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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 many observables do we need to confirm a qubit state?

Suppose I have many copies of a qubit in the pure state $\vert\psi\rangle$. How many distinct observables do I need to choose to determine that I indeed hold $\vert\psi\rangle$? For example, if $\vert\...
Alber's user avatar
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1 vote
1 answer
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Computing expectation of a SparsePauliOp using StateVector

I have a SparsePauliOp object $H$ acting on $N = 21$ qubits, and a statevector $|\psi \rangle$ acting on $N=21$ qubits. I need the expectation of $H$ using this state $|\psi \rangle$: $$\langle H \...
Soumyadeep sarma's user avatar
3 votes
1 answer
61 views

How to calculate guessing probability for quantum key distribution?

There are 3 Projections $P_1$, $P_2$, and $P_3$ corresponding to 3 inputs $x = 1, 2, 3$ for Alice. Similarly, the same projections are used by Bob for $y = 1, 2, 3$. Each input has 2 outcomes, $a = 1, ...
alpacino's user avatar
3 votes
1 answer
152 views

What's so bad about preparing magic states by measuring Clifford gates?

Suppose we want to perform a gate from the third level of the Clifford hierarchy for example $ T,CS, CCZ, CCX $. To implement such a gate using gate teleportation we need to take as an input certain ...
Ian Gershon Teixeira's user avatar
2 votes
2 answers
195 views

What exactly is the computational or standard basis?

A qubit is described by the elements of a vector space, right? Out of all those vectors why do we select 2 vectors and call them the computational or standard basis? Is the choice of these vectors ...
Boay's user avatar
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1 answer
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Can mixed states be on the boundary of the set of states?

I am confused over the behaviour of states that occupy the boundary of a given set of states. Can they be only pure states, or some mixed states too can occupy the boundary?
Anindita Sarkar's user avatar
1 vote
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33 views

Alice and Bob play a Multi-Qubit game

Well I am quite new to this so excuse me if the question is absurd Alice and Bob each can "measure" variables A and B respectively: Alice can use $a_1$ and $a_2$ methods of measurement while ...
qinnairen's user avatar
2 votes
1 answer
86 views

What is the connection between an observable and a gate?

I am reading some introductory quantum mechanics and I don't understand the connection between an observable and a gate. I thought a gate just applies a rotation to a state while a measurement gives ...
Katie's user avatar
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4 votes
2 answers
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What does it mean for a gate to "commute with a measurement"?

I think I understand intuitively what this means. For example, I can apply an $X$ gate and then perform a measurement in the $X$ basis and I will get the same post-measurement states as if I measured ...
user29393's user avatar
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57 views

How I can preform a unitary operation on the third qubit of the GHZ state [closed]

So I create the GHZ state already as the photo below $$ |\Delta\rangle=\frac1{\sqrt2}(|000\rangle+|111\rangle) $$ and also I preform a CNOT on the first qubit (as the target qubit), and the second ...
auswichemert's user avatar
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What is the minimum number of separable states (not necessarily pure) needed to decompose arbitrary separable states?

For a bipartite separable quantum state $\rho$ acting on Hilbert space $H\otimes H'$ with $\dim H=D$ and $\dim H'=D'$, what is the minimum number of separable state needed for a decomposition? That ...
Yujie Zhang's user avatar
1 vote
2 answers
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Is working with the |+> , |-> basis any harder than the |0>, |1> basis?

Say I have a code, for example the $ [[5,1,3]] $ code, and I want to (fault tolerantly) prepare the logical $ |+ \rangle $ state. Is that any harder than preparing the logical $ | 0 \rangle $ state? ...
Ian Gershon Teixeira's user avatar
2 votes
1 answer
141 views

Relation between expectation value and counts in reference to qiskit

I am quite confused with the expectation value. When we make measurements using the measurement gates, we get either 0 or 1. When we execute a large number of shots, we get the counts of different ...
Manu's user avatar
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1 answer
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States that verify behaviour of Pauli operators in Clifford circuits

I have a circuit composed of Clifford gates and Pauli-basis measurements. I am also told that a set of Pauli operators $P = \{ P_1, P_2, ..., P_n\}$ commute with the circuit. When I say that $P_i$ ...
Paulo's user avatar
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How does qiskit implement a given superposition in the actual quantum computer?

My question is phrased in 2 parts: Is there a quantum circuit to implement the following 4-qubit state: $$\frac{1}{2}(|1000 \rangle + |0100 \rangle + |0010 \rangle + |0001 \rangle)$$ When we use the ...
Soumyadeep sarma's user avatar
0 votes
1 answer
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How to convert from choi to chi matrix in qiskit

I have done a quantum process tomography experiment on a two qubit system. ...
idislikecoding's user avatar
1 vote
1 answer
55 views

Quantum algorithms to implement polynomial oracles

Let $N = 2^n$, and suppose $x = (x_0, x_1,\dots,x_{N-1}) \in \mathbb{C}^N$, such that $||x||_2 = 1$. Suppose we are given the $n$-qubit quantum state $\lvert x \rangle = \sum_{i=0}^{N-1} x_i \lvert i \...
Rahul Sarkar's user avatar
-1 votes
0 answers
12 views

Is there any method to obtain the post projection state using Qiskit?

As shown in image, I have two qubit state and a projection state. I want to obtain the normalized state after the projection operation using Qiskit. There is a way to do that using ancilliary qubit ...
Piyush Verma 19349's user avatar
1 vote
1 answer
183 views

Single bit teleportation for Hadamard gate

The circuit in Figure 13.7 of Gottesman's book https://www.cs.umd.edu/class/spring2024/cmsc858G/QECCbook-2024-ch1-15.pdf shows how to take the magic state $ T | + \rangle $ and use single bit gate ...
Ian Gershon Teixeira's user avatar
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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
1 vote
2 answers
65 views

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 [closed]

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
75 views

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
0 votes
0 answers
18 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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4 votes
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165 views

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
156 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
97 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
96 views

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
1 vote
0 answers
49 views

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
61 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
  • 153
0 votes
0 answers
32 views

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
61 views

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
  • 33
0 votes
1 answer
111 views

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
1 answer
36 views

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
26 views

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
252 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
  • 13
2 votes
1 answer
53 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
  • 57
2 votes
2 answers
60 views

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
  • 153
2 votes
0 answers
84 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
77 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
46 views

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
88 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
63 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
  • 23
0 votes
0 answers
41 views

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
33 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. ...
Lucas H's user avatar
  • 11
0 votes
1 answer
84 views

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
  • 33
1 vote
1 answer
53 views

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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