Questions tagged [quantum-state]

Questions about or related to quantum states. Consider using the density-matrix tag when relevant.

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Better Way Of Separating Two CQ-States

I have this cq-state: $$\frac{1}{2} \times (|0\rangle \langle0|_A \otimes \rho^0_E + |1\rangle \langle1|_A \otimes \rho^1_E)$$ Where Alice (A) is classical and an adversary Eve (E) has some ...
QuestionEverything's user avatar
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Measurement of a qubit and storage of the information on a bit

Suppose we have the quantum circuit below with a quantum register of 2 qubits and a classical register of 2 bits. The Hadamard gates and CNOT gate are not important for the question. When we measure a ...
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FPGA qubit simulation

This question is regarding the simulation of qubits, using FPGAs. My question is: how does using FPGAs to simulate qubits help us understand or give us an insight into how quantum computers could be ...
alfonso guevara's user avatar
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Why is this Hamiltonian matrix diagonal?

I've only recently started using density matrices in my work but I am confused with the following code that I have whether I am getting the right matrix: ...
M00N KNIGHT's user avatar
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How to use get_statevector in Qiskit SDK 1.0?

I am Using Qiskit SDK 1.0. I have a problem with get_statevector in qiskit SDK 1.0 and using BasicSimulator. My code is attached ...
Naeem Ullah's user avatar
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Projective measurement notation

I don't understand how projective measurements work; I think my confusion comes from the notation. How would this be written in matrix notation? Is it just [w row vector] [Ma matrix] [w column vector]^...
researcher101's user avatar
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On difference in the number of two-qubit stabilizer states that are separable (36) vs those that are maximally entangled (24) and partial entanglement

We have a set of two-qubit stabilizer states. There are 60 of them: 36 separable and 24 maximally entangled (MES). I was wondering whether we can somehow compare the size of the set of partially ...
Sutasu's user avatar
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Expected trace distance between two types of random ensembles

Consider a Haar random state on $n$ qubits, and denote it by $|\psi\rangle$. Now consider the following state $$|\phi\rangle = \frac{1}{\sqrt{k}} \sum_{i=1}^{k} |\phi_{1, i} \rangle \otimes |\phi_{2, ...
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Run a circuit on "simulator_statevector" of the IBM Quantum Platforms

I would like to obtain the statevector of a QuantumCircuit using the simulator_statevector (and Qiskit) of the IBM Quantum ...
stopper's user avatar
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Measuring one qubit in an entangled pair in another basis?

Qubits are usually measured in the computational basis, but we can change the basis by a unitary $U$ to measure in the basis formed by the columns of $U$. For example, if $| \psi \rangle = | 0 \rangle$...
Andrew Baker's user avatar
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An operator that checks the second qubit

Applying Hadamard gate to classical bit $|0, \psi, \phi\rangle$ $$H|0\rangle =\frac{1}{\sqrt{2}}\begin{pmatrix}1 & 1\\ 1 & -1\end{pmatrix}|0\rangle = \frac{1}{\sqrt{2}}|0, \psi, \phi\rangle + \...
Koray's user avatar
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The Qiskit code's output doesn't seem to be what I expected

...
Anees Ur Rehman's user avatar
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Does integrating w.r.t. the Haar measure commute with taking partial trace?

Consider a density matrix $\rho(U)$ which depends on $U \in SU(2^n)$, corresponding to a state of a composite, finite-dimensional Hilbert space $\mathcal{H} \cong \bigotimes_{i=1}^{2^n} \mathbb{C}^2$ ...
Silly Goose's user avatar
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Understanding quantum computing power of entanglement

I read here that the power of quantum computing lies in the fact that the Hilbert space size of a $n$ qubits register grows exponentially with $n$, but only when entangled. I would like to understand ...
deb2014's user avatar
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How is the depth of a circuit creating "Constant size vector states" $O(\log b)$

In Prakash's thesis - (link to PDF), section 2.2.2 Constant size vector states: We show that the vector state $|x\rangle$ for $x\in R^b$ can be created in time $\widetilde{O}(\log(b))$ using a ...
bubakazouba's user avatar
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Why are the basis unit vectors |0⟩ and |1⟩ written as column vectors [1, 0] and [0, 1], respectively?

I am starting to learning quantum computing and am currently reading Quantum Computing: A Gentle Introduction. As I started reading into the first section after the Introduction, it talks about basis ...
Jayex_Code01's user avatar
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How to write a two qubit state as "diagonal" in the basis of Pauli matrices?

