Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

Questions tagged [mathematics]

DO NOT use this tag. Use more specific tags such as [linear-algebra] instead.

523 questions
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When would I consider using an outer product of quantum states, to describe aspects of a quantum algorithm?

I know the inner product has a relationship to the angle between two vectors and I know it can be used to quantify the distance between two vectors. Similarly, what's an use case for the outer product? You can exemplify with the simplest case. It…
R. Chopin
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What kind of mathematics is common in quantum computing?

From what I have seen so far, there is a lot of linear algebra. Curious what other kinds of maths are used in QC & the specific fields in which they are most predominately invoked.
user820789
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Why are orthogonal spins $(1,0)$ and $(0,1)$ represented as collinear vectors in the Bloch sphere?

I'm reading the book "Quantum Computing 4 real IT people" by Chris Bernhardt and I have a question about the following phrase in chapter 3 which says that An ordered orthonormal basis corresponds to measuring the spin in the vertical direction and…
Ksenia
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Why use inner and outer product?

Inner product: how similar the vectors are Outer product: ??? For inner product I can find this explanation. "The inner product of two vectors therefore yields just a number. As we'll see, we can interpret this as a measure of how similar the…
guest
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Is geometric algebra/calculus used in quantum computing?

This is really a question out of curiosity. I am aware that geometric algebra and geometric calculus provide simplifications in many aspects of physics. I'm wondering if this framework's usefulness extends to the realm of quantum computing.
roshoka
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How can surreal maths be used in quantum computing?

The question whether surreal or hyperreal numbers (that both contain the reals, even if they have the same cardinality) could be useful to provide a more satisfactory theory of QM is maybe more interesting. -yuggib Background I indirectly ended up…
user820789
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Conditional probability between parameter and operator in quantum mechanics?

Background So I came across a question on conditional probability in quantum mechanics: There's an interesting comment which tells why this does not work for "the non-commutative case". I was wondering, however, since there are more than operators…
More Anonymous
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Strange binomial formula for operators?

Does the binomial formula $(a+b)^n=\sum_i C_n^ia^ib^{n-i}$ still work when $n$ is replaced by operator $\hat{n}$(an operator), where $a$ and $b$ are numbers? Since it's not the normal binomial formula mentioned in a lot of cases, and also can't be…
narip
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Alternative derivation of $P(\text{First qubit}=0)$ for the swap test

I'm trying to derive $P(\text{First qubit}=0) = \frac{1}{2} + \frac{1}{2}|⟨a|b⟩|^2$ for the swap test. The wiki page shows one way, but the result should also be obtainable via direct expansion of the tensor products, as attempted here. Present…
Attila Kun
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How to read a Qubit rotation lookup table?

In A New Quantum Inspired Genetic Algorithma a lookup table is used to decide the Qubit rotation. But how the lookup table is used is not briefed. Does anyone know how it is done ? An example is shown below. $\delta\theta$ is chosen equal to…
Adhisha Gammanpila
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Is the computational basis for Hilbert space transfinite?

In What is the Computational Basis? gIS states: One also often speaks of "computational basis" for higher-dimensional states (qudits), in which case the same applies: a basis is called "computational" when it's the most "natural" in a given…
user820789
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Modular Addition general explanation

This is an incredibly basic question, but basically I'm really struggling to understand what the "addition modulo 2" is and why is it used in quantum computing. I've tried Wikipedia, endless QC lecture notes and forums, but everywhere they just give…
user_confused
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What is a projection operation and how does it work?

I am reading about the Quantum Pigeon Hole Principle and having trouble understanding how the states are measured. Specifically from this paper. From equation (4) through equation (7).
Maxsash
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Projection is trace-decreasing?

I'm studying Mark Wilde's "Quantum Information Theory" and the author sometimes use the inequality $\mathrm{Tr}(\prod_\mathcal{H'}Y) \leq \mathrm{Tr}(Y)$ where $Y\in \mathcal{H}'$ is a density matrix and $\prod_\mathcal{H'}=V^{\dagger}V$ with…
asdf
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Calculus and perturbing expectation values

Consider the following quantity: $$ f_O(|\psi\rangle) = \langle \psi | O | \psi \rangle $$ How would we study a perturbation on $|\psi\rangle$, given that it has to be a valid quantum state? What mathematical tools underlie this quantity? For…
C. Kang
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