Questions tagged [permutation]
5 questions
11
votes
1 answer
The quantum complexity of implementing a permutation matrix
Suppose we are given a permutation matrix (which is unitary since it corresponds to a permutation of the basis), acting on a $2^n$-dimensional Hilbert space, which can be seen as a quantum system of $n$ qubits. Is there a way to find an efficient…
Danylo Y
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4
votes
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Expressing a permutation invariant Hermitian as a sum over symmetric Hermitian matrices
Let $H$ be a Hermitian matrix of dimension $2^k$ - i.e. on a system with $k$ qubits. Let $H$ be invariant under permutations of qubits. I would like to express $H$ in the following form:
$$H=\sum_{\alpha} c_{\alpha} H_{\alpha}^{\otimes k},$$
where…
hahmez
- 41
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3
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2 answers
I am looking for a way to implement a matrix permutation without ancillary qubits or workspace qubits
Good morning, enthusiasts of the quantum world.
I am learning Peter Shor's algorithm by "period finding" or "order finding".
The order of a modulo N. When N is even and is not a prime power.
My a = 2, and N= 11.
So my permutation matrix Ma…
3
votes
1 answer
Are these equivalence relations for the Permutation group equivalent?
Definitions
$\mathcal{C}$ is the $n$-qubit Clifford group.
$\mathcal{P}_C$ is the group of $n$-qubit permutation matrices in the $n$-qubit Clifford group. This group is generated by all CNOTs and Pauli $X$ strings. Note that for all $n$,…
Jonas Anderson
- 701
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1
vote
2 answers
Can I efficiently decompose this flexible unitary matrix into 1 and 2 qubit gates?
Consider the unitary matrix $A \in \mathbb{R}^{n^2\times n^2}$ which has only the first $n$ rows explicitly defined, with the remaining rows having some flexibility. $A$ can be written in block form as
$
A=
\left( {\begin{array}{cccc}
B\\
…
thespaceman
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