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About Quantum tomography

Imagine I have a classical data(normalised to fit qubit) in the form of$\alpha_1,\alpha_2,\beta_1,\beta_2$ I assumed data to be in qubit $$\left| \psi \right> = (\alpha_1 + i\alpha_2 ) \left|0\...
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Number of measurements in quantum state tomography

I'm very curious to know more about bounds of number of measurements (or number of independent copies of state) required to reconstruct full density matrix $\rho$ such that it is $\epsilon$-close (...
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How to implement SU(2) rotation with qiskit?

Before I start, I would like to say sorry for this possibly stupid question of mine. I just recently got into the topic of quantum computing and try me there. I'm currently trying to display a SU(2) ...
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1 vote
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Techniques to parallelize controlled-unitaries controlled by the same qubit but acting on different target qubits

I need to find a way to parallelize a set of controlled-unitaries that are all controlled by the same qubit and are targetting $n$ different qubits. The main constraint that I have is that I can only ...
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1 vote
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Optimising state tomography for fully entangled states

As tomography methods are usually inefficient, it's interesting to find good approximation. I was wondering the following: Assume one wants to estimate a state $\rho$ on $n$-qubits. Given a basis of ...
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2 votes
1 answer
57 views

What makes dynamical decoupling a good method since the fidelity after using it can only reach 0.85 or so?

From this paper, I see that the fidelity of single qubit gate after using dynamical decoupling only reach around 0.85 while I normally saw experiment papers state their fidelity can reach around 0.99 ...
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  • 553
1 vote
1 answer
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Jordan-Wigner map for ionic molecule H_2^+

I want to derive the Hamiltonian of the ion molecule H_2^+ by making use of Jordan-Wigner map. Thus, I used qiskit nature. I wrote down same command of given in qiskit nature. The only difference is ...
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2 votes
0 answers
63 views

How to construct a quantum circuit that given $|\psi_0\rangle,|\psi_1\rangle$ outputs $\frac{1}{c}(|\psi_0\rangle+|\psi_1\rangle)$?

Suppose I have two arbitrary quantum states $\lvert \psi_1 \rangle $ and $\lvert \psi_2 \rangle$. Further suppose that we know $U_1$ such that $\lvert \psi_1 \rangle = U_1 \lvert 0 \rangle$, but we ...
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1 vote
0 answers
9 views

What are the differences between discrete-time quantum walks between dimensions?

When working with quantum walks in other dimensions (1D – 2D – 3D...) do your results tend to be different from what is proposed in theory with the probability density? The results obtained in the ...
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1 vote
1 answer
51 views

Why use superpositions to write states even when they are not entangled?

I am reading book "Dancing with Qubits. How quantum computing works". I had learned the rule of entangled state: when quantum state is separable(i.e. it can be written as such a tensor ...
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1 answer
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Quantum algorithm to determine the existence of a solution

Consider two vectors $u$, $t$ living in some space (let's say $ℝ^{n}$), and the following (simple) problem: Find a vector $v$ such that $∃a,b\inℝ$, $au+bv=t$ Imagine I want to use Grover to find a ...
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6 votes
1 answer
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Can W gate be written only using H,T?

I want to write the decompose the gate $W=(X+Y)/\sqrt{2}$ using only $H$ and $T$ (and all the derived Clifford gates basically). I know $H=(X+Z)/\sqrt{2}$ is it possible to obtain exactly $W$ from ...
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1 vote
2 answers
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Some of the qubits are not evaluated at Qiskit

When I implement a 3-qubit circuit in Qiskit, circuit is executed smoothly at the simulator but counts I read back as results does not contain all of the qubits that are defined and included in the ...
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-2 votes
0 answers
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PhD topics in quantum computing [closed]

I am looking for PhD topics in quantum computing related to computer Engineering background (I don't have a background in physics). I tried searching for Machine learning, neural networks and Quantum ...
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2 votes
1 answer
59 views

Barren Plateau as a consequence of 2-design?

Initializing a parameterized quantum circuit with a unitary sampled from a uniform distribution (so sampling from the Haar distribution) or in a weaker form: a unitary which is a unitary 2-design, ...
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2 votes
2 answers
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Expected Minimum Clique Coverage?

I'm curious if there is literature on this and, if there is, where to find it. Here I'm using ``clique" to mean a set of observables which all commute with each other. I also include the identity ...
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3 votes
1 answer
29 views

T-depth in Qiskit

How to find T-depth in Qiskit? Is there any inbuilt function or some method to find T-depth? I know that the .depth() function exists which returns circuit depth (i....
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2 votes
1 answer
62 views

Qiskit: How to implement a classical function?

