All Questions

In Quantum Computation and Quantum Information, $C(U) = AXBXC$ where $A=R_z(\beta)R_y(\gamma/2) , B=R_y(-\gamma/2)R_z(-(\delta + \beta)/2), and C=R_z((\delta - \beta)/2)$ . Instead is it possible ...

This question refers to Nielsen and Chuang's Exercise 4.22: Prove that a $C^2(U)$ gate (for any single qubit unitary U) can be constructed using at most eight one-qubit gates, and six controlled-not ...

I'm actually searching two types of documents (could be the same): 1) A synthesis about all the main gap/problems that make the physical realisation of a quantum computer actually infeasible. 2) ...

I have a state $${|\psi\rangle} = s {\Bigl(|1\rangle_1|1\rangle_2-|0\rangle_1|0\rangle_2\Bigr)}\otimes{\Bigl(|0\rangle_3|1\rangle_4-|1\rangle_3|0\rangle_4\Bigr)}\otimes{\Bigl(|0\rangle_5|1\rangle_6-|1\...

You are given a source of an unknown qubit state. You make measurements in the computational basis, that is, your measurement is {|0⟩⟨0|,|1⟩⟨1|} . You observe that you see the outcome zero 30 times ...

How are 2 qubit Controlled Z gates (1 control / 1 target) typically implemented? Do we seek physical realizations of this gate, or have an alternate decomposition?

I have a state |p> that has an extractable Bell state and I want to write it as a Bell state, |b>, with a local unitary acting on one side. Basically I am trying to find a local unitary U that ...

I want to use Blender and Blender Python Scripts working with Qiskit. (want to make 3D creations) (www.blender.org) How can I do this ? (because when I try to install Qiskit inside Blender Python, it ...

A common argument for quantum computational "supremacy" assumes that there exists a classical sampler that outputs a probability $q_x$, $x \in \{0,1\}^{2^n}$ that approximates an output probability $...

I want to implement 2 equations in python, I can't understand notations in equations?

Assuming the quantum gate model, I'm trying to understand the correspondence between a quantum gate acting on qubits in superposition and the probability amplitude associated with each state of ...

I have created a 9 qubit register: q = QuantumRegister(9) c = ClassicalRegister(9) qc = QuantumCircuit(q, c) I want to measure only 1 of the register(let's ...

In Quantum Machine Learning for data scientists, Page 34 gives an algorithm to calculate the distance between two classifical vectors. As mentioned in this question, it is not clear how the SwapTest ...

I'm trying to reproduce the results of this article https://arxiv.org/abs/1801.03897, using Qiskit and Xanadu PennyLane. Particularly, this part with expected values of the Pauli operators: For ...

Quantum depth-2 circuits can be efficiently simulated classically, as shown in Proposition 2 of this paper. The following is a quote of the proof. After the first time step the quantum state of the ...

I want to run code on ibm qx, and I choose the backend "simulator", I also use the monitor to check the queue, but I have this problem. "Job is actively running" still a long time, how can I solve ...

From what I read classical computing evolved so quickly because of the funding-applications cycle. Even though the cost to make denser IC's was increasing rapidly, the applications were also getting ...

Scott Aaronson gives the outline of an algorithm to evaluate whether there exists a satisfying assignment for a given game tree. The idea is to use Grover's search recursively, for each level of the ...

Since the entropy of the universe always increases. And in quantum information, we define information in terms of entropy, in such a way that more the entropy, more is the information. Does it mean ...

The diamond norm distance between two operations is the maximum trace distance between their outputs for any input (including inputs entangled with qubits not being operated on). Is it the case that ...

When I perform $2$ Hadamard $H$ gates on a single qubit, why is the probability of getting $0$ as the outcome 100%? Why is it not 50% 0 and 50% 1 instead? Why is the second $H$ gate not putting the ...

As per IBM's documentation for quantum circuits, the general unitary operator is defined as: $$\hat{U}=\begin{bmatrix}\cos(\frac{\theta}{2})&-e^{i\lambda}\sin(\frac{\theta}{2})\\e^{i\phi}\sin(\...

Wikipedia states that a controlled U gate maps the basis states to the following: $$ |00\rangle \mapsto |00\rangle\\ |01\rangle \mapsto |01\rangle\\ |10\rangle \mapsto |1 \rangle \otimes U |0 \...

I am trying to understand Grover's algorithm. I read that this algorithm is able to find an entry in an unsorted list in just $\sqrt N$ steps, and needs only $\log N$ space. I understand entanglement ...

There is a famous paper by Childs, et al, in which it is shown that a quantum algorithm can find the name of the exit node for a certain graph in a way that is exponentially faster than any classical ...

