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Questions tagged [continuous-variable]

Continuous-variable quantum computing is a type of quantum computing that makes use of physical observables, like the strength of an electromagnetic field, whose numerical values belong to continuous intervals.

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Truncated Qumode States and Support

I am currently running numerical simulations of a single qumode state acted upon by a parameterised unitary. The qumode state is realised as a Fock state with a fixed cutoff dimension $(d)$ and is ...
Song of Physics's user avatar
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What are the postulates of Continuous Variable Quantum Computing?

I am a computer scientist. When I learned quantum information for the first time (in the circuit model, with qubits), I was presented four postulates that described mathematically (i) the possible ...
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What is an example of the need for complex numbers implied by the need of continuity of linear operators?

Not a duplicate. Question and answers given elsewhere do not answer this one. Context. Scott Aaronson, lecture 2, course 6.896 Quantum Complexity Theory, september 2008 says that a matrix such as $$\...
user1145880's user avatar
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How to update angles

I am struggling to understand the concept of updating angles in a parameterized algorithm. Assume I have an objective function $x^2+1$ that I want to optimize using QAOA which can handle continuous ...
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What are necessary and sufficient conditions for the output of a parametrized unitary $U(\theta)$ to be smooth?

Let us consider a unitary $U$ parameterised by $\theta \in \mathbb{R}$, i.e, $U(\theta)$. What are the necessary and sufficient conditions for the output states of this unitary to be smooth? One ...
Song of Physics's user avatar
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Superposition of Cubic Phase States, are they useful?

Consider the context of continuous variable quantum information. Let $\hat{a},\hat{a}^\dagger$ be the creation and annihilation operators of a bosonic oscillator with the usual commutation relations $[...
Lost In Euclids 5th Postulate's user avatar
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'Continuous' (Classical) Cost function for QAOA

I have some combinatorial optimization problems which I would like to analyze using QAOA. These problems are coming from various applications in scientific computing such as solving PDEs. Some of ...
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Why do phase space representations satisfy a covariance property?

In (Ferrie and Emerson 2008), the authors define (Definition 2 in page 5 of the arxiv) a generic quasi-probability representation of quantum states as any map $\operatorname{Herm}(\mathcal H)\to L^2(\...
glS's user avatar
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Variational Algorithms - Is there a way to avoid discontinuities in optimal variational parameters?

Often algorithms utilize an ansatz $V(a)$ and rely on a classical optimization scheme over a Hamiltonian loss function $L(V(a))$ in order to find the optimal parameters $a$. Due to many factors such ...
consthatza's user avatar
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1 answer
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Implementing a simple 3 mode gate using Strawberry Fields

I'm looking to implement the operator the 3 mode operator $e^{-i\frac{s}{h}\hat{x_1} \otimes \hat{p_2} \otimes \hat{p_3}}$ using Strawberry Fields. I know that using the ...
sheesymcdeezy's user avatar
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I am optimising a variational quantum circuit to learn a distribution $p(x)$, but it doesn't converge over a training set $\mathcal{X}$?

I am training a variational quantum circuit to learn distributions: given data $s(\vec{\lambda})$, what is the probability distribution for the parameterisation $\vec{\lambda}$, i.e. the posterior ...
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Algorithms in Continuous Variable Quantum Computing

I have recently been exploring Continuous Variable Quantum Computing. I would like to know if there are any resources or literature I can read to get a general understanding of how one can extend ...
Song of Physics's user avatar
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QuTiP, Continuous variable systems: Calculating the expectation value of an operator from the covariance matrix

Let's say I have the covariance matrix for a 4-mode system, $\sigma$, which is an $8 \times 8 $ matrix (the first moments are zero). I want to calculate the expectation value for an operator, for ...
Bard's user avatar
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Doesn't a beamsplitter contradict the nocloning theorem?

I am new to continuous variable quantum computing. From my understanding, in homodyne detection, the state (usually coherent) is duplicated and two measurements with different photon counting ...
eternalstudent's user avatar
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How to translate between continuous variable model and discrete model?

If I understand correctly, the discrete and continuous variable (CV) version of quantum computation are equivalent. However, the continuous aspect of the CV model makes me wonder to what extent can ...
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Looking for detailed comparisons between photonic vs other quantum hardware

I’m looking for resources or literature that compares photonic devices and other quantum computing hardware using some performance metric. In other words, I am looking for grounds that compare the ...
evil_potato's user avatar
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What is the difference between CV QKD and DV QKD?

I know what QKD is, as a concept but I recently found papers mentioning continuous-variable quantum key distribution , and discrete-variable quantum key distribution . So I would like to know what is ...
user206904's user avatar
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How to write the covariance matrix of a quantum gaussian state as a function of photon numbers?

Assume having a one-mode quantum Gaussian state with quadrature observable vector $\hat r = [\hat q , \hat p ] $ and covariance matrix $\sigma$. According to definition [1]: \begin{equation} \sigma = \...
hafezmg48's user avatar
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How are two photons entangled in the Xanadu computer?

I was recently reading about how Xanadu made a scalable, room-temperature-operating quantum computer using photons as qubits (see this link). It said that in the logic gates, it entangles two photons ...
Blue Herring's user avatar
5 votes
1 answer
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What is the relation between a Fock state and a qudit?

