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0answers
9 views

What do states that are uncorrelated with respect to a given local measurement look like?

Consider a bipartite state $\rho$, and let $\Pi^A\equiv \{\Pi^A_a\}_a$ and $\Pi^A\equiv\{\Pi^B_b\}_b$ be local projective measurements. Suppose that measuring $\rho$ in these bases gives uncorrelated ...
1
vote
1answer
20 views

Is the final state in the quantum period finding algorithm entangled?

In the period finding algorithm (see the picture), through the standard procedure in quantum computing algorithms, we have $$U_f|\Psi\rangle|0^n\rangle=\frac{1}{\sqrt{2^n}}\left(\sum_{x=0}^{2^n-1}|x\...
-1
votes
0answers
16 views

After creating the Ising Hamiltonian, how it can be used in QAOA to find the optimal solution? Instead of using quadratic program

qubitOp, offset = qp.to_ising() print('Offset:', offset) print('Ising Hamiltonian:') print(str(qubitOp))
0
votes
1answer
38 views

How do I apply a matrix to a ket state?

If we have the following matrix: $$\frac{1}{\sqrt{2}}\begin{pmatrix}1&1&0&0\\ 1&-1&0&0\\ 0&0&1&-1\\ 0&0&1&1\end{pmatrix}$$ How do we find the output for ...
0
votes
0answers
11 views

Solution to Qiskit textbook Lab 3. Accuracy of Quantum Phase Estimation

I am trying to verify the accuracy of the Quantum Phase Estimation as outlined in the Qiskit textbook lab 3 (https://qiskit.org/textbook/ch-labs/Lab03_AccuracyQPE.html). Please I wanted to know if ...
1
vote
0answers
16 views

issues running a 32 qubit grover's algorithm

I have a 32 qubit grover's algoritm however whenever I run it on the simulator that IBM offers it always ouputs a probability of 1 on every single result. Is there a way to run circuits larger then 32 ...
2
votes
0answers
31 views

Set the bounds for ansatz parameters in VQE

How can I make intervals for free parameters when I use VQE function? (https://qiskit.org/documentation/stubs/qiskit.algorithms.VQE.html) I have built a parametrized ($\theta_1,...,\theta_n$) circuit ...
2
votes
1answer
33 views

Knill-Laflamme condition derivation in Nielsen&Chuang: issue to understand a part of the proof

I have some trouble to understand the proof in Nielsen&Chuang about Knill-Laflamme conditions. The conditions: Let $C$ be a quantum code and $P$ the projector onto $C$. Suppose $\mathcal{E}$ is a ...
1
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1answer
32 views

Transform circuit with 3 CNOTs in one with limited interactions on the first qubit

Is it possible to translate the above circuit into an equivalent one where the number of interaction gates with the first qubit is 1?
2
votes
0answers
18 views

Clean definition and interpretation of “error” in quantum error correction

Let us consider a noise channel $\mathcal{E}(\rho)=\sum_i E_i \rho E_i^{\dagger}$, where $\{E_i\}$ are one choice of Kraus operators associated to it. I assume I will perform error correction and that ...
2
votes
0answers
31 views

From QUBO problem to quantum circuit [duplicate]

Can you describe how to convert some QUBO problem $$f(x_1, ..., x_n) = \sum\limits_{1 \le i < j \le n} \alpha_{i,j} \, x_i \, x_j$$ into its equivalent quantum circuits? Is it preferrable to start ...
5
votes
2answers
2k views

What is the square root of the NOT gate?

I have encountered different matrix of operator "the Square Root of NOT gate". For example, the matrix is specified here: $\sqrt {NOT} = \frac{1}{2}\left( {\begin{array}{*{20}{c}} {1 + i}&...
2
votes
1answer
27 views

Add FreezeCoreOrbitals on ElectronicStructureProblem

I want to freeze core orbitals of my molecule and I know ElectronicStructureProblem has the possibility (es_problem = ElectronicStructureProblem(driver=driver, q_molecule_transformers=...
4
votes
1answer
50 views

CNOT error rate of 1 in IBM Quantum Experience

I have noticed that some CNOT gates (for instance, between qubits 1 and 2 in ibmq_casablanca) display an error rate of 1 while typical error rates are of course ...
2
votes
1answer
40 views

What's free evolution for a period T?

I am currently studying a model of a quantum (atomic) clock. And in this paper, I came across the term "Free evolution for a period T": Free evolution for a period T where a phase ...
5
votes
1answer
79 views

Can we calculate the quantum volume of a classical computer?

