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Question 1

1vote

1answer

71views

Confirm $f \otimes g$ is a linear map

In the textbook, "Dancing with Qubits," it states:"Let $V, W, X,$ and $Y$ be finite dimensional vector spaces over $\mathbb{F}$. If $f: V \rightarrow X$ and $g: W \rightarrow Y$ are ...

user2521987

391

askedNov 10 at 15:28

Question 2

3votes

1answer

116views

A question about CSS codes

Consider an $[[n, k, d]]$ quantum CSS code with $C^{\perp} \subset C$. If I consider the state,\begin{equation}\frac{1}{\sqrt{|C^{\perp}|}} \sum_{x \in C^{\perp}} |x\rangle;\end{equation}is this a ...

BlackHat18

1,629

askedOct 24 at 4:58

Question 3

2votes

0answers

52views

What are the know uses of Quantum Linear Systems?

Quantum Linear Systems is an algorithm for find the expectation value of x^tMx of a Matrix M.The question is, what are use cases for finding x^tMx of a Matrix M?I am looking in particular for ...

Charles Mahon

63

askedOct 2 at 12:12

Question 4

3votes

1answer

69views

How can $|e_0\rangle$ be “moved” across the tensor product and $\rho$ in the derivation of Kraus operators?

In the standard derivation of the operator-sum (Kraus) representation, one starts with the reduced state of a system after interaction with an environment:\begin{equation}\rho' = \operatorname{Tr}_E\...

seeker

241

askedSep 24 at 8:19

Question 5

1vote

3answers

147views

QSVT Phase Angles for Chebyshev Polynomials

I have a block-encoded matrix $A$ (for example, a diagonal matrix) encoded in a unitary $U_A$. I would like to apply a Chebyshev polynomial to the singular values of $A$ using Quantum Singular Value ...

user82261

315

askedSep 18 at 13:25

Question 6

4votes

0answers

94views

The converse problem for the maximal Schmidt coefficient in antisymmetric subspaces

Let $\mathcal{V}$ be the $\frac{m(m-1)}{2}$-dimensional antisymmetric subspace of $\mathbb{C}^m \otimes \mathbb{C}^m$. It is known that the maximal Schmidt coefficient of any unit vector in $\cal V$ ...

ZhiweiSong

41

askedSep 17 at 7:29

Question 7

3votes

2answers

261views

LSD decomposition of Pauli error

Consider a $[[n, k, d]]$ stabilizer code $C$ and an $n$ qubit Pauli error.Let $\mathcal{E}$ have syndrome $s$ with respect to the code $C$. Then, $\mathcal{E}$ (and, in fact, any $n$ qubit Pauli ...

BlackHat18

1,629

askedSep 8 at 4:34

Question 8

1vote

1answer

74views

Projector onto stabilizer subspace using destabilizers

Consider an $[n, k, d]$ stabilizer code $C$.Say I want to compute the probability of getting syndrome $s$ when measuring the $n$ qubit noisy code-state $\tilde{\rho}$ (I am fine with a destructive ...

BlackHat18

1,629

askedSep 8 at 3:04

Question 9

6votes

1answer

214views

When is a generalized semi-Clifford gate also a semi-Clifford gate?

A semi-Clifford gate is defined as an $n$-qubit unitary: $U_{sC} = C_L D C_R$ where $C_L, C_R$ are $n$-qubit Clifford gates and $D$ is a diagonal matrix. In other words, it is a unitary gate that can ...

Jonas Anderson

803

askedAug 22 at 17:03

Question 10

2votes

1answer

130views

Hardness result for Guided Local Hamiltonian problem for varies parameter regime

Definition (Guided 2-Local Hamiltonian). $\mathsf{2GLH(\delta, \gamma)}$Input: A 2-local Hamiltonian H with ||H|| $\leq 1$ acting on n qubits, and a semi-classical quantum state $u \in \mathbb{C}^{2^...

Manish Kumar

953

askedJul 30 at 7:35

Question 11

8votes

5answers

617views

When is $UAU^\dagger B\ge0$ for all $U$?

Let $A$ and $B$ be such that for all unitaries $U$, $UAU^\dagger B$ is positive semidefinite.Does this imply that either $A$ or $B$ must be proportional to the identity?(Motivated by the question ...

Norbert Schuch

9,087

askedJul 21 at 14:17

Question 12

4votes

1answer

296views

Complexity of finding a fixed-point of a unitary / eigenstate with eigenvalue 1?

Recently, while working on a problem I've been trying to solve I came across a formulation that requires me to find $|\phi\rangle$, such that$$U|\phi\rangle = |\phi\rangle$$Of course this ...

Ramezzez

366

askedJul 7 at 19:10

Question 13

2votes

0answers

107views

Simplifiying trace of Paulis

Let $\mathcal{P}$ denote all Pauli operators (Heisenberg-Weyl operators in general). I want to see that$\frac{1}{d^4} \sum_{A_i, B_i \in \mathcal{P}} tr(A_1 U^\dagger B_1 U A_2 U^\dagger B_2 U \...

user1577744

63

askedJun 17 at 11:57

Question 14

-1votes

1answer

115views

What is ${\rm tr}((A \otimes B) \text{SWAP} (C \otimes D )\text{SWAP})$ equal to?

The SWAP operator in the computational basis is given by $\sum_{ij} |i \rangle \langle j | \otimes|j \rangle \langle i| $.It satisfies for any operators $A,B, \; tr((A \otimes B) \text{SWAP}) = tr(...

user1577744

63

askedJun 17 at 9:15

Question 15

0votes

0answers

63views

Equivalence of projective measurement with general measurement

Nielsen and Chuang in page 91 say a very important thing: "projective measurements augmented by unitary operations turn out to be completely equivalent to general measurements, as shown in ...

moshtaba

121

askedJun 15 at 3:26

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Stack Exchange Network

Questions tagged [linear-algebra]

Confirm $f \otimes g$ is a linear map

A question about CSS codes

What are the know uses of Quantum Linear Systems?

How can $|e_0\rangle$ be “moved” across the tensor product and $\rho$ in the derivation of Kraus operators?

QSVT Phase Angles for Chebyshev Polynomials

The converse problem for the maximal Schmidt coefficient in antisymmetric subspaces

LSD decomposition of Pauli error

Projector onto stabilizer subspace using destabilizers

When is a generalized semi-Clifford gate also a semi-Clifford gate?

Hardness result for Guided Local Hamiltonian problem for varies parameter regime

When is $UAU^\dagger B\ge0$ for all $U$?

Complexity of finding a fixed-point of a unitary / eigenstate with eigenvalue 1?

Simplifiying trace of Paulis

What is ${\rm tr}((A \otimes B) \text{SWAP} (C \otimes D )\text{SWAP})$ equal to?

Equivalence of projective measurement with general measurement

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