Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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Is the diamond norm subadditive under composition?

The diamond norm distance between two operations is the maximum trace distance between their outputs for any input (including inputs entangled with qubits not being operated on). Is it the case that the Diamond norm is subadditive under…
Craig Gidney
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Can the Kraus decomposition always be chosen to be a statistical mixture of unitary evolutions?

If $\mathcal{E}$ is a CPTP map between hermitian operators on two Hilbert spaces, then we can find a set of operators $\{K_j\}_j$ such that $$\mathcal{E}(\rho)=\sum_j K_j\rho K_j^\dagger $$ in the same spirit as any density matrix $\rho$ can be…
user2723984
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How are arbitrary $2\times 2$ matrices decomposed in the Pauli basis?

I read in this article (arXiv) Appendix III p.8, that for $A\in \mathcal{M}_2$, since the normalized Pauli matrices $\{I,X,Y,Z\}/\sqrt{2}$ form an orthogonal matrix basis. $$A=\frac{Tr(AI)I+Tr(AX)X+Tr(AY)Y+Tr(AZ)Z}{2} $$ I don't understand, where…
lufydad
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What is intuition for the trace distance between quantum states?

Given two mixed states $\rho$ and $\sigma$, the trace distance between the states is defined by $\sum_{i=1}^n |\lambda_i|$, where $\lambda_i$'s are eigenvalues of $\rho - \sigma$. I know the definition of eigenvalues, but I don't have intuition on…
satya
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2 ways to do the three qubits bit-flip code

I'm trying to understand the three qubits bit-flip code. I use the book of Phillip Kaye An introduction to quantum computing. In this book he introduce the three qubits bit-flip code with this circuit : But, I saw in Quantum Error Correction for…
lufydad
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$n$ qubit vs. a $d=2^n$ qudit states and measurements

The pure states of a qudit inhabit the $\mathbb{CP}(d-1)$ manifold. Is it true that the pure states of $n$ qubits live on the $\mathbb{CP}(2^n-1)$ manifold? If the answer to the first question is yes, then how do the sets of measurements on $n$…
mavzolej
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How to program a controlled Hadamard-Hadamard gate?

I'm trying to program a controlled gate as the figure below in Qiskit. Should it be sufficient to separate and control individually the Hadamard gates?
German Alamilla
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Understanding a quantum algorithm to estimate inner products

While reading the paper "Compiling basic linear algebra subroutines for quantum computers", here (arXiv), in the Appendix, the author/s have included a section on quantum inner product estimation. Consider two vectors $x,y \in \mathbb{C}^n, x= (x_1,…
IntegrateThis
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Grover algorithm for a database search: where is the quantum advantage?

I have been trying to understand what could be the advantage of using Grover algorithm for searching in an arbitrary unordered database D(key, value) with N values instead of a classical search. I assumed that the oracle function is a function…
Foxhole
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How is the decoherence rate connected to the error rate?

I'm reading about the threshold theorem, which states that "a quantum computer with a physical error rate below a certain threshold can, through the application of quantum error correction schemes, suppress the logical error rate to arbitrarily low…
VannyUW
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Controlled Hadamard gate in ZX-calculus

What is the representation of the CH gate in ZX-calculus? Is there a general recipe for going from a ZX-calculus representation of a gate to the representation of the controlled version?
Daniel Mahler
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Simulating a system inside a system

The minimum size of a computer that could simulate the universe would be the universe itself. This is quite a pretty big theory in classical computing and physics because to contain the information of the whole universe, you require a minimum…
Yuzuriha Inori
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Is there a BQP algorithm for each level of the polynomial hierarchy PH?

This question is inspired by thinking about quantum computing power with respect to games, such as chess/checkers/other toy games. Games fit naturally into the polynomial hierarchy $\mathrm{PH}$; I'm curious about follow-up questions. Every Venn…
Mark Spinelli
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Homeomorphism or stereographic projection corresponding to the set of mixed states within the Bloch sphere

The Bloch sphere is homeomorphic to the Riemann sphere, and there exists a stereographic projection $\Bbb S^2\to \Bbb C_\infty$. But this only holds for pure states. To quote Wikipedia: Quantum mechanics is mathematically formulated in Hilbert…
Sanchayan Dutta
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Which quantum computing programming language should I learn?

Which quantum computing programming language should I learn? What are the benefits of said language? As of Wikipedia, there's quite a bit to choose from. I'm looking to develop end-user applications (when quantum computers become end-user ready).
AJ_4real
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