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Questions tagged [quantum-state]

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

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How to represent unitary evolution in Python?

How to represent $U(t)$ (a unitary operator) in a code? Is there any package available for that in Python?
saaru darshini's user avatar
3 votes
1 answer
598 views

Expressing a quantum state as a polynomial

Let us consider the state $\left|\psi\right>$ obtained by applying $m$ 1- and 2-qubit gates to $n$ qubits, starting from the state $\left|0,0,\dots\right>$. Let us express it as: $$ \left|\psi\...
Doriano Brogioli's user avatar
1 vote
1 answer
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What is the input when simulating a quantum state?

Currently I am simulating a quantum gate using verilog. I learned that: $$ |\psi\rangle = \alpha|0\rangle + \beta|1\rangle $$ I want to ask: when simulating, should I let alpha and beta be complex ...
Bakeu's user avatar
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coding a hamiltonian for an ion trap system

How do I represent $$a_k ∣n_1 n_2 n_3 ,,,,n_n⟩ = √nk-1 ∣n_1 n_2 n_3 ,,,,n_n⟩$$ and $$a_k^\dagger ∣n_1 n_2 n_3 ,,,,n_n⟩= √nk-1 ∣n_1 n_2 n_3 ,,,,n_n⟩$$ in python(qutip or qiskit preferably) and where ...
saaru darshini's user avatar
1 vote
1 answer
62 views

How cat state is constructed?

Context: On Wikipedia, a cat state (2-component) is defined as $$ |\text{cat}_+\rangle = C_+(|\alpha\rangle + |-\alpha\rangle) $$ $$ |\text{cat}_-\rangle = C_-(|\alpha\rangle - |-\alpha\rangle), $$ ...
Martin Vesely's user avatar
4 votes
2 answers
218 views

Can a non-local unitary operator preserve separability

Consider a $2$-qubit system with Hilbert space $\mathcal{H} \cong \mathcal{H}_1 \otimes \mathcal{H}_2$. A pure separable state in $\mathcal{H}$ is of the form $\lvert \psi_1 \rangle \otimes \lvert \...
Silly Goose's user avatar
8 votes
1 answer
532 views

Is there a comprehensive list of counterexamples in quantum information?

As was already asked about in this phys.SE question many years ago---which, sadly, got closed and never received an answer---is there a collection of counterexamples in quantum information theory, &...
Frederik vom Ende's user avatar
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51 views

State tomography in Qiskit on a subset of qubits of real QPU

Could anyone please explain how should I carry out a state tomography on a real device in Qiskit (version 0.43.2)? I have access to devices with 127 qubits, but I want to perform a simulation using ...
Andrea's user avatar
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1 vote
1 answer
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Proability of measuing a qubit in a two qubit system without having a perpendicular basis

I am trying to understand how to apply Born's rule on two qubit systems. From class, the teacher told us that we can write the state like so: only if $\theta_0$ and $\theta_1$ are ortogonal. But now ...
Filat Nicolae's user avatar
3 votes
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+50

Almost perfect quantum encryption of a mixed state using only $n + O(\log(n) +\log(\frac{1}{\epsilon}))$ shared bits

Alice holds a state $\psi$ of $n$-qubits, and wants to send it to Bob using a single quantum message. Bob and Alice share only $n + O(log(n) +log(\frac{1}{\epsilon}))$ random bits, for some value $\...
Gabi G's user avatar
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2 votes
1 answer
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To understand the notation of $| a, a \oplus b \rangle$

This must be trivial but I can't find a clear explanation of the notation of $| a, a \oplus b \rangle$. It is the resulting state after applying a CNOT gate to $|a,b\rangle$: $\rm{CNOT}|a,b\rangle = | ...
fishjojo's user avatar
3 votes
2 answers
91 views

Are measurements in $X$ and $Z$ bases being equal enough to prove equality of quantum states?

