Questions tagged [unitarity]
For questions related to the unitarity (unitary evolution) of quantum systems, as applicable to quantum computing or quantum information.
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Are operators unitary on a real quantum computer?
The question is more from the physical side of quantum computers. Can we say that operators are unitary or due to the NISQ nature, the operator (impact on particles) in reality deviates from this ...
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unitary that transform $\sigma^x \pm \alpha \sigma^z$ into $\sigma^x$ and $\sigma^z$
Consider $\sigma^x \pm \sigma^z$, where $\sigma^x$ and $\sigma^z$ are Pauli $X$ and $Z$ matrices. Let unitary $U$ be a $\pi/4$ rotation matrix around $Y$-axis. Then,
\begin{equation}
U(\sigma^x + \...
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Show that transformation $U_f: \left| x, y \right\rangle \to \left| x, y \oplus f(x) \right\rangle$ is unitary [duplicate]
I am reading Quantum Computation and Quantum Information by Chuang and Nielsen and they claim that it is easy to show that transformation $U_f: \left| x, y \right\rangle \to \left| x, y \oplus f(x) \...
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Getting a Hermitian operator from a Quantum circuit, and taking its expectation value
I have a circuit $C$, which acting on a state $|\psi \rangle$ is equivalent to a Unitary $U$ acting on the state: $$C(|\psi \rangle) = U|\psi \rangle$$ Now, this circuit is just a Hamiltonian ...
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Definition of a quantum gate
A quantum gate is usually defined as a unitary transformation, like the definition found in "Mathematics of Quantum Mechanics" by Scherer. According to this definition, can we consider a ...
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Why does it matter that Schmidt number is invariant under unitary transformations?
I am reading Nielsen & Chuang and they say this:
"The bases $|i_A\rangle$ and $|i_B\rangle$ are called the Schmidt bases for A and B, respectively, and the number of non-zero values $\...
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Reasoning behind unitary freedom in the ensemble for density matrices theorem
Although my question has the same title of a different question, it is not a duplicate. I am asking a different question. I don't care why it made it into the book.
Here is a theorem from Nielsen &...
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Alternative algorithm for quantum phase estimation problem
The Quantum Phase estimation problem is stated below:
Input: Given $U$ as a unitary operator acting on an m-qubit register. If $| \psi \rangle$ is an eigenvector of $U$, then U$| \psi\rangle$ = $e^{ ...
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A maximally distant unitary from a parameterized circuit
I have a parameterized circuit that includes a certain number of rotation gates, each parameterized by an angle. By sampling over these angles, I can obtain various unitaries. What are the unitaries ...
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Axis and Angle of rotation of $\frac{1}{\sqrt{2}}\begin{bmatrix}-i&-1\\1&i\end{bmatrix}$
I have made use of the following formulas,
\begin{align}
\theta&=2\cos^{-1}\bigg(\frac{e^{-i\alpha}Tr(X)}{2}\bigg)\\
n_i&=\frac{e^{-i\alpha}Tr(X\sigma_x)}{2\sin\theta/2}\\
e^{i\alpha}&=\...
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How to represent unitary evolution in Python?
How to represent $U(t)$ (a unitary operator) in a code? Is there any package available for that in Python?
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What is the relationship between gate fidelity and norm?
I've seen a lot of analyses on quantum circuit error bound based on the norm difference $\Vert U - V \Vert$.
On the other hand, I've also seen a lot of papers that use the gate fidelity $\frac{1}{2^n}\...
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Inner product as unitary operation
Inner products of two states $\psi$ and $\phi$ are usually performed at the end of a quantum algorithm where we measure the final state, e.g. using the swap test. However, this operation is not ...
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U(2) vs. SU(2) for single-qubit gates; ignoring global phases
So, while the only immediate restriction on an operator evolving a quantum state in time, is that it be unitary, in quantum computation/information, it is considered somewhat common knowledge that all ...
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Evolution of a state vector: Why is the action of $N$ equivalent to the action of $UNU^{†}$?
There is another question asked on this on stack exchange but I did not find any answers there that fully answered the question. In Gottesman's paper "The Heisenberg Representation of Quantum ...
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