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Can we reduce the $C^1(U)$ operation from $AXBXC$ to $AXBX$?

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 ...
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4 views

How to reduce circuit elements of a decomposed $C^2(U)$ operation?

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 ...
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8 views

Document pessimism about the feasibility of a quantum computer

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) ...
1
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1answer
29 views

Representing a Bell measurement on non adjacent qubits

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\...
2
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0answers
13 views

(Quantum Computing/Machine Learning) Estimate of the absolute value of the probability amplitude of |0⟩ in the superposition?

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 ...
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18 views

How is the Controlled Z Gate implemented?

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?
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0answers
7 views

Find the local unitary that takes the bell state to a state phi that has an extractable bell state

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 ...
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0answers
23 views

Using Qiskit with Blender

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 ...
2
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0answers
16 views

Strong vs weak simulations and the polynomial hierarchy collapse

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 $...
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18 views

anyone can help me to implement 2 equations ( Python Implementation ) [on hold]

I want to implement 2 equations in python, I can't understand notations in equations?
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0answers
18 views

What is the correspondence between a quantum gate and the interference pattern generated?

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 ...
1
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1answer
14 views

qiskit - measure only 1 of the register out of n registers

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 ...
5
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0answers
40 views

Distance calcluation between two vectors

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 ...
2
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1answer
31 views

Expected value of a product of the Pauli matrices in different bases

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 ...
2
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0answers
35 views

Simulating depth-2 circuits

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 ...
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0answers
75 views

Why does my code run a long time?

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 ...
1
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1answer
53 views

Software for Quantum Computing

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 ...
2
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0answers
23 views

Grover's algorithm for game tree

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 ...
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1answer
39 views

Information and entropy [on hold]

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 ...
3
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1answer
72 views

Is the diamond norm subadditive under composition?

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 ...
2
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3answers
87 views

How do 2 Hadamard gates act on a single qubit?

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 ...
2
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1answer
34 views

Does the general form of a unitary operator define strict signs for the second column?

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(\...
1
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1answer
28 views

How to derive the way a controlled $U$ gate acts on an input state?

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 \...
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3answers
125 views

Grover's algorithm in a nutshell

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 ...
4
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0answers
21 views

Oracle for welded tree walk

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 ...
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0answers
33 views

Questions regarding quantum computing [closed]

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 ...
2
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1answer
29 views

What are the Main Classes of Quantum Error-Correcting Codes?

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, ...
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19 views

Why cant i open any of the guides? [closed]

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.
1
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1answer
36 views

How to do subplots when plot_histogram etc. closes the figure

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 ...
3
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0answers
33 views

Are there any quantum algorithms to compute the norm of a vector, better than the classical version (O(d), where d is dimension)

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 ...
1
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1answer
30 views

Is there any meaning for a density operator if we omit the j-th row and column in quantum mechanics?

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 ...
2
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1answer
53 views

Understanding how control gates are written in tensor notation

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 ...
1
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1answer
20 views

The control phase gate in Quantum fourier transform and the question it brings up regarding control gates in general

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 . ...
3
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1answer
98 views

What is the average value of $|c_i\bar c_j|$ for a random state $|\psi\rangle=\sum_i c_i|i\rangle$?

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}=...
2
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1answer
34 views

Why is $Z_1Z_2$ spanned by this set ? Surely it's too small?

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 ...
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0answers
15 views

Help with understanding Unitary Operator of Quantum Optical Fredkin Gate

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....
3
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1answer
58 views

What is the IBM Q credits?

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 ...
0
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1answer
26 views

Q#: dynamically assigning (or updating) multidimensional Qubit arrays

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 $dim$ ...
1
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1answer
18 views

Performing a measurement in the standard computational basis of a three qubit system on two qubits

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....
2
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2answers
36 views

Confusion about the relation between POVMs and projective measurements

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\...
2
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1answer
29 views

Bloch Sphere - Rotation Matrix

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 ...
4
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2answers
33 views

Bounding advantage of a 'no cloning theorem' counterfeiter

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 ...
4
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1answer
53 views

Why can any LOCC operation be written as $\sum_k (A_k\otimes B_k)\rho(A_k^\dagger\otimes B_k^\dagger)$?

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 ...
1
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2answers
51 views

Q#: How to setup a project correctly (on Linux, command line)?

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 ...
3
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1answer
135 views

Deutsch-Jozsa on non-balanced oracles

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 ...
1
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0answers
47 views

Job execution issue while using IBMQ Experience

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 ...
4
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1answer
43 views

Number of Qubits Required for Simulation of Caffeine and Penicillin Molecules

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 ...
4
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1answer
27 views

Non maximally entangled states for QKD

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?
7
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0answers
86 views

What are examples of non-oracular versions of famous oracular problems?

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 ...
5
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1answer
44 views

Do the eigenvalues of the Choi matrix have any direct physical interpretation?

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)=...

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