Suppose I have two single qubit states $\rho$ and $\sigma$. In my example, they are pure but I keep it general here. Suppose I know that $$\text{Tr}(\vert +\rangle\langle +\vert\rho) = \text{Tr}(\vert ...
user1936752's user avatar
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What is the role of color in color code? ( theoritically and exprimentally)

We know that the color code has an extra element relative toric code . It is color . I want to know what is the role of color ?
Mohsen's user avatar
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7 votes
2 answers
304 views

How can quantum error correction correct small rotations/continuous errors?

I'm having trouble understanding the so-called "digitization of errors" argument in QEC. Suppose I have to encode my logical qubit into $n$ physical qubits to do error correction. I will use ...
Joan's user avatar
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1 answer
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How to convert one state of a quantum system to a desired state?

I have a state of 3 qubits: The first number inside the brackets gives the probability of each state, and the second number gives the phase. $$\begin{align} |000\rangle &= (12.5,0^{°}),\\ |001\...
Root Groves's user avatar
1 vote
2 answers
57 views

How to generate the Bell state $\frac{1}{\sqrt{2}}(|01\rangle+|10\rangle)$ from the state $|00\rangle$ using Qiskit?

I want to generate the Bell state $(|01\rangle+|10\rangle)/\sqrt{2}$ from the state $|00\rangle$ in qiskit, applying the Hadamard gate followed by the $\text{CNOT}$ gate. But it generates $(|11\rangle-...
Xilot Xilot's user avatar
3 votes
1 answer
152 views

Why is the coefficient-squared the probability, and not just the coefficient itself?

Context: I have decided not to accept the postulates of quantum mechanics blindly as gospel. There must be a way someone arrived at those postulates, and I want to know the basic reasoning behind them,...
Abhay Agarwal's user avatar
0 votes
2 answers
52 views

How can I get the state of my quantum circuit like save_statevector() in qiskit 1.0.2?

Just as the title, I want to get the state of my quantum circuit when running simulation locally with fake provider. But I cannot use save_statevector since Aer has been removed from qiskit. My code ...
MrEightL's user avatar
2 votes
2 answers
59 views

How to create a qudit of any dimension $d$ in qiskit?

How to create qudit, not qubit (which is a special case of qudit with $d = 2$) in qiskit of any dimension $d$? Actually, I searched this on chatgpt, but not-so-helpful info was found. It just uses ...
sudhanshu's user avatar
2 votes
1 answer
65 views

Getting rid of extra qubits without changing phase

If I have the state $\frac{1}{\sqrt2}|0000\rangle + \frac{e^{i\phi}}{\sqrt2}|1111\rangle$ and need to get $\frac{1}{\sqrt2}|0\rangle + \frac{e^{i\phi}}{\sqrt2}|1\rangle$, does anyone have any ideas ...
bruhcobell's user avatar
3 votes
2 answers
250 views

Prove that there is no polynomial size quantum algorithm for a Simon's problem with no promise on the input

We look at the following variant of Simon's problem. There is an algorithm $A$ that solves a problem with the following settings: The input is an oracle $f:\{0,1\}^n \to [M]$. The output of the ...
Gabi G's user avatar
  • 199
2 votes
2 answers
57 views

Can Interaction with the environment cause $|0\rangle$ to evolve into a superposition like $|+\rangle$?

We say if a qubit is in state $|0\rangle$, and it is possible if it interacts with the environment it can result in a bit flip to a state $|1\rangle$, so I was wondering why can't it go to a ...
Kutubkhan Bhatiya's user avatar
4 votes
2 answers
94 views

Show that all extensions of $\rho$ can be obtained as a channel applied to its purification

I am struggling with this exercise here: Let $H:A, H_E$ and $H_{E′}$ denote complex Euclidean spaces. Consider a purification $|ψ_{AE}⟩⟨ψ_{AE}| ∈ D(H_A ⊗ H_E)$ of a quantum state $ρ_A ∈ D(H_A)$ and a ...
Pink Elephants's user avatar
1 vote
3 answers
176 views

Equivalence of quantum circuits

I have these 2 quantum circuits: Are they equivalent?I think they are but I cannot understand how this could be possible.Lets assume that the initial condition of the first circuit is:] Lets assume ...
Root Groves's user avatar
2 votes
1 answer
48 views

