Questions tagged [quantum-state]
Questions about or related to quantum states. Consider using the density-matrix tag when relevant.
1,633
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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 ...
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932
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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 ...
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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:
...
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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 ...
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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]^...
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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 ...
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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
$$|\phi\rangle = \frac{1}{\sqrt{k}} \sum_{i=1}^{k} |\phi_{1, i} \rangle \otimes |\phi_{2, ...
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Run a circuit on "simulator_statevector" of the IBM Quantum Platforms
I would like to obtain the statevector of a QuantumCircuit using the simulator_statevector (and Qiskit) of the IBM Quantum ...
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Measuring one qubit in an entangled pair in another basis?
Qubits are usually measured in the computational basis, but we can change the basis by a unitary $U$ to measure in the basis formed by the columns of $U$.
For example, if $| \psi \rangle = | 0 \rangle$...
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An operator that checks the second qubit
Applying Hadamard gate to classical bit $|0, \psi, \phi\rangle$
$$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 + \...
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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 $\mathcal{H} \cong \bigotimes_{i=1}^{2^n} \mathbb{C}^2$ ...
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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 ...
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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 ...
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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 ...
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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 ...
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315
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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 ...
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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. ...
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222
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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 ...
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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 \...
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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
...
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161
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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 ...
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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 ...
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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 (...
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76
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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 ...
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213
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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'...
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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 ...
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281
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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 ...
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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
$$
\left(\begin{array}{ccc}
1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
0 & 1 & 0 & 0 & ...
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82
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Two Qudit custom gate error in Cirq
I am trying to build two qudit CX (d-dim) gate.
and getting below error.
There is no issue in the unitary matrix.
Please suggest to resolve the error.
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Store/load superposition state of a qubit into/from classical register
I know this question looks ridiculous.
But I simply want to know if possible to store/load a superposition state into classical register from qubit. Specifically two bit of classical register.
...
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87
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Qubit reset using Grover iteration
Suppose I’m building a long circuit and I need to reuse a qubit from a previous step but I don’t want to use the reset operation (or I’m not using an IBM computer so I don’t even have the reset option)...
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How simulation of noisy quantum circuits is done in Qiskit using the statevector method
While performing VQE calculations of medium-sized molecules like H2O, using Qiskit AerSimulator with noise, I noticed that even for a large number of shots, the speed of simulation using statevector ...
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Decomposing a projector in the computational basis in terms of Pauli matrices
I have a $x \in \mathbb{N}$, and I would like to decompose it in terms of the Pauli matrices $\sigma_x, \sigma_y, \sigma_z$ and the identity. My first steps are as follows:
$$
\begin{align}
|x \...
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678
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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
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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, ...
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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-...
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172
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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}}|...
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193
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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 ...
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159
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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 ?...
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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=(...
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340
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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(...
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209
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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?
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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 ...
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362
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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 ...
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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, ...
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981
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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 ...
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618
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How to generate statevector evolution?
I have created the following 2-qubit circuit in qiskit:
...
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150
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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 ...