# 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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### Parallel run of qiskit circuits

I am trying to run simulation instances of a parametrized circuit in parallel but my algorithm is extremely slow. Excuse my ignorance, but I just want to be sure that the circuits are indeed running ...
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### Quantum Signal Operator and the unitary state preparation oracle?

I am looking into IL Chuang and GH Low's Hamiltonian Simulation with Qubitization paper. I am very confused on the terminology and motivation behind definition 1. I do not understand what the unitary ...
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### Circuit for pre-factors +-i, -1

Setting I have a (6 qubit) circuit which implements a unitary $U$. Goal I need the circuits which implement $-U, iU, -iU$. Phase matters, because I later embed a controlled version of $\pm i U$ into ...
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### How can extract reduced dynamics of a bipartite system from unitary evolution in quite

Let us assume that I have a bipartite system $A\otimes B$ and an initial product state undergoing some evolution $H^{AB} = H^A+H^B+V^{AB}$, which is time independent. I want to simulate the reduced ...
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### When can pairs of states be transformed into other pairs of states via unitary mapping?

The states $|+\rangle, |-\rangle$ can be mapped to $|0\rangle, |1\rangle$ by a simple rotation. But if I now have other states ($|\psi_0\rangle, |\psi_1\rangle$) which are not orthogonal, does a ...
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### Proof for Cardinality of the Clifford Group

In this article: (http://home.lu.lv/~sd20008/papers/essays/Clifford%20group%20[paper].pdf) a proof is given for the cardinality of the Clifford group. I understand all the parts of it except for how ...
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### Why are all the eigenvalues of a "Hermitian block-encoding" equal to $\pm1$?

I was looking at the paper : https://arxiv.org/abs/2002.11649 and the eigenvalue discussion is not clear to me. Block-encoding is a general technique to encode a nonunitary matrix on a quantum ...
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For pure states, it is known that one can always find a unitary that relates the two i.e. for any choice of states $\vert\psi\rangle$ and $\vert\phi\rangle$, there exists a unitary $U$ such that $U\... • 395 3 votes 0 answers 93 views ### Can a triplet be a qutrit? Original question A triplet is a space that consist of three states that have the same total angular momentum (spin 1). If we restrict ourselves to a set of quantum gates that keep triplet states in ... • 1,584 2 votes 1 answer 343 views ### How does the Kraus decomposition imply the Stinespring representation? To show that the Kraus decomposition$\Phi(\rho)=\sum_{k=1}^D M_k\rho_S M_k^\dagger$implies the Stinespring form $$\Phi(\rho)=\text{tr}_E[U_{SE}(\rho_S\otimes|0\rangle\langle 0|_E)U_{SE}^\dagger]$$ ... 7 votes 1 answer 677 views ### Are anti-unitary gates possible? According to Wigner’s theorem, every symmetry operation must be represented in quantum mechanics by an unitary or an anti-unitary operator. To see this, we can see that given any two states$|\psi\...
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I was going through Qiskit online text book and came across this part. The relevant (slightly modified) paragraph is - Suppose we have two states $|\psi_0\rangle$ and $|\psi_2\rangle$. Their inner ...