Existence of a two-outcome measurement $M$ such that the induced distributions differs between different density matrices

Let $\rho \neq \sigma$ be density matrices. I want to show that there exists a two-outcome measurement $M$ such that the induced distributions $M(\rho)$ and $M(\sigma)$ differ. From what I learned, ...
Gabi G's user avatar
  • 199
2 votes
0 answers
19 views

Interested in software helping with projecting multi-qubit states onto irreducible components

My interest in QC comes from a problem in geometry called the Atiyah problem on configurations of points. In short, there is a nice one-to-one correspondence between quantum states of a single qubit ...
Malkoun's user avatar
  • 178
0 votes
1 answer
37 views

Efficient computation of probabilities for an N-particle state

Suppose we have a state that is written as: \begin{eqnarray} |\Psi\rangle=\frac{1}{\mathcal{N}}\sum_{\mathcal{P}}e^{i\phi_p}\phi_{1p}(x_{1p})\phi_{2p}(x_{2p})...\phi_{N_p}(x_{N_p})|x_{1p}...x_{Np}\...
Zarathustra's user avatar
2 votes
1 answer
52 views

What is the difference between symmetric states and geometrically uniform states?

On the one hand, in this article, symmetric states are defined as: The $M$ symmetric quantum states which should be distinguished by means of the quantum measurement are described by statistical ...
yosh's user avatar
  • 127
1 vote
0 answers
46 views

State amplification in Grover when starting with W state

I have two 3-qubit registers, each one is prepared in $W$ state, so my two registers are in state: $$\left|W_3\right\rangle\otimes \left|W_3\right\rangle \ ,$$I use this (6-qubits) diffusion operator ...
user12910's user avatar
  • 451
2 votes
3 answers
131 views

Is $|A\rangle = \frac{1}{\sqrt2} |00\rangle + \frac{1}{\sqrt2} |01\rangle$ a valid quantum state?

Is $|A\rangle = \frac{1}{\sqrt2} |00\rangle + \frac{1}{\sqrt2} |01\rangle$ a valid quantum state? Or does a quantum state need to be a superposition of the entire basis, i.e., $$ |A\rangle = \frac{1}{...
user29495's user avatar
1 vote
0 answers
32 views

How to obtain this measurment result for arbitrary qubits in $X$ basis?

I have seen the following claim. Suppose one has two qubits $\vert\psi\rangle = a\vert 0\rangle + b\vert 1\rangle$ and $\vert\phi\rangle =a'\vert 0\rangle + b'\vert 1\rangle$ and both are measured in ...
Lorraine's user avatar
3 votes
2 answers
241 views

Is it always possible to write the state corresponding to a set of stabilizer generators?

Given a set of stabilizer generators, is it always possible to write down the state corresponding to it? Is there a way to write down the quantum state corresponding to a stabilizer generator?
Dotman's user avatar
  • 133
0 votes
1 answer
51 views

How can I shift elements around in my state vector according to a specific pattern?

Consider the statevector $|\psi_1\rangle=(a_0,...,a_{N-1})^T$. My goal is to shift the elements around to end up with $|\psi_2\rangle=(a_{3N/4},...,a_{N-1},a_0,...a_{N/2},\vec{\phi})^T$ where $\vec{\...
thespaceman's user avatar
1 vote
2 answers
124 views

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
1 vote
1 answer
41 views

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
1 vote
1 answer
81 views

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
  • 153
1 vote
1 answer
57 views

Is there a proof that any pure two-qubit Partially entangled state lies somewhere in between a separable and maximally entangled state?

Intuitively this seems true, but is there a proof of the following: We have two-qubit pure state. Given a Partially entangled state (PES) $|P\rangle$ we can always find a separable state $|S\rangle$, ...
Sutasu's user avatar
  • 153
1 vote
0 answers
23 views

Entanglement generation for commuting Hamiltonian

Consider an $n$ qubit Hamiltonian $H$ given by \begin{equation} H = \sum_{i=1}^{m} H_i, \end{equation} where each $H_i$ is a $k$-local term and it holds that \begin{equation} e^{H} = e^{H_m} \cdot e^{...
BlackHat18's user avatar
  • 1,313
-1 votes
1 answer
93 views

How to calculate a density matrix of a given circuit?