I apologize in advance if any of these questions have been answered already. For my English course I have to ask a couple basic questions regarding quantum computing and screenshot them. Thank you in ...

Classically, we have the Hamming Code, Turbo Code, Reed-Solomon Code, etc. I am interested in knowing the classes of quantum error-correcting codes. They don't have to be analogous to classical codes, ...

Why cant i open any of the guides? The page just keeps working and never opening. Are the guides located somewhere else? Or is my machine just that slow.

I would like to display two histograms next to each other, using something like matplotlib's subplot function. This doesn't seem to work because plot_histogram() closes the figure. It is possible to ...

I am researching how to speedup optimization problems using quantum algorithms. Many such algoritms use the Euclidean norm of a vector. Hence, I tried to find a quantum algorithm that speedups the ...

Assume we have a density operator (Hermitian, PSD, with trace 1) called A for a particle. $v_i$ shows the i-th eigenvector of A and $\lambda_i$ shows the i-th eigenvalue. I assume that the elements of ...

I'm very confused about the tensor representation of Control gates. I had thought that all control gates were of the form $P_0 \otimes I+P_1\otimes \hat{A}$, where this does nothing to the first qubit ...

I have a question that's arose from reading "Quantum computing explained" by David McMahon. On page 212 there's an aspect of his description of the quantum Fourier transform which I don't understand . ...

Consider the density matrix $\rho=|\psi\rangle\!\langle\psi|$ of a random pure state in an $N$-dimensional space (in other words, an $N$-dimensional qudit, $|\psi\rangle\in\mathbb C^N$), $\rho_{ij}=...

In the context of stabilizer codes my lecturer writes that $Z_1Z_2$ is spanned by $\{|000\rangle,|001\rangle,|110\rangle\, |111 \rangle \}$. But I don't see how this spans the matrix as it's given by ...

I'm referring to the textbook "Quantum Computation and Quantum Information" 10th Anniversary Edition by Nielsen and Chuang. Chapter 7.4 has a Box 7.4 which introduces the Quantum Optical Fredkin Gate....

I find in this link that "A User has a maximum of 15 credits, and these credits are replenished upon the greater of 24 hours or when your execution has run off the queue." But what is credit? Is ...

Question: how to dynamically assign qubits to variables? e.g., say I want to represent a matrix of qubits: $matrix := \{\vec{v_1}, \vec{v_2}, ..., \vec{v_r}\}$ where each vector consists of $dim$ ...

I often see written "and then we perform measurement in the standard computational basis" but I'm a little fuzzy on what this means as it's never stated what type of measurement we're supposed to take....

I'm a little confused about the terminology of measurement. So say that we have the single qubit state $|\phi \rangle=c_0|0\rangle+c_1|1\rangle$. If we perform the projective measurement $P_0=|0\...

A qubit is given in the following form: $\left|\psi\right\rangle = \cos\left(\dfrac{\theta}{2}\right)\left|0\right\rangle + e^{i\phi}\sin\left(\dfrac{\theta}{2}\right)\left|1\right\rangle$. Let's ...

No cloning theorem states that if a counterfeiter is given a state $|\psi\big>$ picked from a bunch of non-orthogonal states, then he cannot clone the state perfectly. But this seems far from ...

This statement can be found in Vedral et al. 1997, eq. (1). More precisely, given a bipartite state $\rho_{AB}$, they claim that any operation on $\rho_{AB}$ involving local operations plus classical ...

When setting up projects with Q# I used to start with the given Quick-Starting Guide. Following the tutorial I am able to setup the example problem and the program works well. However, there seems to ...

I'm interested in deciding if an oracle is constant or not, but cannot guarantee that the non-constant oracles are balanced. The Deutsch-Jozsa seems like the obvious starting place, but handling the ...

I am trying to run QSVM algorithm on the IBMQ backend devices using the API_TOKEN. Below is the snippet of the code that I am running. The code fails the validation test and throws an exception after ...

I recently read this report from BCG, which stated: For scientists trying to design a compound that will attach itself to, and modify, a target disease pathway, the critical first step is to ...

Why aren't non maximally entangled states produced and used in quantum key distribution schemes? What would be the advantage/disadvantage to use such states rather than maximally entangled ones?

Most quantum algorithms proposed, including Deutsch-Jozsa, Simon's, Bernstein-Vazirani etc, involve querying an oracle. If I understand correctly, the speedups depend on the oracle being efficiently ...

Let $\Phi\in\mathrm T(\mathcal X,\mathcal Y)$ be a CPTP map, and let $J(\Phi)$ be its Choi representation. As is well known, any such map can be written in a Kraus representation of the form $$\Phi(X)=...