What is the relation between a Fock state and a qudit? Is the Fock state $|n\rangle, n=0, 1, 2, ...$ a qudit having $d=\infty$?
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Is there a way to directly construct controlled gates in continuous variable (CV) quantum computation?

We know that a universal gate set for CV quantum computation is that of squeezing, beam splitters, and some nonlinear gate (e.g. this answer). We also know from Knill, Laflamme, and Milburn that ...
Quantum Mechanic's user avatar
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Why is a state Gaussian if and only if its covariance matrix satisfies $\boldsymbol\sigma+i\boldsymbol\Omega\ge0$?

Let $\rho$ be a Gaussian state, described by the $2N\times 2N$ covariance matrix $\newcommand{\bs}[1]{{\boldsymbol{#1}}}\bs\sigma$. Denote with $\bs\Omega$ the $N$-mode symplectic form associated with ...
glS's user avatar
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Is Gaussian boson sampling (used for showing quantum advantage) a subcategory of the continuous variable approach?

I read about the photonic QC Jiŭzhāng that showed quantum advantage by Gaussian boson sampling. I read that boson sampling itself is a sub-universal technique of QC (where they use single-photon ...
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What is meant with "reconciliation" in CV QKD?

I am working on a paper about Continuous Variable QKD. (https://arxiv.org/abs/1711.08500v2) I read about direct and reverse reconciliation in this paper. I don't understand what exactly Reconciliation ...
Kianoosh.kargar's user avatar
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Is continuous-variable quantum computing a model of a quantum universal Turing machine?

In this question of a few days ago, it was raised the question about the similarities or differences between the notion of universality in discrete-variable (DV) quantum computers and continuous-...
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Is the universality of a qubit based quantum computer different from the universality of a continuous-variable quantum computer?

I understand that a quantum computer is universal if it can compute anything that a quantum Turing machine can. Another way to think about universality is that any unitary transformation on, e.g., a ...
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Are there already hypothetical durations of how long a continuous-variable gate would take on a continuous-variable quantum computer?

I've heard that you run up against the very large constant factors when comparing run times of quantum and classical computers -- things simply take much longer in a carefully controlled quantum setup ...
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1 answer
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Relation between Wigner quasi-probability distribution and statistical second-moment

Is there any relation between the Wigner quasi-probability distribution function $W$ and the statistical second-moment (also known as covariance matrix) of a density matrix of a continuous variable ...
Kianoosh.kargar's user avatar
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What is the explicit action of the non-linear gate in CV quantum computing on the quadratures?

In this excellently answered question 'How are gates implemented in a continuous-variable quantum computer?' the typical gates for CV quantum computing were listed and described. In particular for ...
East's user avatar
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What is infinite squeezing?

I am working my through the Strawberry Fields documentation & the section on state teleportation states: Here, qumodes $q1$ and $q2$ are initially prepared as (the unphysical) infinitely squeezed ...
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3 votes
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What types of quantum systems use infinite values?

Background I am curious to learn more about any work that has been done regarding quantum systems that deal with infinite values. I am primarily interested in photonic quantum computing; however I am ...
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1 vote
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How can I prove the universality of this set of gates?

I was reading this article. A brief explanation: Here we have a circuit, the registers are a stepfunction state, an single photon state and a function state. The first two have position operators $X$ ...
tererecomchimarrao's user avatar
1 vote
1 answer
707 views

What is the mean value of displacement operator for the coherent state?

Can anyone help me to find the mean value of the displacement operator $$D(\alpha) = \exp( \alpha a^\dagger -\alpha^* a)$$ for a Coherent State $\left|\beta\right> = D\left(\beta\right)\left|0\...
user8655's user avatar
4 votes
1 answer
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Quantum teleportation over continuous variables?

I came across this circuit diagram for CV quantum state teleportation: Source: Xanadu Strawberry Fields: Docs / Quantum algorithms / State teleportation It was accompanied by a brief ...
Jack Ceroni's user avatar
8 votes
1 answer
383 views

Does a Wigner function uniquely determine a quantum state?

We know that the Wigner function of a Gaussian quantum state is (up to a constant) a Gaussian distribution. The first moment and the covariance of this distribution uniquely specify a quantum state. ...
taper's user avatar
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What is continuous quantum register and how it relates to qubits?

I would like to understand what is a continuous quantum register. I know the direct definition is a quantum register that stores a real number defined by an observable with a spectrum consisting of $\...
cnada's user avatar
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7 votes
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Are qubits preferred over qumode, and if so, why?

Qubit and qumode are different forms of quantum computation. But most existing quantum computers/chips seems to be of discrete variables. I heard that a group chose qubit for a quantum optical ...
raycosine's user avatar
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8 votes
2 answers
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Matrix representation of continuous-variable gates

In the introduction to continuous-variable quantum computing by Strawberry Fields (Xanadu), it lists the primary CV gates (rotation, displacement, squeezing, beamsplitter, cubic phase) along with ...
user820789's user avatar
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20 votes
1 answer
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Is "probabilitistic,universal, fault tolerant quantum computation" possible with continuous values?

It seems to be a widely held belief within the scientific community that it is possible to do "universal, fault-tolerant" quantum computation using optical means by following what is called "linear ...
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How are gates implemented in a continuous-variable quantum computer?

I've mostly worked with superconducting quantum computers I am not really familiar with the experimental details of photonic quantum computers that use photons to create continuous-variable cluster ...
Mark Fingerhuth's user avatar