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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(Quantum Computing/Machine Learning) Estimate of the absolute value of the probability amplitude of |0⟩ in the superposition?

You are given a source of an unknown qubit state. You make measurements in the computational basis, that is, your measurement is {|0⟩⟨0|,|1⟩⟨1|} . You observe that you see the outcome zero 30 times ...
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Find the local unitary that takes the bell state to a state phi that has an extractable bell state

I have a state |p> that has an extractable Bell state and I want to write it as a Bell state, |b>, with a local unitary acting on one side. Basically I am trying to find a local unitary U that ...
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Is there any meaning for a density operator if we omit the j-th row and column in quantum mechanics?

Assume we have a density operator (Hermitian, PSD, with trace 1) called A for a particle. $v_i$ shows the i-th eigenvector of A and $\lambda_i$ shows the i-th eigenvalue. I assume that the elements of ...
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What is the average value of $|c_i\bar c_j|$ for a random state $|\psi\rangle=\sum_i c_i|i\rangle$?

Consider the density matrix $\rho=|\psi\rangle\!\langle\psi|$ of a random pure state in an $N$-dimensional space (in other words, an $N$-dimensional qudit, $|\psi\rangle\in\mathbb C^N$), $\rho_{ij}=...
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Bloch Sphere - Rotation Matrix

A qubit is given in the following form: $\left|\psi\right\rangle = \cos\left(\dfrac{\theta}{2}\right)\left|0\right\rangle + e^{i\phi}\sin\left(\dfrac{\theta}{2}\right)\left|1\right\rangle$. Let's ...
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Non maximally entangled states for QKD

Why aren't non maximally entangled states produced and used in quantum key distribution schemes? What would be the advantage/disadvantage to use such states rather than maximally entangled ones?
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The correct set of measurement operators on a mutiple qubit system

I was wondering if the complete set of measurement operators for a state : $|\phi \rangle=c_{00}|00\rangle+c_{01}|01\rangle+c_{10}|10\rangle+c_{11}|11\rangle$ Would be given by : $P_0\otimes I=|00\...
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How do I interpret the readout error for a quantum computer?

For example, the ibmqx2 computer has the most recent readout error of $4.40 \cdot 10^{-2}$. Does this mean per 1000 measurements, 44 faulty results exist?
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Holevo quantity and mutual information

On this page, it is stated that the Holevo quantity is an upper bound to the accessible information of a quantum state. In the scenario where Alice encodes classical information into a quantum state ...
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Is phase factor negligible in fidelity of quantum states?

One well-known fidelity is defined as $(Tr\sqrt{\sqrt{\rho}\sigma\sqrt{\rho}})^2$. And for pure states, fidelity is always in the form $|\langle\psi|\phi\rangle|^2$. As we know, in the context of two-...
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How is CNOT gate physically implemented in IBM Q?

This is because if control qubit is in arbitrary state then how can it be made to control the CNOT gate? What is the interface between Control Qubit and CNOT Gate?
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Change entangled far Qbit state without mesaure it

Hello I entangled with Qsharp a far QBit (Bob)to a 3 Qbit register that is also entangled to another marked qbit for a Grover search. When I look for the value 4 with Grover search the Bob qbit is ...
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Maximum number of “almost orthogonal” vectors one can embed in Hilbert space

In a Hilbert space of dimension $d$, how do I calculate the largest number $N(\epsilon, d)$ of vectors $\{V_i\}$ which satisfies the following properties. Here $\epsilon$ is small but finite compared ...
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What's the probability of measuring outcomes give measurement observable $M$ and state $\rho$ when $\mathrm{Tr}\!\:(\!\!\;M\rho)$ is a complex value?

I'm studying the measurement in quantum computation. It's known that the trace is related to the expectation value and the probability of getting certain outcomes. However, when the trace is a complex ...
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What is the purpose of the last bits in the 2-qubit-operation Toffoli implementation?

What is the purpose of these quantum gates? They're appended to the circuit after the value has been computed.
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The meaning of the city plot in Qiskit

I read the documentation of qiskit and I can't understand the meaning of the city plot, like this: Why do we need a 3D plot? Why can't we just use a 2D plot, where $ | 00\rangle$, $ | 01 \rangle$, $ ...
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What is intuition for the trace distance between quantum states?

