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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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Take kronecker product of non-adjacent qubits

Suppose I have 4 qubits and I have the density matrix on qubits 1, 3 and I want to take the tensor product with the identity on the 2nd and 4th qubits for example. What is the fastest way to code this?...
snickers_stickers's user avatar
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2 answers
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No-cloning theorem and distinguishing between two non-orthogonal quantum states revisited revisited

There are many posts to this question from Nielson and Chuang's Quantum Computation and Quantum Information Exercise 1.2 page 57. It is required to prove that if a hypothetical device exists, which ...
Manit Agarwal's user avatar
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How to represent a general 3-qubit state as a symmetric ZX-diagram with 14 parameters?

A general pure 1-qubit state can be written as a ZX-diagram like this: Correspondingly, for a general pure 2-qubit state: How can a general pure 3-qubit state be written as a ZX-diagram? Two things ...
qubitzer's user avatar
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How to determine the single-qubit gate if we know an initial and corresponding final state

HOW TO FIND A QUANTUM GATE IF WE KNOW THE INITIAL AND FINAL SINGLE QUBIT STATES? I tried thinking by using projection vectors like ket 0 goes to ket I, then we can take the ket 0 bra I, but the ...
Anonymous's user avatar
2 votes
1 answer
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How to verify that a certain gate was applied to a quantum code

Suppose I have a quantum error correcting code $|\psi \rangle = \alpha | 0 \rangle + \beta | 1 \rangle$, say the $[[7,1,3]]$ Steane code for concreteness. Suppose there is a black box that either ...
Eric Kubischta's user avatar
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14 views

How do I perform measurements in the X basis for qutrits in cirq?

After applying the hadamard gate to a 0 state qutrit, I should be able to get it into the + state, but how do I then measure the circuit in the X basis as opposed to the computational basis?
Son100's user avatar
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Can the W state, or any non-stabilizer state for that matter, be considered a magic state?

Some examples of magic states (these can all be found here): the $ |T\rangle $ state for implementing the $ T $ gate is $$ T | + \rangle = \frac{1}{\sqrt{2}}(|0\rangle + e^{i\pi/4}|1\rangle) $$ A $ |...
Ian Gershon Teixeira's user avatar
7 votes
1 answer
142 views

What is the stabilizer rank of the W state?

The $ n $ qubit $ W $ state is defined here https://en.wikipedia.org/wiki/W_state The stabilizer rank of a quantum state $|\psi\rangle$ is the minimal $r$ such that \begin{equation} |{\psi}\rangle = \...
Ian Gershon Teixeira's user avatar
2 votes
1 answer
81 views

Finding Eigenvectors of a Unitary in a Quantum circuit

I have a unitary gate $U$, which is applied on some $n$-qubit quantum circuit ($n=7$ for my scenario). I wish to find the $n$-qubit state, which is the eigenvector (and possibly eigenvalues) of this ...
Soumyadeep sarma's user avatar
2 votes
1 answer
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Common ways to fault tolerantly prepare a stabilizer state

It is my impression that it is much easier to fault tolerantly prepare a stabilizer state than it is to prepare a magic state. What are some common ways to fault tolerantly prepare a given stabilizer ...
Ian Gershon Teixeira's user avatar
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is this a novel approach to visualization of qubits?

I am currently working on my Bachelor's Thesis and would love to hear your opinions about my project. The idea is to visualize the Binary parts of complex qubit states. White lines represent binary 0, ...
Mathias Pichler's user avatar
2 votes
1 answer
55 views

What is XX/YY/ZZ-interaction (or coupling)?

I see this term is used in many places [1,2,3,4]. I feel that it is about the $\sigma_{x/y/z}\otimes\sigma_{x/y/z}$ term in the Hamiltonian, but even I take this interpretation, I don't understand ...
Ziyuan's user avatar
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Are $\delta$-close logical states of a code also close in terms of physical states?

If I have two logical states of a quantum code that are close in trace distance i.e. $\vert 0\rangle_L$ and $U_L\vert 0\rangle_L$ where $\|U_L - I\|_{\diamond} \leq \delta$, what is an upper bound (if ...
John Doe's user avatar
3 votes
2 answers
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Is every pure 1-qubit state an eigenstate of $aX + bY + cZ$?

As stated in the question, I have seen this claim made that a pure state can be written as an eigenstate of $aX + bY + cZ$ for some $a,b,c$ where $X,Y,Z$ are Pauli matrices. Why is this true and what ...
qubit's user avatar
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How to convert states |0011⟩, |1100⟩, |0101⟩ to |1111⟩?

