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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Eigenvalues of a quantum state after partial tracing

I am interested in the smallest nonzero eigenvalue of a quantum state. Does this eigenvalue always increasing after a partial trace i.e. the smallest nonzero eigenvalue of $\rho_A$ is always larger ...
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XX and YY and ZZ Hamiltonians in vqe

I'm trying to implement a vqe in cirq and I have sort of a brain knot. I have a 4 qubit chain with periodic boundary condition. So in fact a 2x2 qubit grid. Now 2 of them each are coupled. How do I ...
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Is there a circuit to compare two quantum states?

Lets have two quantum states (single qubits ones for simplicity) $|\psi\rangle$ and $|\phi\rangle$: $$ |\psi\rangle = \alpha_\psi|0\rangle+\mathrm{e^{i\varphi_\psi}}\beta_\psi|1\rangle $$ $$ |\phi\...
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Calculating outcomes of projective measurements

I'm pretty new to quantum computing, and I'm wondering how I can compute the outcome of a projective measurement of a spin along the +Z axis followed by a projective measurement along the -Z axis. I ...
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Can local projections increase entanglement?

Consider a generic bipartite pure state $\newcommand{\ket}[1]{\lvert #1\rangle}\ket\Psi\equiv \sum_k \sqrt{p_k}\ket{u_k}\otimes\ket{v_k}\in\mathcal X\otimes\mathcal Y$, where $p_k\ge0$ are the Schmidt ...
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Why is the lowest energy important to simulate a quantum system?

Quantum computers promise that they will simulate complex quantum systems, and I keep hearing that finding the ground state of that system (using for example Variational quantum eigensolver) is ...
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Deutsch-Jozsa Misunderstanding

I fail to understand Deutsch-Jozsa algorithm. As wikipedia suggests: ${\displaystyle f\colon \{0,1\}^{n}\rightarrow \{0,1\}}$. The function takes n-digit binary values as input and produces either a 0 ...
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Keeping data around in an entangled state: use cases

I'm following the IBM Quantum roadmap and really excited to see what the next 3 years bring. As part of the unveiling, they mentioned that the 1000 Qubit machine goal will really stabilize things with ...
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Bell state preparation

I was watching some lectures on qubits. They were talking about how to generate a Bell state. They described it as follows: Prepare state 00: $$\left |0 \right> \otimes \left |0 \right>$$ Apply ...
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1answer
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What is meaning of 'up to a global phase'? [duplicate]

What is the importance of global phase? How it affect a unit vector if we see it on a Bloch sphere? What is the meaning of 'up to global phase' in exercise 4.3 of Nielsen and Chuang?
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Question on output of SWAP test

Let's say I have two arbitrary quantum states $|\psi\rangle$ and $|\phi\rangle$. I apply the SWAP test circuit (something like what is given here), and measure the first qubit to get either $0$ or $1$....
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Google Colab - ImportError: The class MatplotlibDrawer needs pylatexenc

When I run the following command qc.draw(output='mpl') for my circuit qc, I get this error: ...
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Can Alice and Bob distinguish entangled state coefficients?

Suppose Alice and Bob share the quantum state $\frac{1}{\sqrt 2}(|x\rangle + (-1)^b |y\rangle)$ for some $x\neq y \in \{0,1\}^2$ and $b \in \{0,1\}$. They both do not know $x,y$, and use some ...
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What is the phase of state?

I am pretty new to Quantum Computing and am not exactly sure what the phase is. Could you please explain in terms of the Bloch sphere and point out how to mathematically calculate and represent the ...
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How to plot histogram using statevector simulator?

I'm trying to run my quantum circuit and plot the simulation result (counts) using the statevector simulator (to avoid 'shot noise'). However, instead of a 2-d histogram, the examples on Qiskit ...
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How can we only use 8192 shots for an experiment with 14 or more qubits?

Let's say you want to do an experiment with 14+ qubits. You apply some arbitrary unitary operator $U \in (\mathbb{C}^2)^{\otimes n} \times (\mathbb{C}^2)^{\otimes n}$ to the state $|\psi\rangle \in (...
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Effect of quantum entanglement on measurement

I'm taking a quantum information systems class and thought of this while trying to wrap my head around some material, so I apologize if this comes off as dumb or founded on misunderstandings. Say you ...
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QiskitError: 'No statevector for experiment

This is the code that I have used. Why can't i use get_statevecto when i use quantum computer. I got a state_vector when i have used qasm_simulator. ...
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What are magic states?

