Questions tagged [quantum-state]
Quantum systems can mathematically be described by their 'quantum state'. When the system is closed/isolated, the state is 'pure' and can be written as a sum (i.e. 'superposition') of basis vectors. When the system is a subsystem of an open system, the state is instead usually 'mixed' and cannot be written as a pure state, so has to be written as a density matrix. Consider using the density-matrix tag when relevant
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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 ...
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1answer
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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 ...
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How to find the distance between a given $\rho$ and the nearest pure state(s)?
I have a $d$-dimensional state $\rho$. Is there any way to find the (possibly not unique) trace distance to the nearest pure state:
$$
\min_{|\psi\rangle} \,\,\lVert \rho - |\psi\rangle\langle \psi| \...
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Can I use Grover's algorithm on overlapping sets of qubits?
Let's say I have 3 qubits: $q_1,q_2,q_3$.
I want to apply Grover's algorithm on q1,q2, such that q1,q2 $\neq$ 10 and do the same for q2,q3, so that q2,q3 $\neq$ 11. The final possible combinations of ...
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What is the superop simulator in Qiskit for?
I'm trying to understand what the use case of a superop simulator would be. My understanding is that density matrix is generally more resource intensive than state vector, but it has additional ...
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What is the IQ plane?
I struggle to find any information on Nielsen and Chuang or similar texts on the exact definition of the so-called IQ plane (I think this is a notion closely related to solid state quantum computers ...
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What was the meaning of Lossless Quantum compression?
I was reading few questions regarding lossless quantum compression on stack exchange, then out of curiosity, I started reading this article. After reading I end up being confused about what does ...
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How does the quantum Fisher information provide bounds for the estimation of output states?
Assume you have some quantum process $Q$ (e.g. quantum state tomography) that intakes initialised states $\rho_{i}$, $i=1,\ldots,n$ and gives some output $\rho'_i$.
$$
\rho_1 \to Q \to \rho'_1 \\
\...
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How to calculate the evolution of ket states through a simple quantum circuit?
I am having difficulties with the calculations of qubits.
I think I can do them, but it feels so massivly inefficient!
In this tutorial grover's algorithm for example, there's a simple oracle given ...
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Is it possible to retrieve $|\psi_1\rangle,|\psi_2\rangle$ from their tensor product $|\psi_1\rangle\otimes|\psi_2\rangle$?
Consider two quantum states$$\left| \psi_1 \right> = \alpha \left|0\right> + \beta\left|1\right>$$ and $$\left| \psi_2 \right> = \gamma \left|0\right> + \delta\left|1\right>$$
Now ...
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Intuitions about probabilities relating to evolving a two-qubit state through a CNOT gate
If the initial state of $|x_0\rangle = \alpha |0\rangle + \beta |1\rangle$ and $|x_1\rangle =|0\rangle$, and the final state at the barrier is $|10\rangle$ (in the form $|x_1x_0\rangle$), what would ...
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Does the circuit with qubit-wise CZ gates compute the inner product of two states? If not, is there another circuit that does?
I've been searching for a quantum algorithm to compute the the inner product between two $n$-qubit quantum states, namely $\langle\phi|\psi\rangle$, which is in general a complex number.
One can get $|...
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1answer
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How to keep angles in degrees into quantum circuit using qiskit?
Qubit in polar form $$\left|\psi\right\rangle=\cos(\theta/2)\left|0\right\rangle+\sin(\theta/2)\left|1\right\rangle $$
Now lets say i want to keep $\cos(\theta/2) = 50.400 $ degrees angle and $\sin(\...
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What is the difference between Bloch's sphere and IBM's Q-sphere?
I'm new to Quantum Computing and I've been trying to understand single-qubit operations, quantum phases etc through Bloch's Sphere visualization. However, in IBM's Circuit Simulator, they seem to be ...
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Can we convert two single qubit states into single mixed state?
Consider two qubits
$$\left| \psi_1 \right> = \alpha \left|0\right> + \beta \left|1\right>$$ and $$\left| \psi_2 \right> = \alpha_1 \left|0\right> + \beta_1 \left|1\right>$$
Is it ...
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Is it possible to perform quantum computation between different Hilbert spaces?
Let us consider a protocol between Alice and Bob. Alice works in a $2^n$-dimensional Hilbert space $\mathcal{H}_A$, using $n$ qubits. Bob works in a $(1+2^n)$-dimensional Hilbert space using qdits. ...