Given two mixed states $\rho$ and $\sigma$, the trace distance between the states is defined by $\sum_{i=1}^n |\lambda_i|$, where $\lambda_i$'s are eigenvalues of $\rho - \sigma$. I know the ...
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Find probability of a single qubit's measurement results from a 5 qubit state

I have a tensor product of a 5 qubit state |h>. From this I want to calculate the probability of the 2nd qubit being in state |1>. Can someone show me how I can do this? I know I can use the Born rule ...
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Measuring a quantum wire at t > 0

I saw on the site Brilliant.org a question witch is: "Let's say I'm given a quantum wire, I measure it and find it charged "on". If I come back some time later, what state should I measure?" And the ...
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Is it possible to change the oracle in Grover's search to ponderate probabilities in multiple values search?

If I want to to search 2 values with Grover's algorithm, it outputs the same probability for both that is bigger that the no searched states that have the same lower percent. If I use an oracle ...
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Entangling marked qubit with part of the register in Grover's search

Can the marked qubit be associated only with half of the register? I mean if I can ask the oracle if the $2$ low qubits from a $4$ qubit register have a certain value. I ask this to know if I can ...
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Synchronous Interactions Between Quantum and Macroscopic Systems

Synchronous Interactions Between Quantum and Macroscopic Systems Lester Ingber This project calculates synchronous quantum systems and macroscopic systems with well-defined interactions. I would ...
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Sampling random circuits vs Solovay-Kitaev compiler

Suppose I want to obtain a gate sequence representing a particular 1 qubit unitary matrix. The gate set is represented by a discrete universal set, e.g. Clifford+T gates or $\{T,H\}$ gates. A well ...
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Taking the two qubit reduced density matrix on a 5 qubit system

I am wanting to find the two qubit reduced density matrix on a 5 qubit system. I have the 5 qubit state in the form of a tensor product and I want to find the reduced density matrix of qubits 1 and 3. ...
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GridQubit in Cirq vs LineQubit

It's perhaps a very silly question, but in what ways is it advantageous to use GridQubit vs LineQubits to develop quantum circuits? Specially to develop ansatz ? Are GridQubits Cirq's way of ...
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States of a qubit in a DC-SQUID

Does anybody of you know what are the two states $|0\rangle$ and $|1\rangle$ of a qubit in a DC-SQUID (2 Josephson junctions in a loop)?
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Which state describes carrier transport through channel? A mixed state or a pure state?

A pure quantum state is a state which can be described by a single ket vector. A mixed quantum state is a statistical ensemble of pure states. When carriers transport from source to drain in a Field ...
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Cloning quantum states with a device that distinguishes between two non-orthogonal quantum states

I'm aware that this is basically a duplicate question, but I don't have any rep in this community so I can't comment on it, and I don't think I should "answer" that question with my own question: No-...
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Kronecker product and multiplication operation on qubit states

It may look a silly question but anybody of you knows what's: $$(|0\rangle+|1\rangle)\otimes(|0\rangle+|1\rangle)$$ (x: Kronecker operator) $$(|0\rangle+|1\rangle)*(|0\rangle+|1\rangle)$$ (*: ...
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Non-linear sign shift gate

I'm reading Linear Optics Quantum Computation: an Overview. On page 16 we're given a matrix $$U = \begin{pmatrix}1-\sqrt{2}&\frac{1}{\sqrt{\sqrt{2}}}&\sqrt{\frac{3}{\sqrt 2}-2}\\\frac{1}{\...
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Does the Choi-Jamiolkowski isomorphism really establish a connection between kinematics and dynamics?

I understand the mathematical construction of the Choi-Jamiolkowski isomorphism aka channel-state duality. It all makes sense formally, yet I still struggle to grasp its physical (or quantum-...
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What are the two qubits in the state $a\lvert 00\rangle+b\lvert11\rangle$?

What are the $2$ qubits of the state $a\lvert 00\rangle+b\lvert11\rangle$? Are they $a'\vert0\rangle+b'\vert1\rangle$ and $c'\vert0\rangle+d'\vert1\rangle$? How are they measured, and what would be ...
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How to represent $|+\rangle$ in Python?