The quantum volume is typically taken as a popular metric to determine the capability of a quantum computer to solve complex problems. Since the end goal is to develop quantum computers that can solve ...
2
votes
1answer
38 views

Replacement of FermionicOperator from qiskit.chemistry in qiskit_nature

qiskit.chemistry.FermionicOperator here is very useful for converting fermionic operators to qubits operators. qiskit.chemistry ...
1
vote
1answer
82 views

Argue positivity of mean value of an entanglement witness matrix for all separable state

Given $\ \hat{W}=\mathbf{1}_{A B}+\sigma_{x}^{A} \otimes \sigma_{x}^{B}-\sigma_{y}^{A} \otimes \sigma_{y}^{B}-\sigma_{z}^{A} \otimes \sigma_{z}^{B} $ how can i show that for every separable state $\...
0
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0answers
40 views

How do you build the modified Toffoli gate using only local unitary and CNOT operations?

How do you build a circuit for a modified Toffoli gate using only local unitary operations and CNOT operations? The two-qubit unitary operation is given by: $\text{diag}\{1, 1, 1, e^{i\phi}\}$.
1
vote
1answer
29 views

Qiskit Portfolio Optimization : Does the resulting matrix show the stock combination to select?

The IBM Qiskit Portfolio Optimization sample finally provides an array similar to [1,0,1,1] representing the 4 digits as the stocks. So does the ...
2
votes
1answer
60 views

Prove that any Hermitian Matrix is a real linear combination of Pauli operators [duplicate]

This is an important result in Quantum Computing because it means that the Hamiltonian of a Quantum System can be encoded as a sequence of real numbers and their corresponding Pauli Operator. How do ...
1
vote
1answer
43 views

IBM quantum computer giving the wrong result?

This is the first time I am using the IBM quantum computer. I tried to run a circuit (see below the first picture) but the results I got don't match the theoretical results shown (see below the second ...
2
votes
1answer
34 views

Time result for my algorithm

I've used the function result.time_taken to know the amount of time used to execute a task on the real chip, but I don't understand if the result is in seconds or ...
2
votes
2answers
45 views

Who is responsible for implementing quantum error correction?

There are various options for error correction. For example, the Shore code or a whole class of surface codes. But I don't really understand at what level they should be implemented. For example, I ...
1
vote
1answer
24 views

How to import circuit libraries into qiskit

Im trying to put the QFT circuit in my qiskit circuit but im having trouble: ...
1
vote
2answers
74 views

Show when $a_k$ and $b_k$ are correlated when measuring in different bases, in the BB84 protocol

I'm trying to answer the following question about the BB84 protocol from Nielsen and Chuang's Introduction to Quantum Information. As I understand it, the string $b$ is determining whether we are ...
4
votes
1answer
40 views

Where is entanglement present and absent in the one clean qubit model of computation?

Based on my limited and poor understanding, a quantum circuit in the "one clean qubit" model of quantum computation generally acts on a single pure (clean) qubit tensored with $n-1$ qubits ...
2
votes
3answers
82 views

What is the point of Grover's algorithm, really?

This is a question desguised as a rant. There is a similar question here, What's the point of Grover's algorithm if we have to search the list of elements to build the oracle?, but the answers have ...
0
votes
0answers
44 views

How to simplify a circuit with repeated same parts?

If I have a circuit with 3 qubits and repeated gates as follow: ...
1
vote
1answer
24 views

Quantum gates with respect to phase angles

We can say that $X (\cos \frac{\theta}{2} |0\rangle + e^{i \phi}\sin \frac{\theta}{2} |1\rangle) = \cos \frac{\pi-\theta}{2} |0\rangle + e^{-i \phi}\sin \frac{\pi-\theta}{2} |1\rangle$, a fact that ...
5
votes
2answers
52 views

Can any “control-something unitary” be written with control and target spaces flipped?

Consider a simple two-qubit gate such as the CNOT. The typical presentation of this gate is $$\text{CNOT} = |0\rangle\!\langle0|\otimes I + |1\rangle\!\langle1|\otimes X,$$ with $X$ the Pauli $X$ gate....
1
vote
1answer
28 views

In a Swap Test why is the control qubit influenced and aren't the target qubits altered?

