# Questions tagged [unitarity]

For questions related to the unitarity (unitary evolution) of quantum systems, as applicable to quantum computing or quantum information.

224 questions
Filter by
Sorted by
Tagged with
1 vote
49 views

### Tests for unitarity of a quantum channel that don't require the Choi state

I am aware that the rank of the Choi state is a test for whether or not a channel is unitary. Are there any other equivalent tests that we can do to test if a channel is unitary without involving a ...
• 35
109 views

### Can a unitary $U$ transform $H = aX + bY + cZ$ to $U^\dagger H U = -aX + bY + cZ$?

I am wondering whether there exists a unitary operation $U$ that can transform a given Hamiltonian of the form $H = aX + bY + cZ$, where $X$, $Y$, and $Z$ are the Pauli matrices, into another ...
• 41
687 views

### 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 ...
88 views

### 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, U(\sigma^x + \...
• 63
95 views

45 views

### 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 &...
54 views

1 vote
73 views

### 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 ...
203 views

### 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 ...
• 21
121 views

### 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 ...
• 641
1 vote
88 views

• 680
305 views

### Sufficient conditions for a single-qubit unitary to be the identity

Say I have a unitary $U = e^{-iHt}$ where $H = \alpha X + Z$. First, suppose $U = I$. Then it rotates a set of initial states to themselves. Say I'm working on a computational basis, then on the Bloch ...
• 169
53 views

### Error in repeated applications of a quantum channel?

Suppose I have two quantum channels. Assume they they consist of $r\in \mathbb{Z}$ applications of unitaries, $U$ and $V$ respectively. Let the error between the channels acting on some state $\rho$ ...
117 views

### Conditions for entangling $A$ with $C$ via an interaction on $AB$

I have three qubits in subsystems $A$, $B$, $C$. System $A$ initially contains some state $\rho_A$, and $BC$ contains a bipartite pure state $|\psi\rangle_{BC}$. I apply a unitary operation $U$ acting ...
• 7,278
1 vote
83 views

196 views

### What's the reasoning behind writing the isometric representation of a channel?

I am reading about phase damping channel from Preskill's notes. He writes off the unitary representation of the channel as Unitary representation. An isometric representation of the channel is \begin{...
50 views

### On unitary matrix form suggested in the Elementary gates paper

In the "Elementary gates for quantum computation" paper Barenco et al. start their proofs by defining a generic form of $2\times 2$ unitary matrices as follows: Can you help me with the ...
• 133
452 views

### How to implement a PauliSparseOp object in qiskit if its non unitary?

I have a PauliSparseOp object whose matrix is non-unitary, is there a way I can implement this on qiskit? It is written in terms of sum of tensor products of I,X,Y and Z operators.
337 views

### Finding the rotation angle $\theta$ of a 2x2 unitary matrix

We can represent a 2x2 unitary matrix as follows: $$U = \cos(\theta)I - i \sin(\theta) \vec{n} \cdot \vec{\sigma},$$ where $\vec{n} \in \mathbb{R}^3$ and $\vec{\sigma} = (\sigma_x, \sigma_y, \sigma_z)$...
• 3,019
86 views

### Definition of quantum junta is not basis independent: isn't this a problem?

A quantum $k$-junta is defined as a unitary matrix $U$ acting on $n$ qubits which has the form $U = V \otimes \mathbb I$ where $V$ is a unitary acting some $k < n$ of the qubits. The fact that a ...
• 559
1 vote
189 views

### What is the general unitary matrix for two- and three-qubit states?

As pointed out in the QisKit tutorial here, for one qubit there exists a general unitary (see the expression for it in the previous link). I wonder if there exists equally unambiguous expressions for ...
• 271
80 views

### Understanding notation regarding phase oracle continued

Since I am not able to comment on my post, I had to register an account and start a new post. Maybe my old post can be deleted, which is found : here I am new to quantum computing. I cannot get my ...
• 41