I wonder what are magic states, and a magic state gadget. While I'm reading a paper, the terms 'magic state' and 'magic state gadget' frequently appear.
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Preparing a state given access to projector

Let's say I am given access to a magical box that lets me apply a projector $|\psi\rangle \langle\psi|$, where $|\psi\rangle$ is a quantum state. I do not know anything about $|\psi\rangle$: just that ...
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1answer
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How can I print out the probability of a certain state in histogram?

This is a simulation I did in my program. I'm hoping to print out the probability of the state |0001> (which is 0.052), and store this number in a letter (a). How can I do this? Thanks!!
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1answer
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Relationship between trace distance and total variation distance

Consider two quantum states $\rho$ and $\sigma$ and the probability distributions induced by measuring both of them in the standard basis. Let’s call the probability distributions $p_{\rho}$ and $p_{\...
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1answer
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How do quantum gates work on qubits in the physical world?

How do quantum gates work on qubits in the physical world? What are different ways through which qubits can be manipulated in the physical world? For example, by analogy a classical NOT gate uses ...
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Example of a two-qudit state whose measurement outcomes are independent in one basis but dependent in another

If you have a pure composite system whose two subsystems are in a product state, then the outcomes of measuring the subsystems (in any basis) are statistically independent. If the subsystems are ...
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1answer
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In $|x_1,…,x_n\rangle$, can the individual constituents be called qubits?

A qubit is a quantum system in which the Boolean states 0 and 1 are rep- resented by a prescribed pair of normalised and mutually orthogonal quantum states labeled as ${|0⟩, |1⟩}$ According to [1]. ...
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Optimize chains of single-qubit u1, u2, u3 gates by combining them into a single gate in Qikist

Can anyone explain how Qiskit does the merging of single-qubit gates for the purpose of optimization? u1(lambda1) * u1(lambda2) = u1(lambda1 + lambda2) ...
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Create this state using CIRQ Coding language [closed]

I needed help with CIRQ coding as I'm quite new to Quantum Computing. I read the tutorials on CIRQ but don't really understand it. I'd be very thankful if someone could help. A program to create the ...
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Asymmetry in distributing phase change across components

The quantum computing text books and theory in general seems to have added an asymmetry in the distribution of change in phase across the components in the context of a qubit. Is there any reason for ...
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Can we always find a unitary operation connecting qubit states with given eigendecompositions?

Consider the density matrices $\rho_0 = |0 \rangle \langle 0|$ and $\rho_1 = |1 \rangle \langle 1|$. Let $\{p_1, p_2\}$, and $\{p_3, p_4\}$ be two probability distributions, that is, $$0 \leq p_1, p_2,...
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How to get state vector probabilities in Q#

Is there a similare function in Q# like Statevector.probabilities in Qiskit to get state vector probability, for example, if my circuit contains one qubit with one $H$ gate, the function returns ...
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1answer
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$N(\frac{1}{2},2)=3$ for vectors in a Hilbert Space

Came across This question regarding the maximum number of almost orthogonal vectors one can embed in a Hilbert space. They state that $N(\frac{1}{2},2)=3$, and that explicit construction of the ...
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Terminology: what do $|i\rangle$ and $|\mbox{-}i\rangle$ represent?

$|0⟩$ and $|1⟩$ are usually referred as the computational basis. $|+⟩$ and $|-⟩$, the polar basis. What about $|i\rangle$ and $|\mbox{-}i\rangle$? And collectively? Orthonormal states? References are ...
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Some questions to get intuition on Choi isomorphism [closed]

I have some questions about the Choi-Jamiolkowski isomorphism. I remind how it can be defined. First, we define $|\mathcal{I}_{H_0} \rangle \rangle \in H_0 \otimes H_0$ $$|\mathcal{I}_{H_0} \rangle \...
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Is there a nice characterisation for the set of extensions of a given state?

Let $\rho\in\mathrm{D}(\mathcal H)$ be a state in some (finite-dimensional) Hilbert space $\mathcal H$ and suppose that $\operatorname{rank}(\rho)=r$. This means that we can write it as $$\rho = \sum_{...
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Defining dimension of an operator in qutip

My main question: Can someone please explain to me how the list of array is used to define the dimension in qutip ? context: If I have my density operator ...
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Is there a proof or example to show that a noiseless subsystem is not necessarily closed under addition?

