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Topological Circuit Simulator

Does something like Quirk exist for topological (eg. braided) circuits? Alternatively, any ideas on how @CraigGidney is getting these circuits (or something similar)?
user820789
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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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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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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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What is the difference between quantum gates and quantum channels?

I'm not sure if this is a dumb question, since they seem to be very basic building blocks of quantum information theory; however, I can't seem to wrap my head around the difference between the two. As I understand it, both quantum gates and quantum…
learner1234
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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 the original reference for the Hadamard test?

The Hadamard test is a widely used routine in quantum computing to compute the real and imaginary part of expectation values of unitary operators. However, all papers I have come across in the literature that make use of the Hadamard test fail to…
bm442
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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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Does local Clifford equivalence have a direct graphical representation for qudit graph states of non-prime dimension?

This question is a follow-up to the previous QCSE question: "Are qudit graph states well-defined for non-prime dimension?". From the question's answer, it appears that there is nothing wrong in defining graph states using $d$-dimensional qudits,…
SLesslyTall
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What is D-Wave's "Pegasus" architecture?

How is D-Wave's Pegasus architecture different from the Chimera architecture?
user1271772 No more free time
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Advances in Quantum Channel Capacity

I have been reading about the Quantum Channel Capacity and it seems to be an open problem to find such capacity in general. Quantum capacity is the highest rate at which quantum information can be communicated over many independent uses of a noisy…
Josu Etxezarreta Martinez
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How to justify post quantum encryption security?

Is there some definition or theorem about what a quantum computer can achieve from which post-quantum cryptographic schemes (eg lattice cryptography, but not quantum cryptography) can justify their security? I know the period finding function is…
Joseph Johnston
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Phase-Shift Gate in Qiskit

How to implement the phase shift gate in qiskit or ibmq? Phase Shift Gate : $$\begin{pmatrix}e^{ia} && 0 \\ 0 && e^{ia}\end{pmatrix} = e^{ia}I$$
Debarghya Kundu
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Expressing "Square root of Swap" gate in terms of CNOT

How could a $\sqrt{SWAP}$ circuit be expressed in terms of CNOT gates & single qubit rotations? CNOT & $\sqrt{SWAP}$ Gates Any quantum circuit can be simulated to an arbitrary degree of accuracy using a combination of CNOT gates and single qubit…
user820789
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