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5 views

How to prepare a random 1-qubit superposition for data encoding

Let's assume we have a normalized data vector $\vec{x}= [x_1,x_2]$. How can I prepare a state $$|\psi\rangle = x_1|0\rangle+x_2|1\rangle$$ for any $\vec{x}$. I know that this state is in general not ...
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0answers
5 views

Measurement probability of a state from three hilbert spaces

I'm curious how to find the probability measurement of a state when one qubit is measured. For example this state: $|\gamma\rangle = \frac{1}{\sqrt{2}}(| 010 \rangle + | 101 \rangle )$ Assuming these ...
1
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0answers
6 views

Grover's oracle

Grover's algorithm works by iteration of the operator $$G:=U_S^\perp U_f=H^{\otimes n}U_0^\perp H^{\otimes n}.$$ I know how to write down the matrix for $U_S^\perp$ (the inversion about the average ...
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0answers
7 views

QISKit not installing in PyCharm

I am attempting to setup a PyCharm project to study and work through the QISKit textbook. However I seem to be running into a propblem seting it up. I have setup a python enviroment via anaconda (...
0
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0answers
24 views

Measure qubit $q_0$ in some basis that remotely prepare in qubit $q_1$

I constructed a circuit that characterized the creation of a Bell state. Now I want to measure qubit $q_0$ in some basis depending on the state $|\psi\rangle$ that I want to remotely prepare in qubit ...
1
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1answer
16 views

Is there any quantum gate that can change quantum hardware topology(architecture)?

I read about this paper Hardware-aware Heuristic for the Qubit Mapping problem in the NISQ Era. I wonder there is the only SWAP gate that can change the quantum hardware topology. Is there any gates ...
2
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1answer
31 views

Is it better to initialize quantum circuits in Qiskit by passing QuantumRegister and ClassicalRegister objects?

From the perspective of building quantum computation software based on Qiskit, which approach to defining quantum circuits is more robust? ...
4
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1answer
48 views

What is the general method for creating real gate sequences from mathematical algorithms?

Background I have been doing research on quantum computing on my own for over a year now and I feel like I may have missed a fundamental step. I have no idea how to take a mathematical algorithm and ...
1
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1answer
29 views

Implementing a SwapTest for samples with large numbers of features

I am trying to calculate the distance between sets of vectors. To do this I can create a SwapTest circuit (described here on page 34) and encode a feature vector with a U3 gate, then apply H and CSWAP ...
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0answers
17 views

Symmetric Universal Quantum Cloning Machine (UQCM) N --> M for unknown states

Does it exist a schematic diagram of the quantum circuit implementing the symmetric UQCM N--> M for unknown states? If yes, does anyone know a Qiskit implementation of it?
2
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0answers
24 views

How to convert discrete quantum circuits to their continuous variable equivalents?

With a full set of either CV, or qubit gates, you should be able to implement a universal circuit. I am wondering how to "convert" one circuit to another. If I have a circuit with a U3 gate, ...
3
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1answer
128 views

How can we construct a control-control y-rotation (CCRy) gate in Qiskit?

Qiskit has a CRy gate, however I couldn't find a CCRy (double control Ry) gate implementation. How can we construct the CCRy circuit given below in Qiskit without any ancillary qubits? Edit: A quick ...
1
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1answer
38 views

Why does $\sum_n \langle n|M_m\rho M_m^\dagger|n\rangle$ simplify to $\langle \psi|M_m^\dagger M_m|\psi\rangle$?

I was trying to derive the formula for $p(m)$ in exercise 8.2 on page 357 in Nielsen & Chuang. But I am wondering what rule I can apply to simplify this $$\mathrm{tr}(\mathcal{E}_m(\rho) )= \...
3
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1answer
86 views

What is the action of sandwiching an operator with two CNOT gates?

When a gate is sandwiched (or conjugated) by two CNOT gates, what effect does it have on the gate being sandwiched? For example, in the figure below, it is clear what effect the controlled $R_y(\theta)...
2
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1answer
57 views

Is the order of the tensor product in $|\phi\rangle\otimes|\chi\rangle=|\chi\rangle\otimes|\phi\rangle$ relevant? [duplicate]

I am reading this book “Quantum Computing Explained” by David McMahon. I found the following statement on page 74 Note that the order of the tensor product is not relevant, meaning $|\phi\rangle \...
2
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1answer
65 views

Is the quantum state discrimination success probability always $\lambda_0\langle\mu(0),\rho_0\rangle+\lambda_1\langle\mu(1),\rho_1\rangle$?

Consider the standard quantum state discrimination setup: Alice sends Bob either $\rho_0$ or $\rho_1$. She picks $\rho_0$ and $\rho_1$ with probabilities $\lambda_0$ and $\lambda_1$, respectively. Bob ...
1
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0answers
26 views

Qiskit: is there a quick way to work out the spherical coordinates for a given qubit statevector?