I'm quite lost, I have to implement the following function with qiskit $$ f(x,y,z) = (\lnot x \land y \land z) \lor (x \land \lnot y \land z) $$ but how can we do that ? I don't understand how to do ...
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3 votes
2 answers
66 views

qiskit qaoa.compute_minimum_eigenvalue

I am having some trouble running the compute_minimum_eigenvalue method from qiskit's QAOA: the documentation states that one ...
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0 answers
26 views

Are there hardware platforms that natively implement parametric two qubit gates?

For example, is it possible to implement RXX gate with an arbitrary angle on an ion computer in a single native operation? The RXX gate with an arbitrary angle can be decomposed into two RXX gates ...
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9 votes
1 answer
253 views

Is there a closure property for the entire Clifford hierarchy?

TL;DR Is the entire Clifford hierarchy (as opposed to any one level), a group? Background. The Clifford hierarchy (on $n$ qubits), is a collection of nested subsets $\mathcal C^{(1)} \subset \mathcal ...
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1 vote
0 answers
84 views

Reshaping the 4x4 CNOT gate into 2x2x2x2 in a tensor network

I'm learning how to perform tensor network contraction for simulating a quantum circuit by looking at the documentation for the JET simulator: link. Specifically, I'm trying to do all the calculations ...
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1 vote
1 answer
53 views

Performance metrics in QSVM

I have implemented QSVM on breast cancer dataset using link: "https://qiskit.org/documentation/stable/0.24/tutorials/machine_learning/01_qsvm_classification.html" but unable to compute other ...
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  • 127
1 vote
2 answers
49 views

How to calculate eigenvalues by phase estimation?

I have been learning Quantum PCA recently but I came across a problem. How can I get the eigenvalues of a matrix by phase estimation? And what on what kind of matrix can we implement this algorithm?(...
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1 answer
41 views

Expectation value of Pauli string for VQE

One approach to get the expectation value $\langle\psi|P\psi\rangle$ of a pauli string $P\in \{I, X, Y, X\}^{\otimes n}$ is the following. Let $(a_i, |\lambda_i\rangle)$ be eigenvalue-eigenvector ...
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What role does Landauer's principle play in quantum reverisbility?

In section 3.2.5 of Nielsen and Chuang (starting page 153) they talk about Landauer’s principle, where they discuss the lower bound on the thermodynamic cost of erasing information. In irreversible ...
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3 votes
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37 views

Predator–prey theory

We have a project where we are supposed to simulate the predator–prey theory in qiskit. Can anyone help or suggest of any ways to start from somewhere because we are kinda lost.
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4 votes
2 answers
51 views

Why should we purify a mixed state?

I'm new to quantum computing so I know this question may sound stupid. But I still want to know why purification is necessary sometimes. Please help me with it:)
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1 vote
0 answers
34 views

Conditional measurement using classical bit in qiskit

I am trying to implement Figure 6 in Implementing a distance-based classifier with a quantum interference circuit by Schuld et. al The specific part that I'm struggling with is the controlled (on |0&...
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3 votes
1 answer
159 views

Are the pure quantum states that make up a mixed state orthogonal?

I came a cross a problem when leaning Quantum PCA. I know that a mixed state is an ensemble of several quantum states. But I wonder whether these states that make up for the mixed state are orthogonal....
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2 votes
0 answers
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contraction related Bit flip channel

Studying the bit flip channel using the Nielsen & Chuang's. And ran into the picture with the caption stating y-z plane is uniformly contracted by a factor of 1-2p. I don't quite understand how ...
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1 vote
1 answer
25 views

Qiskit: Transpile circuit with custom equivalences

I would like to automatically get a phase gate of pi/2 converted to a S gate. I have: ...
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1 vote
1 answer
24 views

Converting data into a SHA256 hash using Qiskit quantum computer

I was wondering how can we convert data into a hash using Qiskit quantum computer? e.g, this code below will generate a SHA256 hash based on random data. ...
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16 views

Is there a way to connect a IBM quantum lab code to an Unreal Engine project?

I would like to know whether someone tried this before, I'm interested in be able to connect this tools. I know that Unreal Engine has a plugin to program with python, that all I know. I'll really ...
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3 votes
0 answers
27 views

Decomposing S gate in two T gate with qiskit

Let's suppose I define a basis gate set and the following circuit. ...
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3 votes
2 answers
80 views

Is a "Bell measurement" equivalent to a projective measurement in a different basis?