In a text (section 3.6 page 92) about noiseless subsystems by D. Lidar, it is mentioned:'A subsystem is a tensor factor in a tensor product, and this does not have to be a subspace (e.g., in general ...
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Why does full state reconstruction require at least $N+1$ MUBs?

Consider an $N$-dimensional space $\mathcal H$. Two orthonormal bases $\newcommand{\ket}[1]{\lvert #1\rangle}\{\ket{u_j}\}_{j=1}^N,\{\ket{v_j}\}_{j=1}^N\subset\mathcal H$ are said to be Mutually ...
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Limitations on the number of qubits for a $\mathrm{CNOT}$-gate in cluster states

I'm reading about cluster states using this online source. It is explained that a CNOT can be performed on cluster states using as little as $4$ qubits. However, the standard implementation is with $...
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What are the I, X, Z gates in quantum gates? [closed]

Can someone please explan how the $\rm I$, $\rm X$ and $\rm Z$ gates work? If $\rm{I = X^2 = Z^2}$, can you explain why this is the case or why it wouldn't work?
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Is there a name for $Z_{1}(|\mathrm{GHZ}\rangle)$?

The GHZ state is defined as $|\mathrm{GHZ}\rangle = \frac{|000\rangle + |111\rangle}{\sqrt{2}}$. Is there a name for the phase flipped GHZ state, i.e. $Z_1(|\mathrm{GHZ}\rangle)=\frac{|000\rangle - |...
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1answer
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What is the right way to prepare a specific qubit state in Qiskit / Q#?

There are two possibilities to prepare a qubit in a particular state like $ | - \rangle $ in Qiskit. The first approach is using the initialize function: ...
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Is spontaneous excitation possible?

I know the $|1\rangle$ state can relax spontaneously to the $|0\rangle$ state, but can the opposite also happen?
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Qiskit: Initializing n qubits with binary values (0s and 1s)

Is there a way in Qiskit to initialize $n$ qubits with binary values (0s and 1s)? For example, how can I initialize two qubits in the state $|11\rangle$? Here is a code snippet: ...
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How do you CNOT between qubits faraway from each other?

I'm just curious. Say I have 3 qubits on a straight line 0-1-2. How do you guys (on the IBMQ or Rigetti team for example, or anyone who actually works on quantum computer) entangle 0-2 if I, say, am ...
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How does noise affect the implementation of quantum gates?

I am trying to think about quantum noise visually here. If, for example, one wants to implement an X-gate to perform a 180-degree rotation around the Bloch Sphere. In a perfect world, the X-gate will ...
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Quantum Ising model correlation function query

In this paper on quantum Ising model dynamics, they consider the Hamiltonian $$\mathcal{H} = \sum_{j < k} J_{jk} \hat{\sigma}_{j}^{z}\hat{\sigma}_{k}^{z}$$ and the correlation function $$\mathcal{G}...
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What is the matrix for measuring a superposition of general number of qubits in standard basis?

Let's say I have the state of the system of 2 qubits: $\frac{1}{\sqrt{3}}|00\rangle+\frac{2}{\sqrt{3}}|10\rangle$, and I want to measure it in the standard basis. How would I write it mathematically? ...
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Are all pure entangled states `robust'?

Let $\mathcal{H}_A \otimes \mathcal{H}_B$ be the tensor product of two finite dimensional Hilbert spaces, let $d = \operatorname{dim}(\mathcal{H}_A \otimes \mathcal{H}_B)$ and let $| \psi \rangle \in \...
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Why an element of SU(2) acts as a rotation for Majorana representation of states?

I know that for a given spin-j quantum state, say $\vert\psi\rangle = (\psi_0 , \psi_1 , \cdots , \psi_{2j})$, we can construct a polynomial as follows $ w(z) = \sum_{k = 0}^{2j} (-1)^k \psi_k \sqrt{\...
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How can the Holevo bound be used to show that $n$ qubits cannot transmit more than $n$ classical bits?

The inequality $\chi \le H(X)$ gives the upper bound on accessible information. This much is clear to me. However, what isn't clear is how this tells me I cannot transmit more than $n$ bits of ...

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