I want to find the density matrix of the following quantum circuit, is it correct: [[0.12499999+0.j 0.12499999+0.j 0.12499999+0.j 0.12499999+0.j 0.12499999+0.j 0.12499999+0.j 0.12499999+0.j 0....
Frank Hansen's user avatar
3 votes
1 answer
83 views

A separable pure bipartite quantum state must be a product state

I'm looking for the simple argument to prove that a separable pure bipartite quantum state is in fact a product state. This question comes from a statement in Wikipedia on separable states: In the ...
JMark's user avatar
  • 163
0 votes
0 answers
52 views

Where is my mistake in using a measurement operator instead of Born’s rule to calculate the probability of detecting photons at an arbitrary angle?

As I asked in this question: How can I calculate the measuring probabilities of a two qubit state along a certain axis? From here I know how to calculate the probability of measuring a general state ...
Alex1111's user avatar
-3 votes
1 answer
70 views

How would you name the gate which maps $|x\rangle\rightarrow |(x+1)\text{mod}\hspace{1mm}n\rangle$

Suppose you have a qudit with $n$ decoherent states. How would you name the gate which maps $|x\rangle\rightarrow |(x+1)\text{mod}\hspace{1mm}n\rangle$
Root Groves's user avatar
1 vote
0 answers
38 views

Turn expectation values back into classical data

How are expectation values turned back into classical data for evaluation? I have a circuit performing a regression task that returns the expectation value of the Pauli Z operator. I would like to ...
camaya's user avatar
  • 11
4 votes
1 answer
193 views

Why do we have an infinite number of possible quantum gates?

This question came to me during an online lecture by Prof. Nike Dattani, he mentioned that we have "an unlimited number of quantum gates". Simply my question is: why do we have an unlimited ...
JaafarMehrez's user avatar
2 votes
0 answers
23 views

Implement Phase disk in Qiskit

I'm new to qiskit and looking to enhance my output with visualization. Specifically, I'm interested in using the Phase Disk visualization, similar to the one shown in the image below. Can anyone ...
Milen Ninan's user avatar
2 votes
1 answer
33 views

How is the expression $\frac{\|\rho^{T_B}\|-1}{2}$ obtained from the definition of negativity?

In quantum information theory, negativity is defined as summation of the absolute values of negative eigenvalues of the partial transposed density matrix. The expression of negativity is given as $$ \...
Anindita Sarkar's user avatar
2 votes
2 answers
223 views

What is the relation between the purity of a bipartite state and its subsystems?

I know for a separable state $\rho_{AB}$ we have $$P_{AB}= P_{A}=P_{B}=1$$ Where P is purity. What if the relation between the purities when the bipartite state is entangled? Is there any inequality ...
reza's user avatar
  • 689
2 votes
1 answer
43 views

Quantum Information Retrieval from Bipartite Mixed States under LOCC: Maximizing Individual State Knowledge

In the context of Local Operations and Classical Communication (LOCC), given a bipartite mixed state represented as $\rho=\frac{1}{n}\sum_{i=1}^n|\psi_i\rangle\langle\psi_i|$, where $|\psi_i\rangle$ ...
Pratapaditya Bej's user avatar
0 votes
0 answers
41 views

How to calculate the state vector of a circuit using sampler().run()

I run a circuit using: jobCircuit = Sampler(backend).run(circuit) resultCircuit = jobCircuit.result() How can I access to a state vector of the circuit? I tried ...
alejandra's user avatar
2 votes
1 answer
164 views

Qiskit Runtime forbids reset gate?

Some parts of my quantum circuit uses initialize to prepare specific amplitudes to the qubits. However, the Qiskit Runtime outputs error: ...
Deren  Liu's user avatar

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