Quantum Computing Stack Exchange Community Digest

Top new questions this week:

How can one imagine entanglement in a non-mathematical way?

I understand the theoretical concept of an entanglement and what it means for our computation to have two entangled qubits, but what does it really mean when two qubits are entangled? How are they ...

entanglement physical-qubit  
asked by Blubsiwubsi 8 votes
answered by Adam Zalcman 6 votes

Why can I not apply a control gate/function to a gate like T, S, S dagger, ... (using IBM Quantum Experience)? Is there another option?

I am trying to use the circuit composer of the IBM QE. I am doing the inverse QFT on 3 qubits and therefore need a control on T and S dagger gates, but it won't let me. Does anyone know why or know a ...

quantum-gate ibm-q-experience quantum-fourier-transform quantum-circuit  
asked by Natasha 5 votes
answered by Frank 4 votes

Distinguishing collapsed and uncertain qubit in a quantum circuit

I have been through the Young's double slit experiment. It's a direct proof or instance of showing that a wave is collapsed via observation or measurement, and shows no interference patterns. I want ...

quantum-state circuit-construction measurement superposition quantum-circuit  
asked by Sayan Dey 5 votes
answered by Adam Zalcman 6 votes

What does $M_m |\psi_i\rangle$ mean in the equation $p(m|i)=\langle\psi_i|M_m^\dagger M_m|\psi_i\rangle$?

I have trouble understanding two equations in the Nielsen & Chuang textbook. Suppose we perform a measurement described by the operator $M_m$. If the initial state is $|\psi_i\rangle$, then the ...

quantum-state measurement textbook-and-exercises nielsen-and-chuang probability  
asked by Zhengrong 4 votes
answered by Adam Zalcman 6 votes

How to create the state $\vert 0 \rangle+i \vert 1 \rangle$ using elementary gates?

I am trying to write $|0\rangle+i|1\rangle$ in terms of elementary gates like H, CNOT, Pauli Y, using the IBM QE circuit composer. I was thinking some kind of combination of H and Y since $Y|0\rangle=...

circuit-construction ibm-q-experience gate-synthesis pauli-gates ibm  
asked by Natasha 4 votes
answered by KAJ226 5 votes

Single-qubit rotations on a subspace within two-qubit unitary

I would like to implement the operation $$ U(a,b) = \exp\left(i \frac{a}{2} (XX + YY) + i \frac{b}{2} (XY - YX) \right) $$ ($a,b \in \mathbb{R}$) without using Baker-Campbell-Hausdorf expansion, ...

quantum-gate matrix-representation pauli-gates  
asked by forky40 4 votes
answered by Adam Zalcman 4 votes

Why is the superposition of all states an eigenvector, with eigenvalue 1, of the QFT?

In many descriptions of order finding, but also in this answer here, it is shown that the superposition of all states is an eigenvector for eigenvalue 1.0. To cite: Having found the eigenvalues, we ...

shors-algorithm  
asked by rhundt 3 votes
answered by rnva 4 votes

Greatest hits from previous weeks:

Is my background sufficient to start quantum computing?

I am a first-year undergraduate electrical engineering student. I want to study quantum computing and quantum AI in the future and also possibly work on building quantum computers. I have finished ...

resource-request  
asked by Huseyin Okan Demir 15 votes
answered by Dr. Sarah Kaiser 16 votes

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-gate mathematics gate-synthesis  
asked by ahelwer 21 votes
answered by Niel de Beaudrap 20 votes

How would a quantum computer be used to solve Partial Differential Equations?

Say you have a PDE you want to solve. What kind of quantum algorithms would you use to solve it? How do we input our problem on a quantum computer? What will be the output and in what form? I know ...

algorithm  
asked by cnada 13 votes
answered by viliyar 6 votes

What exactly is "Random Circuit Sampling"?

Many people have suggested using "Random Circuit Sampling" to demonstrate quantum supremacy. But what is the precise definition of the "Random Circuit Sampling" problem? I've seen statements like "the ...

speedup quantum-advantage random-quantum-circuit  
asked by grok 14 votes
answered by James Wootton 13 votes

Classical Memory enough to store states up to 40 qubits quantum system?

As a part of a discussion with my 'classical' friend, he insisted that making a a state machine for calculating the outcome of quantum computer is possible; so, simply calculate the outcomes of (known)...

algorithm simulation  
asked by viliyar 10 votes
answered by James Wootton 14 votes

Why doesn't the Gottesman-Knill theorem render quantum computing almost useless?

The Gottesman-Knill theore states (from Nielsen and Chuang) Suppose a quantum computation is performed which involves only the following elements: state preparations in the computational basis, ...

simulation nonclassicality gottesman-knill  
asked by user2723984 9 votes
answered by DaftWullie 12 votes

What are the models of quantum computation?

It seems that quantum computing is often taken to mean the quantum circuit method of computation, where a register of qubits is acted on by a circuit of quantum gates and measured at the output (and ...

models  
asked by Kiro 44 votes
answered by Niel de Beaudrap 22 votes

Can you answer these questions?

How to formally compute the probabilities in the BB84 protocol?

I've been having a difficult time trying to understand the formal mathematics behind the BB84 protocol. Most resources on this topic describe the procedure in the simple case where each qubit Alice ...

cryptography communication  
asked by Coconut 2 votes

What's the difference between $p(i|m)$ and $p(m|i)$ in measurement?

Suppose we perform a measurement described by measurement operators $M_m$, if the initial state is $|{\psi_i}\rangle$, then the probability of getting result $m$ is \begin{align} p(m|i)=\| M_m|\...

quantum-state density-matrix nielsen-and-chuang probability  
asked by Zhengrong 1 vote

What is the computational complexity of approximate quantum adders, in terms of big O notation?

I have recently found papers on approximate quantum adders. However, the papers do not seem to mention the computational complexities of their algorithms. What are their complexities, in terms of big ...

algorithm complexity-theory  
asked by user3886914 3 votes
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