Any two qubit density matrix can be written as $$ \rho = \frac{1}{4} \sum_{n,m = 0}^{3} M_{nm} (\sigma_n \otimes \sigma_m), $$ where $\sigma_\mu$'s are the identity and Pauli matrices. Is it possible ...
Bard's user avatar
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CZ-gate in neutral atoms computer with Rydberg pulses

I'm trying to understand the protocol to obtain a CZ-Gate with two qubits and Rydberg pulses : https://queracomputing.github.io/Bloqade.jl/dev/3-level/#pulse-CZ-gate Apply Rydberg π-pulse on control ...
Duen's user avatar
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Multi-qubit gates on entangled states

I am a bit confused by the following scenario: Suppose we are given an entangled state $| \psi \rangle$ that has $2$ qubits (we can generalize to $n$ qubits). Suppose we had a circuit like above. ...
Loic Stoic's user avatar
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How to visualize the resulting state vector using CVNeuralNetLayers and Lightning qubit device

I'm trying to learn how to use PennyLane's CVNeuralNetLayers. I wrote this code below but I am not able to use the resulting state of the circuit generated by this layer. I looked for examples in the ...
Luccas Marim's user avatar
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Sequence of controlled gates on non-eigenstates

Quantum phase estimation predicts the eigenvalues of a unitary operator given an eigenstate, using a sequence of controlled versions of that operator. The math relies on the fact that $ |0, \psi \...
Loic Stoic's user avatar
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How to obtain the state vector of a certain number of fixed bits in the output of a multi-bit circuit?

I have a 26 bit output, but I only want to get 8 bit statevector in 26 bit. If I use ...
qin guang's user avatar
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How to prove that maximally entangled state remains maximally entangled under local unitaries?

We have a maximally entangled state $\phi$ of composite system $R$ and $Q$. Apply unitary $U$ to $\phi$ on the Q system. Now how to prove that $U \phi$ is also a maximally entangled state? This ...
Michael.Andy's user avatar
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How to measure an unknown state produced by a source of qubits?

What kind of experiment can allow me to measure an unknown state produced by a source of qubits? For example: the state of photon polarization. But it can be another one. I have no information about ...
Dimitri's user avatar
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Sorting two numbers using quantum computing

To better understand how quantum computing works, I am trying to sort two numbers using unitary matrix. Based on this definition, I understand a quantum Turing machine to have the automorphism (...
Anon21's user avatar
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What is a simple example to showcase quantum computing to a broad audience?

I would like to write a code to demonstrate an advantage of QC over classic computations. However, I'm really struggling to find the simplest example for a broad audience. Can someone suggest an ...
qwerty's user avatar
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How can you create S-GATE with U3?

Hello I am trying to create an Q0->HSSH Q1->HSH using U3 Gate only. I am trying U3(pi/2, 0, pi) for H Gate and U3(4pi/2, 2pi,0) for S gate. The output state vector using normal H and S gate don'...
JaZZyCooL's user avatar
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Can separable, but non-valid "states", be used as a resource to generate entanglement?

Suppose two parties, Alice and Bob, who are separated share the "state" $\sigma_{AB}=|0\rangle\langle1|_A\otimes |0\rangle\langle1|_B$. Of course, this not a valid quantum state as it does ...
Hans Schmuber's user avatar
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How to perform a basis change on a 2x2 density operator?

I have an ensemble described by following density operator: $$ P=3/8 |+\rangle\langle+| + 5/8 |-\rangle\langle-| $$ I am trying to write this operator in $\{|0\rangle, |1\rangle\}$ basis. I know that ...
mohaddese's user avatar
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Move the phase in Controlled-Controlled-Phased-Gate

I wonder how we can move the phase in CCZ gate onto different diagonal element $$ \left(\begin{array}{ccc} 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & ...
Nghia Nguyen Huu's user avatar
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Two Qudit custom gate error in Cirq

I am trying to build two qudit CX (d-dim) gate. and getting below error. There is no issue in the unitary matrix. Please suggest to resolve the error.
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Store/load superposition state of a qubit into/from classical register

I know this question looks ridiculous. But I simply want to know if possible to store/load a superposition state into classical register from qubit. Specifically two bit of classical register. ...
Muhammad Ikhwan Perwira's user avatar
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Qubit reset using Grover iteration

Suppose I’m building a long circuit and I need to reuse a qubit from a previous step but I don’t want to use the reset operation (or I’m not using an IBM computer so I don’t even have the reset option)...
Fabio Dias's user avatar
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How simulation of noisy quantum circuits is done in Qiskit using the statevector method

While performing VQE calculations of medium-sized molecules like H2O, using Qiskit AerSimulator with noise, I noticed that even for a large number of shots, the speed of simulation using statevector ...
Radu M.'s user avatar
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Decomposing a projector in the computational basis in terms of Pauli matrices

I have a $x \in \mathbb{N}$, and I would like to decompose it in terms of the Pauli matrices $\sigma_x, \sigma_y, \sigma_z$ and the identity. My first steps are as follows: $$ \begin{align} |x \...
NYG's user avatar
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How do I draw a multi control cz gate or do I have to make my own gate?