I am using state vectors and operator matrices to test out my knowledge in a Python program. How would I represent the state $|+\rangle$ in Python? I want to then perform several operations in a ...
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$n$ qubit vs. a $d=2^n$ qudit states and measurements

The pure states of a qudit inhabit the $\mathbb{CP}(d-1)$ manifold. Is it true that the pure states of $n$ qubits live on the $\mathbb{CP}(2^n-1)$ manifold? If the answer to the first question is yes,...
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CX gate with Hadamard

Let's say we got a CX with a Hadamard gate on the control gate and any state at the target gate, will the target necessarily become a superposition of two states? Best.
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GHZ - measuring particles

I'm referring to an earlier question. It involves secret sharing based on the different measurement directions 3 people i.e Alice Bob and Charlie do. Now there is a block in the referred paper which ...
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How to find a common eigenstate of commuting operators?

I have multiple different operators in matrix form and I need to find their common eigenstates. The challenge is that the common eigenstate is in a superposition of multiple states and isn't just a ...
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Eliminating a term of a superposition state

Is there a way of eliminating a term of a superposition state? Let's say I have the state $$\frac{1}{\sqrt 2}|00\rangle + \frac{1}{2}|01\rangle + \frac{1}{2}|10\rangle$$ What operation would I do to ...
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Quantum fidelity simplified formula while both of the density matrices are single qubit states

I have a question while reading the quantum fidelity definition in Wikipedia Fidelity of quantum states, at the end of the Definition section of quantum fidelity formula, it says Explicit expression ...
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Quantum secret Sharing using GHZ state paper

I am reading a paper on Quantum Secret Sharing Quantum Secret Sharing using GHZ states I have doubts regarding the initial phase of the paper, which are: Let me state what things I read and ...
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What does “an $n$-qubit array can represent $2^n$ possible array elements” mean?

I read "...an $n$ qubit array can represent $2^n$ possible array elements.." on this post. A classical $n$-bit array can represent $2^n$ possible array elements as well, so I'm confused about the ...
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Measuring first qubit of Bell state

Let's consider the following Bell state: $$\lvert \Phi^+\rangle = \frac{1}{\sqrt{2}} (\lvert00\rangle + \lvert11\rangle)$$ What would happen if I measure the first qubit in the standard basis and ...
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Weeding out qubit states with leftmost qubit as 1

Need help! I was working on a project when I required to use a projection operator. For an example case, I have the Bell state, $$|\psi\rangle = \frac1{\sqrt2}\left(\color{blue}{|0}0\rangle+|11\rangle\...
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How can I write the maximally mixed state on m qubits as a linear combination of basis vectors?

The maximally mixed state on m qubits is defined to be the quantum state with associated density operator $\rho_m = \frac{1}{2^m} I$. Examples are On one qubit this is $\rho_1 = \frac{1}{2}(|0\...
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How to tell if the ground states of two Hamiltonians are solutions of the same optimization problem?

Let's say, that we have an optimization problem in the form: $$ \min_x f(x) \\ g_i(x) \leq 0, i = 1, ..., m \\ h_j(x) = 0, j = 1, ..., p, $$ where $f(x)$ is an objective function, $g_i(x)$ are ...
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Question on state distinguishability

Consider the following protocol. We are given either $|\psi\rangle = \frac{1}{\sqrt{2}}(|0\rangle + |1\rangle)$ or $|\phi\rangle = \alpha_{0} |0\rangle + \alpha_{1}|1\rangle$ where $\alpha_{0}^{2}$ ...
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Complex number in the representation of a qubit

I do not know if the question is not too easy, but I'll put it here, because I'm interested in it. So the state of a qubit is often stated in this form: $$|\psi\rangle=\alpha|0\rangle+\beta|1\rangle$$...
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Understanding a quantum algorithm to estimate inner products

While reading the paper "Compiling basic linear algebra subroutines for quantum computers", here, in the Appendix, the author/s have included a section on quantum inner product estimation. Consider ...
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Can entangled qubits be disentangled without using code or software?

Is there a way to revert two entangled qubits to a separate state without using code...like restarting a quantum computer? Note: By "restarting a quantum computer", I do not mean restarting a virtual ...
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Converting a Qubits state to a binary value in Q#

In Q#, How do I store a Qubits state in a binary-based disk / hard drive for use by regular digital programs? Is this even possible?