I am trying to calculate the spherical coordinates of different qubit states (i.e. working out $\theta$ and $\phi$ from: $|\psi\rangle = e^{-i\phi/2}\cos(\theta/2)|0\rangle + e^{i\phi/2}\sin(\theta/2)|...
2
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1answer
37 views

Qiskit: how can you use a different state for each shot in a quantum circuit? [duplicate]

I am trying to run a quantum circuit many times, each time using a different random state - a single qubit i.e. $|\psi\rangle= a|0\rangle + b|1\rangle$ with different $a$ and $b$. Once each qubit has ...
2
votes
1answer
110 views

What is a good video resource for quantum computing?

Can anyone refer me to a good video resource for quantum computing? I found this post helpful Currently, what are the best structured courses available online on quantum computing?, but Vazirani's ...
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0answers
19 views
+50

Bell's experiment: checking the probabilities

I have some doubts on the calculations behind Bell's experiment, which goes as follows: a pair of entangled photons is shared between two scientists, Alice and Bob, who possess a bunch of polarizers ...
2
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1answer
36 views

What is the difference between SWAP & Bridge gates?

While I'm studying about Qubit allocation (mapping), I wonder what the differences between SWAP and Bridge gates are. I know that a SWAP gate and Bridge gate can be represented with 3 CNOT gates and 4 ...
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2answers
40 views

Phase Kickback - factoring Dirac representation

In section 2.3 of the Qiskit textbook (Phase Kickback), there's an example where a controlled-T gate is applied to $|1+\rangle$. You're asked to attempt the same thing with $|0+\rangle$. I've done ...
1
vote
1answer
53 views

What exactly happening in QAOA in a general way?

So I know that in QAOA we have the two hamiltonians. Mixer and Cost Hamiltonian. Lets start: First we have our Qubits which get in the Superposition if we add the Hadamard Gate. Then we have the both ...
4
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1answer
39 views

Is there an issue preventing people from scaling Grover's algorithm to larger numbers of qubits?

IBM's quantum experience offers computing up to 15 qubits however through my search of current literature the largest implementation for the algorithm has been with 4 qubits. Is there an issue, ...
0
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0answers
32 views

Implementation of remote state preparation circuit on IBM Quantum Experience [closed]

How to build a remote state preparation circuit on IBM Quantum Experience Quantum teleportation uses prior entanglement and forward classical communication to transmit one instance of an unknown ...
4
votes
1answer
28 views

Does $\frac{\Pi_A\otimes I_B}{\text{Tr}((\Pi_A\otimes I_B)\rho_{AB})}\rho_{AB}=\rho_{AB}$ hold for a state $\rho_{AB}$ and projector $\Pi_A$?

For some projector $\Pi_A$ and state $\rho_{AB}$, let $$\sigma_{AB} = \frac{\Pi_A\otimes I_B}{\text{Tr}((\Pi_A\otimes I_B)\rho_{AB})}\rho_{AB}$$ Is it the case that $\sigma_B = \rho_B$? It seems ...
1
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2answers
35 views

Multiple Providers on IBMQ

I am attempting to run parallel computations on two different backends from within the same Jupyter notebook, though it appears these two jobs are running sequentially. I understand the jobs will be ...
2
votes
1answer
39 views

Show algebraically that $U|0\rangle\otimes |0\rangle+U|1\rangle\otimes|1\rangle=|0\rangle\otimes U^T|0\rangle+|1\rangle\otimes U^T|1\rangle$

Suppose that Alice applies a unitary operator $U$ with real entries to her qubit in an EPR pair $|\beta\rangle=\frac{1}{\sqrt 2}(|00\rangle+|11\rangle)$. Is this the same as having Bob apply $U^T$ to ...
2
votes
1answer
32 views

How would I compute a density matrix of a complex qubit mixed state?

I am currently reading Nielsen & Chuang, and one of the questions asks to calculate a density matrix with the following mixed state, $$ \frac{1}{9}\begin{bmatrix} 5 & 1 & −i \\ 1 & 2 &...
2
votes
1answer
36 views

How would I compute a density matrix of a 2 qubit mixed state?

I am currently reading Nielsen & Chuang, and one of the questions asks to calculate a density matrix with the following mixed states, how would I do this? $$ |00> \;with \;probability \; 2/4 \\ ...
1
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1answer
25 views

In VQE, what ansatz would be best used for a maximally entangled $n$-qubit $H$?

What ansatz would be best used for a maximally entangled n qubit H? I came across this question in the Qiskit textbook and I really don't know how I would answer it.
2
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1answer
31 views

How do I represent my 3-qubit state in the computational basis?

I have taken the tensor product of $|0\rangle \otimes |-\rangle \otimes |+\rangle$ which resulted in the matrix $$\begin{bmatrix} 1/2\\ 1/2 \\ -1/2 \\ -1/2 \\ 0 \\ 0\\ 0\\ 0\\ \end{bmatrix}.$$ How ...
1
vote
1answer
99 views

Does sending a qubit using a quantum network through some conventional physical medium mean it is not with sender anymore after sending?

