Quantum Computing Stack Exchange
Quantum Computing Stack Exchange

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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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 optical quantum computing (LOQC)" pioneered by KLM…
rrtucci
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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 states such as the one that the Canadian startup…
Mark Fingerhuth
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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. Therefore a Wigner function uniquely determines a…
taper
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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 their unitary: What are the matrix representations…
user820789
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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 both models be compared. Given a discrete-gate…
Mauricio
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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 frequency comb experiment relating to quantum computing…
raycosine
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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 states as input states). In the paper, the scientists…
ile2N
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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 the space: $$\bs\Omega\equiv…
glS
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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 registry of qubits or their continuous-variable…
Kiro
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Finding the ground state of a Gaussian Hamiltonian

It is well known (arXiv) in continuous variable (CV) quantum information processing that an $N$-mode CV system whose dynamics are entirely Gaussian can be simulated efficiently with a classical computer as the dynamics can be simulated by computing…
atman
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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 $\mathbb{R}$ but that seems really abstract to…
cnada
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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 $d=\infty$?
incud
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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 open to learning about other systems where…
user820789
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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 description, but I still feel as though I am lacking in some…
Jack Ceroni
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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 $$\begin{bmatrix}1&0\\0&-1\end{bmatrix}$$ maps the…
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