Yitian Wang
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Where is the parallelism in Deutsch-Jozsa algorithm?
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7 votes

In fact, in the original paper of Deutsch and Jozsa they actually implemented two oracles, here comes their procedure. If you omit the second $U_f$ and get a state $|\psi\prime>=\displaystyle\sum_{...

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In quantum computation, if the fidelity is high enough to promise over 50% success rate, is quantum error-correction still needed?
4 votes

The comments said well. There is a difference between quantum error correction and your idea. In the case of quantum error correction, these codes have a guarantee that if the fidelity of each ...

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How to perform the unitary transformation $U|i,j_1\rangle = 1/\sqrt{k}(|i,j_1\rangle+|i,j_2\rangle+|i,j_3\rangle...+|i,j_k\rangle)$?
4 votes

There is a question that has something in common with your question, see the answer by @DaftWullie. Since all three input states after the operation, $U$, give the same result, then we can not decide ...

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Nielsen&Chuang 5-qubit quantum error-correction encoding gate
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4 votes

To access and edit the quantum circuit and view the Bloch sphere of the quantum state online, click the hyperlink(to run and see the Bloch sphere you have to sign in). The final code is also posted on ...

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How can I verify that the Pauli group is a group? And is it abelian?
3 votes

For the three Pauli matrices, {${\sigma_1,\sigma_2}=0$}, so certainly this can not form an abelian group. The Pauli group is an isomorphism with $D_4$. The elements of the Pauli group are {${I, \...

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Shor's algorithm: initialization of second register
3 votes

The initial state of Shor's algorithm is $\frac{1}{\sqrt N}\displaystyle\sum_{a=0}^{N-1}|a\rangle$, and it is OK to move this state to $\frac{1}{\sqrt N}\displaystyle\sum_{a=0}^{N-1}|a,x\rangle$ as ...

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What is the probability of error in quantum fingerprinting using cswap test?
2 votes

Conclusion first. The first one is correct, but the scenario is not practical, since it is challenging(or more directly, impossible) to build a perfect channel, so even if the two states are actually ...

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Why isn't output of Deutsch–Jozsa Algorithm simply $|0\rangle$?
2 votes

This answer is a little supplementation of @Martin Vesely. It has been proven that "it is not possible to build a fixed, general quantum computer which can be programmed to perform an arbitrary ...

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Getting started with Quantum Machine Learning
2 votes

Before introducing quantum machine learning, I strongly suggest that understanding important algorithms like Grover search and quantum Fourier transformation might be critical subroutines for quantum ...

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Expected value in a VQE qiskit
2 votes

The output of variational quantum eigensolver(VQE) is a number(the ground state energy of molecules), see qiskit document. This output has the form of a number, so this can de draw from a few ...

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How to get subspace of quantum circuit?
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2 votes

What you are looking for is the partial trace of a density matrix, $|\psi\rangle\langle\psi|$, where $|\psi\rangle=|q_0,q_1,...,ac_0,ac_1,...\rangle$. This matrix is surely a unitary matrix, and it ...

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Transforming $|100\rangle$ state into $|000\rangle + |111\rangle$ state using only Hadamard and CNOT gates
2 votes

The upper figure shows the quantum circuit to do so, the first $X$ gate is to let the first qubit be in the $|1\rangle$ state coherently. The state $\frac{|000\rangle+|111\rangle}{\sqrt2}$ is the GHZ ...

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Which Gate set can be used to perform the function $U|0\rangle =\frac{1}{\sqrt{n}}\sum_{i=0}^{n}(|i\rangle)$?
2 votes

In fact, you just need to implement a lot of Hadamard gates(if lg(n) gives an integer). E.G.

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CSS Code and Fault-tolerant Problem in Nielsen and Isaac Chuang‘s book
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1 votes

I think you just get stuck, this is an easy job. For stabilizer codes, the logical state $|0\rangle_L$ and $|1\rangle_L$ are just superposition of states(maintaining the same state under stabilizer ...