How can I use X gate (quantum not) to convert each of the pure states |0011⟩, |1100⟩, |0101⟩ to |1111⟩ with Qiskit? My programming assignment is Using the idea of a multi-controlled phase gate, now ...
Jettapol's user avatar
-2 votes
0 answers
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What is the meaning of $Tr(L^\dagger L\rho)-Tr(L^\dagger\rho L\rho)$?

Consider the non-Hermitian matrix $L$ and the Hermitian positive semidefinite matrix $\rho\geq0$ with $Tr(\rho)=1$. What is the physical meaning of $Tr(L^\dagger L\rho)-Tr(L^\dagger\rho L\rho)$?
Kohei's user avatar
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2 votes
1 answer
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How to apply gates on a subspace of a superposition of qubits?

Let us say that I have the state $a|00\rangle + b|01\rangle + c|10\rangle + d|11\rangle$. I wish to apply a one-qubit unitary (a $2\times2$ matrix) U on the subspace spanned by $|01\rangle$ and $|10\...
Soumyadeep sarma's user avatar
1 vote
1 answer
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How to calculate the number of m-partitions of an N-partite quantum state?

I am reading the structure of multipartite entanglement from section 3.3. It is stated there that the number of possible partitions of $N$ parties into $m$ parts is given by $\frac{m^N}{m!}$. I could ...
Anindita Sarkar's user avatar
1 vote
1 answer
247 views

Why is the Pauli Y gate eigenstate so hard to create?

In a lot of quantum computing formalism, it is relatively easy to create $\vert 0\rangle$, $\vert 1\rangle$, $\vert +\rangle$ and $\vert -\rangle$. However, it is hard to create $\vert i\rangle$. Why ...
Polp's user avatar
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2 votes
1 answer
31 views

Relation between Rz gate and Phase gate

As I know, the $Rz(\frac{\pi}{2})$ gate is equivalent to the Phase gate $S$ up to the global phase. However, I found using qiskit, the $Rz(\frac{-\pi}{2})$ is also equivalent to the Phase gate $S$. I ...
Amanli's user avatar
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2 votes
2 answers
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Can a SLOCC protocol work only in one direction?

Two states $|\psi\rangle$ and $|\phi\rangle$ are equivalent under SLOCC protocol if $|\psi\rangle$ can be converted to $|\phi\rangle$ and vice versa via LOCC with a finite probability of success. Thus ...
Anindita Sarkar's user avatar
1 vote
0 answers
53 views

Prove that convex combinations of product states admit a hidden variable model

Define product states as simple tensors $\rho_1 \otimes \rho_2$ and separable states to be (trace) norm limits of convex combinations of product states. We say that a state $\rho$ admits a hidden ...
truebaran's user avatar
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2 votes
0 answers
76 views

Uniqueness, absolutely maximally entangled states, and the 3 qutrit code

There is a well known $ [[3,1,2]]_3 $ qutrit stabilizer code with stabilizer generators $ XXX $ and $ ZZZ $. This code is related to a $ [[4,0,3]]_3 $ qutrit stabilizer state with stabilizer ...
Ian Gershon Teixeira's user avatar
1 vote
1 answer
72 views

Does measuring the operator $XX$ preserve superpositions in a given two-qubit state?

Suppose I have a state $$\vert\psi\rangle = a\left(\frac{1}{\sqrt{2}}\vert\Phi^+\rangle + \frac{1}{\sqrt{2}}\vert\Phi^-\rangle\right) + b\left(\frac{1}{\sqrt{2}}\vert\Psi^+\rangle + \frac{1}{\sqrt{2}}\...
Vladimir's user avatar
2 votes
3 answers
92 views

Is an unobserved measurement represented by a mixed state?

If I take a $\vert +\rangle$ state and measure it in the $Z$ basis but do not look at the measurement outcome, how should I describe the state? Is it just a mixed state $$\frac{1}{2}\vert 0\rangle\...
Vladimir's user avatar
2 votes
1 answer
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Is there a unitary mapping every state in the upper half of the Bloch sphere to $|0\rangle$?

I am having trouble finding a way to map certain parts of the Bloch sphere to |0> and leave the rest intact. For example, let's think of a state vector $|\psi \rangle = \alpha |0 \rangle + \beta |1 ...
Honza Svoboda's user avatar
0 votes
1 answer
87 views

How can I represent quantum states $|0\rangle$ and $|1\rangle$ in $x$ and $y$ bases?