I was reading the wiki page on superdense coding algorithm. I am not quite sure what happens in this algorithm. When the photon which is part of entangled pair is being sent to Bob from Alice's side, ...
3
votes
1answer
54 views

What does the identity operator represent when computing $\langle\varphi|I\otimes Z|\varphi\rangle$?

Consider a single qubit state $|\varphi\rangle$ and a hamiltonian $H = Z$. Evaluating $\langle \varphi | H | \varphi \rangle$ corresponds to a measurement of $|\varphi\rangle$ in the computational ...
1
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0answers
15 views

How to write the general state of a corrupted n-qubit codeword in quantum error correction?

I am reading the chapter on quantum error correction in Quantum Computer Science by David Mermim. Which says, for a single qubit in a random state $|\Phi\rangle$ of the superposition of $|0\rangle$ ...
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0answers
36 views

What is the best book or resource to start Learning about Quantum Computing? [duplicate]

What is the best book or resource to start Learning about Quantum Computing ?
3
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1answer
36 views

HHL algorithm, How to implement exp(iAt) gates?

From this paper Quantum Circuit Design for Solving Linear Systems of Equations, in figure 4 The paper shows what inside operator $e^{-iAt}$ but didn't shows how to connect the control qubit (register ...
0
votes
0answers
43 views

Quantum correlation and Bell's inequality [closed]

In quantiki website (https://www.quantiki.org/wiki/bell-state) it is mentioned that verification of quantum correlation in rotated basis states is more important for quantum correlation. I also found ...
1
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1answer
23 views

Can one easily compute the weight enumerator of a CSS code constructed from two binary codes $M_1,M_2$?

Consider a CSS code, which is constructed from two binary codes $M_1$ and $M_2$, so its symplectic matrix is of the form: $$ \begin{pmatrix} M_1 & 0 \\ 0 & M_2 \end{pmatrix}.$$ Suppose one ...
2
votes
1answer
69 views

How to implement the swap test with the help of qiskit?

It's creating a real confusion for me especially the parameterized circuit which I have to create. Can anybody please solve this for me? I want to create this circuit.
1
vote
2answers
36 views

In quantum adiabatic simulation, is the $s$ in $(1-\frac{s}{T})H_{in}+\frac{s}{T} H_{cl}$ related to the $t$ in $e^{-iHt}$?

I just want to do a whole adiabatic calculation on quantum circuit. To prepare two Hamiltonian of $H_{initial}$ and $H_{classical}$ and solve $H_{classical}$ using adiabatic calc like quantum ...
6
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2answers
385 views

How can one argue that the $S$-gate is Clifford while $T$-gate is not?

How can one argue that $S$-gate is Clifford while $T$-gate is not?
2
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0answers
69 views
+50

How significant is achieving electronic transport in a single qubit at room temperature?

This is a follow-up to a previous question I asked: How promising is the possibility of carbon-based qubits to make a qubit that’s stable at room temperature? I am trying to assess the significance of ...
1
vote
1answer
55 views

What is a good program to practice using a quantum algorithm? Should I use Cirq or Qiskit?

I am starting to learn about Quantum Computers and Quantum Algorithms. I also started reading about Qiskit and Cirq. I really like learning about them and hopefully I can be a Software Engineer with ...
2
votes
2answers
42 views

How to implement $\sqrt{iSWAP}$ in Qiskit

I want to implement the $\sqrt{iSWAP}$ operator using simple operations in Qiskit such as it is done for the $iSWAP$ here or $\sqrt{SWAP}$ gate here. How can I do this? If possible I would like to ...
0
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0answers
11 views

unable to install qiskit-aqua[cvx]…While installing, i am getting the below error. If anyone can suggest

I am unable to install qiskit-aqua[cvx]...While installing, i am getting the below error. If anyone can suggest. I have pasted the error snapshot below
0
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1answer
46 views

What does “large-scale universal quantum computation” mean?

I was reading this lecture notes by Sevag Gharibian. He mentioned the following statement: Large-scale universal quantum computer can be built. I do understand what quantum computer is, but I don't ...
0
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1answer
32 views

Qiskit textbook - exercise 2.2 - why doesn't the correct answer give the same statevector?

In the Qiskit textbook, I'm stuck on one of the exercises in section 2.2. The question is: Write the state: as two separate qubits. The answer has already been covered in this question here, and is ...
-2
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1answer
34 views

IBMQ.load_account() fails with “403 Client Error” [closed]

I alredy save an account but when I want to laod it I get a error like this how can I fix it ? ...
0
votes
1answer
18 views

How many real numbers are required to describe density matrix for $n$ qubits?

(All of these coming from the topic of simulation of quantum systems) A density matrix $\rho$ Which describe state of $n$ qubits will have $2^{n} \times 2^{n}$ size. We have couple of conditions like ...

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