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How does feedback work in simple Grovers algorithm where $n=4$?
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1 votes

The quantum register c can be regarded as ancilla. For the first part of each iteration(before the CCCC-NOT), each two cx compares if the state of the two qubits is identical, if not, one ancilla will ...

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Check if $|\psi\rangle$ is equal to a fixed basis state using the standard set of gates
1 votes

Yes, SWAP can be used, this paper gives a quantum mechanical method in it's supplementary to test the fidelity between a known state and an unknown state using two Hadamard gate and a controlled-SWAP ...

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Produce a quantum state with its density matrix an identity matrix up to an constant
1 votes

In fact, I figured out by myself. When I was reading this website, it posts a density matrix that I want(that is a long website, to find the corresponding part, just search the keyword 'identity'). ...

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How to make the gate decomposition of CCCRY
1 votes

There is an automatic way to design a gate, utilizing qiskit. When drawing the figure of a quantum, you can use the code circ.decompose().draw() to show a decomposed circuit. Code first: from qiskit ...

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Is there an explanation for why, to search through an unstructured database, the average number of checks is $\frac{N}{2}$ in classical computation?
1 votes

I think what you are talking about must an unstructured database, which can be improved by Grover search algorithm to $O(\sqrt n)$. When learning courses like computation theory there may be related ...

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Is it possible to plot the average counts from two jobs with multiple circuits on a single histogram in Qiskit?
1 votes

Yes, I have checked the code and find out that this is possible. The qiskit function plot_histogram takes two types of input as the data: either a single dictionary or a list of dictionaries, so what ...

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What are the properties of the matrices representing quantum gates?
1 votes

Since I think question 1 is solved well by the upper answer, I will skip to question 2. They have some similar property with the rotation in $R^3$, but from a group theory point of view, the quantum ...

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Traveling salesman problem in Qiskit: cannot find a solution on simulator
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1 votes

Qiskit has a tutorial documentation about TSP, you can find more detail at that site. As for the problem of your code, I suggest you use the qiskit-built function tsp.random_tsp(3,seed=123) # 3 for ...

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Grover's algorithm: a real life example?
1 votes

I suggest you read this article, which discussed the quantum speedup for unsupervised learning like clustering. This paper gathered the progression of the quantum algorithms to accelerate unsupervised ...

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Further entangling two ebits to obtain $|0000\rangle + |1111\rangle$ state
1 votes

I think this is the quantum circuit that you want, first produce two pairs of Bell states, then undo the second pair coherently, and finally apply two CNOT two flip the last two qubits.

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Get state vector of a single qubit in a circuit in Qiskit
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0 votes

For a boolean-valued result, your code works. If you are looking for a "more quantum mechanical" approach, then the swap trick best suits you. The quantum circuit of the swap trick is as ...

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Find probability of a single qubit's measurement results from a 5 qubit state
0 votes

Since you can get the state vector of the 5-qubit state, you can use the technique of -----partial-trace to get the state of a specific qubit(This git-hub code implements partial trace using only ...

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Import Qiskit fails
0 votes

OS Error refers to an operating system error. On this page, you can see that qiskit is tested on 64-bit os solely. The report says that your operating system is 32-bit, this should be the reason. When ...

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Qiskit programming: convert qubit to quantum register
0 votes

Today I suddenly noticed that my question is stupid, at least for the code I presented. I have rewritten the code and posted it below: from qiskit import QuantumCircuit,QuantumRegister from qiskit....

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Parallel shots on Qiskit
0 votes

There is a question which is quite alike to your problem in Quantum Computing-stack exchange. I have answered it before, you may see that. I think the number of shots nearly does not change the ...

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Is there quantum advantage to be had with a D-Wave computer in 2020?
0 votes

If there is any quantum advantage, this Lockheed Martin paper must show a clue. In this paper, they utilized the D-Wave machine to sample the Boltzmann distribution and thus trained a deep neural ...

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