I want to build a diffuser and an oracle so that's why I wanted a multi control cz gate but I looked everywhere I didn't get any
Rayhan's user avatar
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Formal measurement of the probability of an outcome of a Qubit in the hadamard base

I am fairly new to Quantum Computing and have a question which might be trivial for all of you, but I am really struggling with it. From Quantum Computation and Quantum Information I have learned, ...
dribble290's user avatar
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How can you extract all the state probabilities in e.g. Grover's search?

In the Qiskit tutorial for e.g. Grover's algortihm, there is a 3-qubit implementation on a real quantum computer https://qiskit.org/textbook/ch-algorithms/grover.html#3.1.2-Experiment-with-Real-...
MBache's user avatar
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Factoring some qubits with Kronecker product

I have this quantum state: $$|\phi \rangle =\frac{1}{4\sqrt{2}}|000\rangle +\frac{3-\sqrt{5}i}{8}|001\rangle +\frac{1}{4\sqrt{2}}|010\rangle +\frac{3-\sqrt{5}i}{8}|011\rangle \\+\frac{1}{4\sqrt{2}}|...
LJZB's user avatar
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What actually StatePreparation perform in qiskit?

I used this method to initialize classical data in a circuit. I would like to know what's under the hood and the complexity of this procedure, but I can't find anything on the internet which suits my ...
DYLAN NICO AMBROSI's user avatar
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What is the value of a control qubit as a Controlled-X Gate or Tofolli Gate parameter?

For example in a Controlled-X or Tofolli gate, qubits can be assigned as control bits. But before the measurement ; what are the values of these qubits in the gate tensor since they can not be 1 or 0 ?...
user19095524's user avatar
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A doubt regarding probabilities of a entangled states?

Given an state of entangled particle pair in Horizontal-Vertical basis ($H,V$): $ \psi_{hybrid}= (1/\sqrt2) (HH+VV)$ Let us define a new Right-Left basis ($R,L$) as follows: $L=(1/\sqrt2)(H-iV)$ $R=(...
TheoryQuest1's user avatar
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qml.probs with another computational basis state

I am working with pennyLane library in Python and I have a circuit that involves several operations to 10 qubits. I want to measure the occupation probability of a target state. The function qml.probs(...
Borja Aizpurua's user avatar
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2 answers
209 views

How to write a code to separate two qubits?

Is it possible to write a code to separate $\left|01\right> $ as $\left|0\right> ,\left|1\right> $ or are there any circuits i can use to get output like that?
User1086's user avatar
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345 views

Is there a way to know if a probability amplitude is negative or positive?

I have a quantum system that outputs a state similar to: $|\psi\rangle = \frac{1}{2}(|00\rangle + |01\rangle + |10\rangle \pm |11\rangle)$. So my question is: is there a way (by measurement or by ...
Yousef Zook's user avatar
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1 answer
362 views

Generating a random 32-byte hex integer using Qiskit

Hello I posted here yesterday about generating random 16 digits using Qiskit, and a gentle guy helped me but how about a string? How can I generate random 256 bit key in hex format in a superposition ...
Zakaria Halloumi's user avatar
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1 answer
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Quantum Gate - Negating qubit whose state is known to lie in the equatorial x-y plane

Given a qubit whose state is known to lie in the equatorial x–y plane in the Bloch sphere is it possible to find a quantum gate that will always negate this qubit? If so, exhibit such a gate. If not, ...
Userep's user avatar
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Understanding phase kickback caused by the CNOT gate

Applying the CNOT gate to the state |+-⟩ would result in the state |--⟩ as per: What has occurred is a "phase kickback". The relative negative phase from the target qubit has transferred to ...
Ognyan Tsvetkov's user avatar
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618 views

How to generate statevector evolution?

I have created the following 2-qubit circuit in qiskit: ...
Anthony Knighton's user avatar
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Quantum Teleportation Algorithm Always Ends in State $|0\rangle$

I'm trying to put together a demo using the Quantum Teleportation example provided by qiskit. The quantum circuit runs as intended when it's initialized to the state $|0\rangle$, and the measured ...
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