Questions tagged [mathematics]

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Can a math major get into quantum computing?

I was wondering if by doing a math major I could get into quantum computing and no, doing a degree in physics is not an option sadly. I also want to know if being a software engineer would be a better ...
147 views

Identity for linear codes and their duals: why do we have $\sum_y (-1)^{x\cdot y}=|C|\delta_{x\in C^\perp}$?

I've come across this exercise plenty of times and I still don't understand how to do it. (Here it is from N.C. Ex.10.25) Let $C$ be a linear code (Lets suppose its a binary code, i.e. a $k$-...
288 views

Equality condition for Hölder's inequality if $p=1$

The equality condition for Hölder's inequality, $|{\rm tr}(A^\dagger B)| \leq \| A\| _p\| B\| _q$ is $|A|^p = \lambda |B|^q$ for some scalar $\lambda > 0$; here $\|\cdot\|_p$ the usual Schatten ...
1 vote
125 views

general way to decompose a CZ gate on $n$-qubit system

Suppose I have a CZ(i,j) gate (or CNOT) acting on qubit $i$ and $j$, on a $n$-qubit system. Is there a general way to decompose this gate into a set of gates that only involve single-qubit gates and ...
258 views

384 views

How to exactly implement Trotter-Suzuki formula on quantum computer

Recently, I am studying some topics related to product formula, and I am curious about how to implement such formula on real quantum devices. The $(2k)$-th order product formula can be witten as \...
381 views

closeness between two unitaries on the bloch sphere

The fidelity between two (single-qubit) quantum states can be easily translated into the euclidean distance between the two states on the Bloch sphere (hilbert-schidmit distance). I'm curious if this ...
753 views

Correct Formulation of N&C Exercise 4.11 and other textbooks misquoting

Inspired by the comments in this question How to approximate $Rx$, $Ry$ and $Rz$ gates?, there is the errata for question 4.11 pg 176 in N&C. The original form states that for any non parallel $m$ ...
64 views

What are necessary and sufficient conditions for the output of a parametrized unitary $U(\theta)$ to be smooth?

Let us consider a unitary $U$ parameterised by $\theta \in \mathbb{R}$, i.e, $U(\theta)$. What are the necessary and sufficient conditions for the output states of this unitary to be smooth? One ...
1 vote
86 views

Representing networks with qubits as edges

I am looking to take a classical non-negative real valued network and generalize it to the quantum case for processing. A network is given by an adjacency matrix, essentially edge weights $e_{ij}$ for ...
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417 views

Exotic transversal gate group for stabilizer code

What are examples of interesting $[[n,1,d]]$ or $[[n,2,d]]$ stabilizer codes, $d \geq 2$, whose group of transversal gates is not isomorphic to a subgroup of the Clifford group (on 1 and 2 ...
What does Pauli's $Y$ matrix represent?
It is easy to see that Pauli's $X$ matrix represents the bit flip operation, i.e. $X \lvert 0 \rangle = \lvert 1 \rangle$ and $X \lvert 1 \rangle = \lvert 0 \rangle$. Similarly, Pauli's $Z$ matrix ...