it possible to construct Grover search from Clifford gates only?

In the article Is Quantum Search Pratical the authors emphasized that a complexity of an oracle is often neglected when advantages of Grover search are discussed. In the end, a total complexity of the ...
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### Speed up in Bernstein-Vazirani algorithm and Gottesman-Knill theorem

The Bernstein-Vazirani problem: Let $f$ be a function from bit strings of length $n$ to a single bit, $$f: \{ 0, 1\}^n \to \{0, 1\}$$ thus all input bit strings $x \in \{0,1\}^n$. There exists a ...
There are two groups of quantum gates - Clifford gates and non-Clifford gates. Representatives of Clifford gates are Pauli matrices $I$, $X$, $Y$ and $Z$, Hadamard gate $H$, $S$ gate and $CNOT$ gate. ...