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Quantum Computing Stack Exchange Community Digest

Top new questions this week:

Base codes with transversal non-Clifford - why not?

A leading approach to circumventing the Eastin-Knill theorem involves using stabilizer codes which support a transversal implementation of the full Clifford group, and obtaining universal gateset via ...

error-correctionclifford-groupfault-tolerancehadamardstate-injection-model 
user avatarasked byCurious_non_expert Score of 3
user avataranswered byDaftWullie Score of 4

What is the fundamental reason that error reduction so often costs only $O(\log(1/\epsilon))$?

I have noticed a lot of quantum algorithms that do not output an exact answer generally scale as $O(\log(1/\epsilon))$ where $\epsilon$ is the error threshold. I initially thought that this is because ...

quantum-gatequantum-algorithms 
user avatarasked byHabouz Score of 2
user avataranswered byMark Spinelli Score of 0

stim: why would order of CNOT operations affect detectors

I have two circuits (below) : first works fine (no complaints from stim); second comes back with a "non-deterministic detector" error. The difference between the two circuits is that the ...

simulationstim 
user avatarasked byunknown Score of 1
user avataranswered byAG47 Score of 1

Why is the fastest quantum time complexity of unstructured search O(sqrt(n))?

Recently, I have watched video on 3Blue1Brown about Grover's algorithm. He give an example that:To find a secret number in the range from 0 to n−1, you can query ahidden function that returns “true”...

grovers-algorithmcomplexity-theorysuperposition 
user avatarasked byHenry Tom Score of 1
user avataranswered byCraig Gidney Score of 1

Greatest hits from previous weeks:

Are there emulators for quantum computers?

Is there any way to emulate a quantum computer in my normal computer, so that I will be able to test and try quantum programming languages (such as Q#)? I mean something that I can really test my ...

emulation 
user avatarasked byMichel Gokan Khan Score of 79
user avataranswered byCraig Gidney Score of 30

How accurate is this figure by TIME magazine?

Below is a figure from a TIME magazine edition. I have a few questions regarding this representation of quantum computing:Is saying "0 and 1 at the same time" a correct statement? Isn't ...

superposition 
user avatarasked byRydberg Score of 8
user avataranswered byCraig Gidney Score of 21

What is the "Stinespring Dilation"?

I've consulted Nielsen and Chuang to understand the Stinespring Dilation, but wasn't able to find anything useful. How does this operation relate to partial trace, Kraus operators, and purification?

quantum-operation 
user avatarasked byJimit Bavishi Score of 14
user avataranswered byAmara Score of 15

What does it mean for two qubits to be entangled?

I have done some sort of online research on qubits and the factors making them infamous i.e allowing qubits to hold 1 and 0 at the same time and another is that qubits can be entangled somehow so that ...

experimental-realizationentanglement 
user avatarasked byArshdeep Singh Score of 20
user avataranswered bysnulty Score of 19

Density matrices for pure states and mixed states

What is the motivation behind density matrices? And, what is the difference between the density matrices of pure states and density matrices of mixed states?This is a self-answered sequel to What&#...

quantum-statedensity-matrix 
user avatarasked bySanchayan Dutta Score of 22
user avataranswered byDaftWullie Score of 18

Circuit construction for Hamiltonian simulation

I would like to know how to design a quantum circuit that given a Hermitian matrix $\hat{H}$ and time $t$, maps $|\psi\rangle$ to $e^{\frac{i\hat{H}t}{\hbar}} |\psi\rangle$ with $\hbar =1$.Thank you ...

quantum-algorithmscircuit-constructionhamiltonian-simulation 
user avatarasked byGradius Score of 29

How to derive the CNOT matrix for a 3-qubit system where the control & target qubits are not adjacent?

In a three-qubit system, it's easy to derive the CNOT operator when the control & target qubits are adjacent in significance - you just tensor the 2-bit CNOT operator with the identity matrix in ...

quantum-gatelinear-algebragate-synthesis 
user avatarasked byahelwer Score of 38
user avataranswered byNiel de Beaudrap Score of 38
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