Quantum Computing Stack Exchange Community Digest

Top new questions this week:

Represent Hadamard gate in terms of rotations and reflections in Bloch sphere

I read in a book that any single qubit operation can be decomposed as $$ \bf{U} =e^{i\gamma}\begin{pmatrix}e^{-i\phi/2}&0\\ 0&e^{i\phi/2}\end{pmatrix}\begin{pmatrix}\cos{\theta/2}&-\sin{\...

textbook-and-exercises bloch-sphere hadamard  
user avatar asked by A1Y Score of 5
user avatar answered by Craig Gidney Score of 9

methodology for design quantum circuits according to a given unitary

This is a general question. Given an arbitratry unitary matrix. How to desigin a quantum circuit to implement it? I am not asking for a specific unitary matrix, but for a general methodology to tackle ...

quantum-gate quantum-circuit  
user avatar asked by tangyao Score of 3

Efficient Clifford circuit simulation for composite dimensional qudits

I'm looking for a reference that states that Clifford circuits can also be efficiently simulated for qudits with composite dimension $d$. It is folklore that this result is true for qubits ($d=2$ case)...

clifford-group classical-computing  
user avatar asked by Rahul Sarkar Score of 2

Why do we need/have the operator sum representation (Kraus representation)?

I am reading through Nielsen & Chuang, and I am on the section about operator sum representation. They performed this derivation. Why is it important and useful for us to bundle together the ...

quantum-operation nielsen-and-chuang kraus-representation  
user avatar asked by researcher101 Score of 2
user avatar answered by Frederik vom Ende Score of 4

How to apply gates on a subspace of a superposition of qubits?

Let us say that I have the state $a|00\rangle + b|01\rangle + c|10\rangle + d|11\rangle$. I wish to apply a one-qubit unitary (a $2\times2$ matrix) U on the subspace spanned by $|01\rangle$ and $|10\...

qiskit quantum-gate quantum-state programming  
user avatar asked by Soumyadeep sarma Score of 2
user avatar answered by Egretta.Thula Score of 1

Do we consider the entangled-based protocol E91 to be a device-independent protocol?

Since both rely on Bell inequalities to maintain security, does the Ekert protocol rely on trustworthiness of the devices?

entanglement key-distribution  
user avatar asked by ibtissam Score of 2
user avatar answered by DaftWullie Score of 2

How to calculate the Schmidt decomposition of a state without SVD

I have this state of two qubits here: $$ |\psi_{AB}\rangle = \frac{1}{2}(|0\rangle_A |0\rangle_B + |1\rangle_A |1\rangle_B + |1\rangle_A |0\rangle_B - |0\rangle_A |1\rangle_B) $$ Which means that the ...

density-matrix schmidt-decomposition  
user avatar asked by Alessandro Romancino Score of 2
user avatar answered by glS Score of 4

Greatest hits from previous weeks:

An impossible quantum adder claimed by a journal article?

In Quantum adder of two states that are themselves superpositions, I asked: I have two states $|a\rangle = \frac{1}{\sqrt N}\sum_{i=0}^{N-1}|i\rangle|a_i\rangle$ and $|b\rangle = \frac{1}{\sqrt N}\...

quantum-algorithms quantum-circuit superposition  
user avatar asked by Paulske Score of 22
user avatar answered by Craig Gidney Score of 35

Implementing "Classical AND Gate" and "Classical OR Gate" with a quantum circuit

Quantum cNOT Gate (Classical XOR Gate) A "Controlled NOT (cNOT) Gate" flips the 2nd qubit if the 1st qubit is $\left|1\right>$, and returns the 2nd qubit as-is if the 1st qubit is $\left|0\right&...

quantum-gate classical-computing unitarity  
user avatar asked by Siu Ching Pong -Asuka Kenji- Score of 18
user avatar answered by Sanchayan Dutta Score of 13

What is a Haar random quantum state?

Can somebody please explain me what is a Haar random state? I am not able to find any friendly resource to read about it.

quantum-state unitarity haar-distribution  
user avatar asked by Shweta Aggrawal Score of 14
user avatar answered by Quantum Mechanic Score of 15

Did D-Wave show quantum advantage in 2023?

I would like to know your thoughts on whether or not D-Wave has shown a a smoking-gun example of quantum advantage this year. I am genuinely not quite sure what to think, but I believe the answer to ...

quantum-advantage d-wave annealing adiabatic-model qubo  
user avatar asked by sheesymcdeezy Score of 19
user avatar answered by user1271772 No more free time Score of 23

How do I build a gate from a matrix on Qiskit?

I'm creating a gate for a project and need to test if it has the same results as the original circuit in a simulator, how do I build this gate on Qiskit? It's a 3 qubit gate, 8x8 matrix: $$ \frac{1}{...

quantum-gate programming qiskit gate-synthesis  
user avatar asked by Nillmer Score of 32
user avatar answered by cnada Score of 5

Why is it harder to build quantum computers than classical computers?

Is it because we don't know exactly how to create quantum computers (and how they must work), or do we know how to create it in theory, but don't have the tools to execute it in practice? Is it a mix ...

experimental-realization classical-computing  
user avatar asked by Archil Zhvania Score of 43
user avatar answered by Anti Earth Score of 10

What is the "surface code" in the context of quantum error correction?

I am studying Quantum Computing and Information, and have come across the term "surface code", but I can't find a brief explanation of what it is and how it works. Hopefully you guys can ...

error-correction terminology-and-notation surface-code  
user avatar asked by Ivanovitch Score of 43
user avatar answered by James Wootton Score of 30

Can you answer these questions?

What could be intermediate steps towards a fully fault-tolerant quantum algorithm with added value for each step?

Starting from an algorithm without any error correction or detection, what incremental improvements can be made towards fully fault-tolerant encoding and operation? It seems that fault-tolerant error ...

error-correction experimental-realization fault-tolerance  
user avatar asked by qubitzer Score of 1

How to approximate the time-dependent Hamiltonian in quantum adiabatic theory by the non time-dependent Hamiltonian?

Recently, I am learning how to solve the linear equation $A\left | x \right \rangle =\left | b \right \rangle $ using quantum adiabatic theory. In the solving process, people usually need to set the ...

linear-algebra hamiltonian-simulation adiabatic-model  
user avatar asked by user30173 Score of 1

Are these two codes the same?

There is an $ ((11,2,5)) $ CWS code given in table B2 at the end of https://kth.diva-portal.org/smash/get/diva2:894450/FULLTEXT01.pdf I know that some CWS codes are equivalent to stabilizer codes, but ...

error-correction stabilizer-code stabilizer-state graph-states  
user avatar asked by Ian Gershon Teixeira Score of 2
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