## 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

### 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

### 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

### 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

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