I am in a study group learning about quantum computing using O'Reilly - Programming Quantum Computing. I'm a developer, not a physicist. :) I feel like my question is rudimentary but I can't seem to ...
1
vote
1answer
56 views

Is there a way I can reduce the code for generating simple circuits with the same structure?

here's the code I'm using to generate 3 quantum circuits with the same structure (They're only differed by the first U3 gate on the qubit): ...
2
votes
1answer
26 views

Performing a generic single-qubit Pauli error channel in stim

I have a Pauli channel with disjoint probabilities $P_I$, $P_X$, $P_Y$, $P_Z$ (meaning $P_I + P_X + P_Y + P_Z = 1$) corresponding to Pauli errors I, X, Y, Z. Is there some way apply this Pauli ...
3
votes
1answer
59 views

When and how do we use basis embedding?

It is suggested in various sources that a possible approach to representing classical data as a quantum state is simply to take the binary sequence $x$ and turn it to $|x\rangle$ (i.e., "basis ...
2
votes
1answer
27 views

Gate Cost to Transform Superposition of Hamming weight 1 states to superposition of arbitrary basis states?

Say you have something like a general-coefficient $n$-qubit W-state, i.e., $$ |\psi\rangle\equiv\sum_{j=1}^n a_j X_{j}|0\rangle^{\otimes n} \ , $$ where $a_j$ are normalized complex coefficients. ...
3
votes
1answer
42 views

How does $|00\rangle$ evolve through an Hadamard and a CNOT gate?

If we have this given circuit: So the output for $|0\rangle$ will be: $\frac{1}{\sqrt{2}}\left(|00\rangle + |11\rangle\right)$ And we have this given circuit: What will be the output for $|00\rangle$...
3
votes
2answers
46 views

Inverse of Statevector.from_label in Qiskit

In Qiskit I can construct a computational basis statevector in the following fashion ...
3
votes
1answer
32 views

Quantum State Tomography from IQ plane data

Background: I am given to understand that the steps of Quantum State Tomography (QST) are as follows for a single qubit: The qubit is in the state $\psi=a_0|0\rangle+a_1|1\rangle$ with density matrix ...
-1
votes
0answers
23 views

Quantum Feature Importance [closed]

Hi Is there anyone here who has experience using Existing Quantum kernel trick to do Feature importance like RFECV/PCA/ Random foreset which can give importance score for each feature.
3
votes
1answer
42 views

Toffolli upside down - an equivalent circuit

It is known that an "upside-down" CNOT is equivalent to a "normal CNOT" surrounded by Hadamard gates as shown in this picture. I am wondering whether there is a similar circuit ...
3
votes
1answer
26 views

How to decide bias in Hamiltonian Ising model?

I am trying to code finance portfolio optimisation problem into a quantum annealer, using the Hamiltonian Ising model. I am using the dwave module ...
1
vote
0answers
64 views

Does a quantum computer exist today? [closed]

I agree that this may not be an easy question to answer. But lately, I increasingly come across the fact that many news materials and research papers in the field of quantum technologies say that at ...
2
votes
1answer
57 views

configuration of FakeOpenPulse2Q

Can you help me to configure the FakeOpenPulse2Q() to produce more realistic pulses? The code below instantiates 2 circuits and generates the waveforms for each. ...
3
votes
1answer
32 views

Unit vanishes in the Quantum Cramer-Rao Bound?

The Quantum Cramer-Rao Bound states that the precision we can achieve is bounded below by: $$(\Delta \theta)^2\ge\frac{1}{mF_Q[\varrho,H]},$$ where $m$ is the number of independent repetitions, and $...
2
votes
1answer
68 views

Is RYY gate not available in IBM Quantum Composer?

If so, why? How to create the RYY-gate in the composer?
0
votes
1answer
54 views

constructing a CNOT gate using a CZ and H gates

How can I construct a CNOT gate using a CZ and H gates? And I also need to prove it using these identities: \begin{equation} H = (1/\sqrt{2})(X+Z)\\ XZ = -ZX\\ X^2 = Z^2 = H^2 = 1\\ HXH = Z\\ HZH = X\\...
2
votes
2answers
148 views

Making a Controlled-Z from a CNOT

How can we draw a circuit that is based on the gates $H, CZ$ that implements $CNOT$. I know that the $H$ gate is like that: And also the $CZ$ gate is: But I'm not sure how to draw this with the ...
2
votes
1answer
53 views

Qiskit: Transpilation and the CircuitSampler

I am using Qiskit's opflow and its CircuitSampler to evaluate matrix elements / expectation values. Now, going beyond ...
2
votes
1answer
43 views

How do you compute the compiled unitary of a quantum circuit comprised of different $n$-input gates?

Given a quantum circuit consisting of two qubits, how is the compiled unitary of the circuit computed when we have different input type gates? (X-gate, H-gate are single-input gates, CNOT is a 2-input ...

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