For example, two persons choose at random whether to measure their particle in the $x$ or $y$ direction (basis). We first define $x$ and $y$ eigenstates: $|+x\rangle =\frac1{\sqrt2}(|0\rangle + |1\...
ibtissam's user avatar
2 votes
1 answer
60 views

weird negative sign in a state vector in qiskit

I run the following simple code in qiskit, which get statevector of a quantum circuit. ...
mike_gz's user avatar
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0 answers
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Is there any well defined notion of "the state of a qubit X" if $X$ is a member of a larger qubit system

I'm trying to understand the effect of "measurement" as a gate. But my question is more elementary than that. Consider the following simple quantum circuit: $(X,Y)$ begins in the state $1 ...
Sidharth Ghoshal's user avatar
0 votes
1 answer
32 views

Two Quantum State Density Matrices with Unequal Off-Diagonal Elements but Equal Magnitudes

I recently read Kitaev's paper on magic state distillation. I want to verify whether the circuit for the [5,1,3] encoder can map a single qubit state T_0 to the logical state T_1 in the encoded space. ...
Xiao H's user avatar
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0 votes
1 answer
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How to implement a depolarizing noise channel for qutrits using cirq?

Anyone have any idea how I can implement a depolarizing noise channel for qutrits using cirq? Say using the kraus operators within a class inheriting from cirq.Gate or so?
Son100's user avatar
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1 vote
1 answer
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Quantum circuit of stateful oracle

Suppose I have operator $U_f$ that maps state $|x\rangle|y\rangle|0\rangle$ to another state $|x\rangle|y\rangle|f(x, y)\rangle$. The function $f$ has its internal state, that changes on each ...
Georgy Firsov's user avatar
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0 answers
17 views

Quantum Channel with least disturbance for any input and output dimensions

Let $n$ and $m$ be two arbitrary dimensions of the input Hilbert space and output Hilbert space respectively. What is the quantum channel that preserves information as much as possible (i.e. with the ...
Shadumu's user avatar
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1 vote
1 answer
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Matrix representation of the symmetric subspace for two copies

Consider two copies of an $n$ qubit Haar random state, given by: \begin{equation} \rho = \mathbb{E}_{U \sim \mathsf{Haar}}\left[U |0^n\rangle \langle 0^n| U^{*}\otimes U |0^n\rangle \langle 0^n| U^{*}\...
BlackHat18's user avatar
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6 votes
2 answers
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If Alice measures a qubit and doesn't tell Bob the result, what's Alice's state from Bob's perspective?

Suppose Alice has a qubit $|\phi\rangle=\alpha|0\rangle+\beta|1\rangle$ and measures it. Bob knows the initial state but not the result of her measurement. So after the measurement, Alice knows what ...
mp12853's user avatar
  • 63
2 votes
2 answers
54 views

Can save_statevector() be used on a real quantum computer?

In a real quantum computer, can the save_statevector function be used to obtain the state vector of a circuit? I attempted to run the following code on a real ...
MrEightL's user avatar
2 votes
1 answer
109 views

What are classical analogies for the notions of superposition, entanglement, and interference?

I'm working on a conceptual explanation of quantum computing properties and have used analogies to make the ideas more accessible. I'd appreciate feedback on the validity of these analogies from those ...
qwerty's user avatar
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3 votes
1 answer
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Is there a quantum circuit to distinguish between $|0 \rangle$ and $\frac{1}{\sqrt{2}} (|0 \rangle + |1 \rangle)$?

Is it possible to construct a quantum circuit, using any unitary and measurement operations, that can distinguish $|0 \rangle$ and $\frac{1}{\sqrt{2}} (|0 \rangle + |1 \rangle)$? In my estimation, the ...
Julia Kim's user avatar
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3 votes
1 answer
159 views

How to understand the idea of maximal entanglement intuitively?

I am trying to understand what it means for 2 qubits to be maximally entangled. When I look for information online or in books all I can find are rigorous mathematical definitions which I find a bit ...
Omeglac's user avatar
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2 votes
1 answer
115 views

Is $\rho = \sum_{j} p_j|n_j\rangle\langle n_j|$ a valid construction for any mixed state?

I have a mixed state $\rho$ and its hamiltonian $H$. Firstly, I find the eigenvalues $\{p_j\}$ of $\rho$, and orthonormal basis of $H$. I write $\rho$ in terms of $H$'s eigenstates and $\rho$'s ...
Việt Nguyễn's user avatar
1 vote
1 answer
146 views

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
946 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
54 views

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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1 vote
1 answer
64 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
230 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
20 votes
6 answers
1k views

Counterexamples in quantum information theory

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
1 vote
0 answers
58 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
  • 11
1 vote
1 answer
67 views

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
2 votes
1 answer
61 views

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
92 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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