Let \begin{align} H = \frac{1}{\sqrt{2}}\begin{bmatrix} 1 & 1 \\ 1 & -1\end{bmatrix}\in M_2(\mathbb C), \quad \mathrm{CNOT} = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 &...
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Usage of slack variables by Dimod (D-Wave)

I have a general question of the application of slack variables. For example, if I want to solve the following inequality: $x_{0}+x_{1}+x_{2}+x_{2} \leq 2$ Then I can reformulate the inequality above ...
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1 vote
1 answer
156 views

Why do we have only 3 Pauli gates X, Y and Z

This question is out of curiosity thus might not be of much importance. We have Pauli X, Y, Z gate which rotate the phase by π along X, Y and Z basis. Just wondering why not do we have these 3 gates ...
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1 vote
2 answers
30 views

How is the ket of a quantum state calculated in this code?

For the following code qc = QuantumCircuit(2) qc.h(1) qc.cx(1,0) ket = Statevector(qc) ket.draw() the output will be the following: ...
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3 votes
0 answers
28 views

How is this Variational Quantum Singular Value Decomposition paper efficient in any way?

Link to paper here. This algorithm seems neat but the unitary decomposition of the matrix M generally takes an exponential number of Pauli basis elements in the number of qubits $N$, therefore an ...
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2 votes
1 answer
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What is the difference between $|+\rangle$ and $|-\rangle$?

What is the difference between $|+\rangle$ and $|-\rangle$. I was reading about quantum states and found that $|+\rangle$ and $|-\rangle$ represent state in superposition of other states. I was just ...
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1 vote
1 answer
42 views

What is the original paper introducing the Variational Quantum Eigensolver?

My question is very simple. I am looking for original paper where Variational Quantum Eigensolver (VQE) has been introduced. After some Googling I was able to find many applications of VQE and its ...
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0 votes
1 answer
30 views

How to calculate parameters of U3 gate from a certain quantum state?

I'm trying to do Quantum PCA but I came across a problem. I now have a quantum state, say $\frac{|00\rangle+|01\rangle+|11\rangle}{\sqrt{3}}$ and I want to know how to prepare it from two $|0\rangle$ ...
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2 votes
2 answers
135 views

Why can the CNOT representation $e^{i\frac{\pi}{4}\left(I-Z\right)\otimes\left(I-X\right)}$ hardly be found in books?

The CNOT gate is usually written as $|0\rangle\langle0|\otimes I + 1\rangle\langle1|\otimes X$ (with $X,Y,Z$ being the Pauli Basis and $I$ the Identity). I have yet to stumble across the ...
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2 votes
3 answers
91 views

Why do we need physical qubit if qubit can be simulated?

I do not see any advantage in constructing very costly and imperfect physical qubit while this qubit can be simulated with using conventional computer memory (noise-free). So what is the purpose when ...
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  • 354
2 votes
1 answer
27 views

Why does the condition $\langle \varphi _k\left( t \right) |\dot{\varphi}_l\left( t \right) \rangle =0$ called parallel transport condition?

I'm reading this paper about nonadiabatic holonomic quantum computation and met the condition eq.(2) states that $\langle \varphi _k\left( t \right) |\dot{\varphi}_l\left( t \right) \rangle =0$ is the ...
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  • 553
0 votes
0 answers
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How to use QubitConverter and ParityMapper to do chemistry simulation?

After viewing the question: Hamiltonian & QubitMappingType cannot be imported from qiskit.chemistry.core, I also want to implement the same Jupyter notebook and browsed the response below. However,...
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2 votes
1 answer
29 views

Oracle for amplitude addition

Assume one is given two oracle circuits providing access to matrices $A_{ij}$ and $B_{ij}$ as follows (see eq. (6.2) here): \begin{equation} O_A |0\rangle|i\rangle|j\rangle=\left(A_{ij}|0\rangle+\sqrt{...
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  • 1,408
1 vote
1 answer
56 views

Computing characteristic polynomial of unitary operation

I am trying to replicate a calculation from the linked paper but I am unsure if I understand their math. A locally invariant function defined as the characteristic polynomial is as follows: $$F_U(t) = ...
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2 votes
0 answers
20 views

How to set the meas_level and optimization_level in Quantum Azure IonQ provider?

I am performing a benchmark process using the Azure Quantum IonQ provider. I use Qiskit in the Azure platform, and I was trying to see how to control the transpiling and compiling process. It seems ...
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