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How to get Bloch sphere Cartesian coordinates from density matrix
I am vexed by a particular derivation. Given a state $\psi$ and corresponding density matrix $\rho = |\psi\rangle \langle \psi|$, or $\rho = \begin{bmatrix} a & c \\ b & d \end{bmatrix}$, I ...
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1answer
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Transformation of Operation Order for H,T Single Quantum Gate
Suppose I want to apply an $H$-gate transformation to an arbitrary quantum state $|\sigma\rangle$, and then a $T$-gate transformation to the arbitrary quantum state $|\sigma\rangle$.
The quantum state ...
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1answer
54 views
How do you visualize multi-qubit interactions?
I am trying to understand single qubit operations from Bloch sphere, but I was told that the limitation of Bloch sphere is that it can only visualize or simulate 1 qubit.
What are some instances do I ...
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is it possible to eliminate a certain possibility of an outcome of 3+ qbits
Let's say I have n qbits each in a superposition $\begin{pmatrix} \frac{1}{\sqrt{2}}\\ \frac{1}{\sqrt{2}} \end{pmatrix}$ so each possible outcome has a probability of $\frac{1}{2^n}$. Is it possible ...
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States used in lossless quantum compression?
I was reading about quantum compression in this article and have some doubts regarding an example mentioned. Specifically, I have two questions:
In example they represented $|a\rangle = \dfrac{1}{\...
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2answers
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Can I understand mixed states using the Bloch sphere? [duplicate]
I'm a bit confused with the representation of mixed states in a Bloch sphere. Are they represented as points or vectors? For pure states, they're vectors on the surface of the Bloch sphere and have a ...
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Understanding Deutsch Algorithm
From the image below, if we focus on the first qubit, we know after Hadamard (state 1) $|0\rangle$ will become $|+\rangle$ and the second qubit $|1\rangle$ will become $|-\rangle$.
What exactly would ...
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What is the probability of detecting Eve's tampering, in BB84?
Alice sends a 0 in computational basis
I understand that theres a $\frac12$ probability that eve guesses the basis wrong, and can go with Hadamard. So it's $\frac12$ chance Eve will pick computational ...
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2answers
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How to prove that EPR outcomes have equal probability no matter the basis?
Recently in class, we learned about the EPR state. I know that no matter what basis the first qubit is measured in, the two outcomes have an equal probability. However, how does one prove this? I ...
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Exercise 4.6 in Quantum Computing and Quantum Information Nielsen and Chuang
Question 4.6: One reason why the
$R_\hat{n}(θ)$ operators are referred to as rotation operators is the following fact, which
you are to prove. Suppose a single qubit has a state represented by the ...
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Partial trace instead of trace in definition of entropy
For a bipartite quantum state $\rho_{AB}$, we have that the von Neumann entropy is
$$S(\rho_{AB}) = -\text{Tr}(\rho_{AB}\log\rho_{AB})$$
If instead, one took the partial trace above and obtained
$$\...
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2answers
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Is Grover's algorithm suitable for this search problem?
I wonder if we can utilize Grover's algorithm to solve the following search problem.
Leetcode 33. Search in Rotated Sorted Array
Example 1:
Input: nums = [4,5,6,7,0,1,2], target = 0
Output: true
...
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1answer
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Quantum hardness of XQUATH conjecture
Consider the XQUATH conjectures, as defined here (https://arxiv.org/abs/1910.12085, Definition 1).
(XQUATH, or Linear Cross-Entropy Quantum Threshold Assumption). There
is no polynomial-time ...
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1answer
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How can one geometrically represent a 2-qubit state?
I know that a one-qubit $|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$, where $\alpha, \beta \in \mathbb C$, can be represented geometrically on a Bloch sphere as $|\psi\rangle = \cos\theta |0\rangle +...
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Why does the trace of density operators need to be one?
Usually, the textbook starts with a few assumptions of what density operator $\rho$ has.
One of them is $Tr(\rho) = 1$.
Why is that?
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4answers
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How do I get the Unitary matrix of a circuit without using the 'unitary_simulator'?
I am using jupyter notebook and qiskit. I have a simple quantum circuit and I want to know how to get the unitary matrix of the circuit without using 'get_unitary' from the Aer unitary_simulator. i.e.:...
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Single qubit gates (or CNOT) sequence to transform SWAP to Sqrt of SWAP
I'm trying to figure out how to transform the SWAP state gate into the square root of SWAP gate using only CNOTs or single qubit gates.
