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Are these gate sets proven to be not universal?

I was reading the paper An introduction to measurement based quantum computation (Josza, 2005) and on page 13 they say the following: Theorem: Any gate array using gates from the set $\{CX,R_x(\theta) \text{ all } θ\}$ or from the set…
Ethan Davies
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Can we avoid repetition in Shor's algorithm by using the quadratic formula?

Shor's algorithm is a quantum algorithm to find a non-trivial factor of a composite integer $N$. It is assumed that $N$ is odd and not a perfect power. The first step is to find the multiplicative order $r$ of $x$ modulo $N$, where $x$ is randomly…
Dave R
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Universal Gate Set, Magic States, and costliness of the T gate

The usual universal gate set is $\mathcal{C} + T$ where $\mathcal{C}$ is the Clifford group and $T = \begin{pmatrix} 1 & 0 \\ 0 & e^{i\pi/4} \end{pmatrix} $ is the $\pi/8$ rotation gate. In practice we find a code that has $\mathcal{C}$ transversal…
Eric Kubischta
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Does post selection of a qubit introduce non-linearity?

Problem I have a multi-qubit state $\lvert \psi \rangle$ and an ancilla qubit $\lvert 0 \rangle$ that I use to extend my state, getting the new state $\lvert 0\rangle \otimes \lvert \psi \rangle$. Suppose now I apply a generic unitary operation on…
Andrea
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Can you programatically check whether a given set of gates is universal?

I am wondering if there is an automated way to determine whether a given set of quantum operations is universal. More precisely, given a set of 1 and 2 qubit gates, can we write a program to determine whether this constitutes a universal gate set?…
Callum
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What kinds of objects are Liouvillian, Lindbladian, and Davies generator?

I have a rather basic question. I'm starting to read papers such as Chen–Brandao, Chen–Kastoryano–Brandao–Gilyen, and I'm having trouble parsing even what kind of objects a Liouvillian, Lindbladian, and Davies generator are. It seems that the Davies…
zjs
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Is APPROX-QCIRCUIT-PROB a BQP-complete problem?

I've read contradictory information: on the Wikipedia page for BQP, it is written without proof that "APPROX-QCIRCUIT-PROB is a BQP-complete problem", while I have read elsewhere (don't remember) that "it is usually assumed that are no BQP-complete…
Pierre Yves Schobbens
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Is it known that BQP is not contained within NP?

I recently stumbled upon this paper here and here on the "deep ai" website that claims "BQP is not in NP." I thought that this result would be huge (as a corollary would be that $BQP \neq P$), so I find it strange that I haven't heard about the…
wavosa
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When is the square root of a Clifford gate a Clifford gate?

Is there any condition for the square root or any rational power of a Clifford gate to be a Clifford gate (generated by $S$, Hadamard $H$, and CNOT)? It can be easily shown that $\sqrt{X}$ is Clifford (because $S=\sqrt{Z}$ is a generator, and powers…
Mauricio
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What is a POVM?

I am having a hard time understanding what exactly a Measurement is by its definition? What I read is that a POVM $M$ is defined by its set of elements $M_i$. So is $M$ itself an operator? In circuit diagrams its a little "Measure" box, but I've…
TTa
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Prove that a channel is close to acting on only one system

Background Suppose I have a quantum channel $\Phi:B(\mathcal{H}_1)\rightarrow B(\mathcal{H}_1)\otimes B(\mathcal{H}_2)$, such that there is some small $\epsilon$ such that for any two input states $\rho$ and $\sigma$ $$ \Vert \rho - \sigma\Vert_1…
Sam Jaques
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What are theta, phi and lambda in cu1(theta, ctl, tgt) and cu3(theta, phi, lam, ctl, tgt)? What are the rotation matrices being used?

I was reading the documentation for qiskit.QuantumCircuit and came across the functions cu1(theta, ctl, tgt) and cu3(theta, phi, lam, ctl, tgt). Looking at the names they seem to be controlled rotations. ctrl represents the controlled qubit and tgt…
Sanchayan Dutta
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HHL algorithm -- problem with the outcome of postselection

See edit at the end of the question All the references in this question refer to Quantum algorithm for solving linear systems of equations (Harrow, Hassidim & Lloyd, 2009). HHL algorithm consists in an application of the quantum phase estimation…
Adrien Suau
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Basic approximation in Solovay-Kitaev algorithm

I read the Solovay-Kitaev algorithm for approximation of arbitrary single-qubit unitaries. However, while implementing the algorithm, I got stuck with the basic approximation of depth 0 of the recursion. Can someone help me on how to implement the…
Debarghya Kundu
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Simplified explanation of Shor/QFT transformation as thumbtack

As a non-mathematician/software programmer I'm trying to grasp how QFT (Quantum Fourier Transformation) works. Following this YouTube video: https://www.youtube.com/watch?v=wUwZZaI5u0c And this blogpost:…
Roy van Rijn
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