As you might guess, I'm new to this whole concept, but I'm ...
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1answer
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How to upload our dataset using pytorch when it is not present in torchvision?
I am trying to upload my dataset(SWELL-KW) instead of MNIST in "Hybrid quantum-classical Neural Networks with PyTorch and Qiskit" provided by IBM qiskit but it says ...
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1answer
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how to implement Quantum tomography on an arbitrary state using Qiskit?
Can quantum tomography helps to reconstruct the state? How is this possible with arbitrary quantum state?
For example if I have a $$|\psi\rangle= (0.24506+0.9633i)|0\rangle + (0.0046238+0.10943i)|1\...
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1answer
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Upper bounding a permutation invariant state
Let $\rho_{A^n}$ be a permutation invariant quantum state on $n$ registers i.e. $\pi(A^n)\rho_{A^n}\pi(A^n) = \rho_{A^n}$ for any permutation $\pi$ among the $n$ registers.
If we trace out $n-1$ ...
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Is there a characterization for the set of states with given marginals?
Let $\rho_A,\rho_B$ be two states. Is there any way to characterise the set of bipartite states $\rho$ such that $\mathrm{Tr}_B(\rho)=\rho_A$ and $\mathrm{Tr}_A(\rho)=\rho_B$?
If I assume $\rho$ to be ...
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1answer
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Why would measuring a qubit determine the states of the other qubits?
In Quantum Algorithm Implementations for Beginners, page 7 it is stated,
Suppose we have a three qubit state, $\vert\psi\rangle$, but we only measure the first qubit and leave the other two qubits ...
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1answer
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How to read a Q sphere representation?
I'm trying to understand the Q-sphere representation of a 3-qubit system. I get that the 3-qubits are in a superposition of 2 different states. The first qubit (rightmost) is in a superposition of <...
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1answer
32 views
Ranges of quantum states that are related via a quantum channel
Let $\rho\in M_n$ and $\sigma\in M_m$ be two quantum states. We denote the orthogonal projections onto $\text{range}(\rho)$ and $\text{range}(\sigma)$ by $P_\rho$ and $P_\sigma$, respectively. Now, if ...
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Does a partial transpose always have real eigenvalues?
I am working with a tripartite system, but when I partially transpose the $8\times 8$ density matrix I get two complex eigenvalues. I know the criteria for the positive and negative eigenvalues, but ...
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1answer
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How would I apply rotations to both qubits in a 2 qubit system?
Say I have the two qubit system $\frac{1}{\sqrt{2}}\begin{bmatrix}
0 \\
1 \\
1 \\
0
\end{bmatrix}$.
I have two 2x2 unitary gates, one is a rotation ...
2
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1answer
53 views
Constructing a state with constraints on reduced states
Suppose $\rho'_{AB} \approx_\varepsilon \rho_{AB}$ in trace distance. Is there an explicit construction of some state $\tilde{\rho}_{AB}$ using $\rho'_{AB}, \rho'_A, \rho'_B, \rho_A$ and $\rho_B$ (but ...
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Is there any difference between “value of a qubit” and its “state”?
Value of a qubit and its state - is there any difference between these two terms in sense of terminology?
For example, can we name this state of a qubit also a value of a qubit:
$$
|\psi\rangle = \...
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2answers
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How to initialize a qubit with a custom state in Qiskit Composer
I'm trying to initialize a qubit with a custom state in IBM's Qiskit Composer. I wrote the code in the Qiskit Lab and obtained the QASM code as shown below
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1answer
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How to calculate the overlap of the orthogonal state?
This is probably a very obvious question, but I am going through this problem set and I don't understand why in 1b) it says that it is obvious that $|\langle\psi_1^\perp|\psi_2\rangle|=\sin\theta$ ...
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1answer
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What is the most general quantum operation that preserves the marginal?
Suppose I have two states $\rho_{AB}$ and $\sigma_{AB}$ such that the marginals $\rho_A = \sigma_A$. What is the most general operation that could have acted on $\rho$ to output $\sigma$?
For example, ...
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If you apply a unitary transformation to an entangled state, is it still entangled?
See title. If this is not true, is there a counter example? If it is not true, does it hold true for certain combinations of unitaries and entangled states?
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Folded MPS state with Mid-circuit measurement
Among some documents I found to make a MPS state on quantum circuit, I can make it with stepped arrangement of unitary operators.
...
