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I was looking for why optical quantum computers don't need "extremely low temperatures" unlike superconducting quantum computers. Superconducting qubits usually work in the frequency range 4 GHz to 10 GHz. The energy associated with a transition frequency $f_{10}$ in quantum mechanics is $E_{10} = h f_{10}$ where $h$ is Planck's constant. Comparing the ...


10

Background First of all, I'll use $\lvert H\rangle$ as a horizontally polarised state and $\lvert V\rangle$ as a vertically polarised state1. There are three modes of light involved in the system: pump (p), taken to be a coherent light source (a laser); as well as signal and idler (s/i), the two generated photons The Hamiltonian for SPDC is given by $H = \...


9

The existing answer does a good job at describing the state that comes from a SPDC configuration at low conversion efficiency, but it's also worth noting that the single-photon behaviour is not all there is to the process. Thus, in particular, if your conversion efficiency (or you detection time / efficiency / SNR) is good enough that you can detect (and ...


8

It appears to be true, up to a point. As I read Scott Aaronson's paper, it says that if you start with 1 photon in each of the first $M$ modes of an interferometer, and find the probability $P_S$ that a set $s_i$ photons is output in each mode $i\in\{1,\ldots, N\}$ where $\sum_is_i=M$, is $$ P_s=\frac{|\text{Per(A)}|^2}{s_1!s_2!\ldots s_M!}. $$ So, indeed, ...


8

A standard reference for linear optical quantum computing is Kok et al. 2009 (quant-ph/0512071). If one qubit is encoded in the polarization degree of freedom of a single photon, and the second qubit in the path degree of freedom of the same photon, then a CNOT gate is trivially implemented by a polarizing beamsplitter. This is a kind of beamsplitter that ...


7

Because light, at the right frequencies, interacts weakly with matter. In the quantum regime, this translates to single photons being largely free of the noise and decoherence that is the main obstacle with other QC architectures. The surrounding temperature doesn't disturb the quantum state of a photon as much as it does when the quantum information is ...


6

To start off, I would really suggest you to read this review on "Quantum information with continuous variables(cv)". It covers most of your questions with cv architecture. Since it is a very big review, I will try to address your questions with what I can remember from reading that paper and glancing over it again now. For discrete variables(dv), as you ...


6

You cannot efficiently recover the absolute values of the amplitudes, but if you allow for arbitrary many samples, then you can estimate them to whatever degree of accuracy you like. More specifically, if the input state is a single photon in each of the first $n$ modes, and one is willing to draw an arbitrary number of samples from the output, then it is ...


6

According to this UK-oriented report by Gooch and Housego dated May 8, 2018, quantum computing is only one of several main key applications expected to have a market impact: Clock technology/timing (e.g. bridging between the optical frequencies typical of atomic clocks and electrical/microwave frequencies typical of timing signals within ...


6

At Xanadu, we're using integrated quantum photonics to build our photonic quantum computing chips. In this case, we have integrated chips containing waveguides --- these are coupled to lasers to generate input resource states, undergo manipulation on the chip, and then are measured via a variety of detectors available in quantum optics. These can include ...


6

The major quantum computing providers that comes to me right the way are usually: IBM Quantum (superconducting qubit) Google Quantum (superconducting qubit) Honeywell Quantum (trapped ions) Rigetti (superconducting qubit) IonQ (trapped ions) The players in this list are primarily focus on two technologies, superconducting and trapped ions. Note that ...


6

QML researcher at Xanadu here. Our X-series chip produce entangled states by squeezing light and then combining it at beam splitters: those 'cables' are waveguides in a chip, which when they are close enough they allow tunnelling between them and effectively couple those two modes. Note that the squeezing is necessary in this case (for example, had we used ...


5

There are various ways in which one or multiple photons can be used to encode qubits. Potentially the most widely used encoding (at least when quantum communication is assumed to within the scope of 'quantum computing' for this question) is the polarization-encoded photon. Here, a single photon is used as a qubit, where two orthogonal polarization directions ...


5

By photon qubits, I'm assuming that you meant single-photon qubit systems. Can one use squeezed light to effect multi-qubit operations on photon qubits, or are these completely independent approaches? There are two protocols in quantum communication namely, discrete-varibale (dv) and continuous variable (cv). Squeezed light qubits are a part of cv ...


4

Your question asks two questions that are less-related than you might hope. First, how do we increase the probability of down-conversion occuring? This is fundamentally a question about material properties: the chance per unit length of down-conversion occurring is proportional to $\chi^{(2)}$; if our material of choice doesn't have good phase-matching ...


3

Yes. The kets themselves can have arbitrary labels, and it's just for you to establish the connection between them and the physical scenario. There's no reason why you can't have the physical scenario you've specified and, indeed, people frequently do.


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For a general overview about hardware and the difficulties they present, I recommend section three of Quantum Computing: An Overview Across the System Stack. Another good introduction would be Quantum Computing Hardware Implementation Methods: A Survey over Categories. Let me also give you some papers specific to certain implementations and their recent ...


3

One idea is to do polarimetry. By using a polarizing beam splitter, the polarization qubit can have each of its polarization components directed to a different detector for photon counting (ideally a single-photon detector, here). A polarizing beam splitter might send horizontally polarized photons in one direction and vertically polarized photons in another....


3

First, the operators $a$ and $b$ ($a^{\dagger}$ and $b^{\dagger}$) are the annihilation (creation) operators of the two photonic modes in your problem. For an introduction to the subject I recommend you to look for some decent lecture notes on quantum optics. A well readable introductory book is Mark Fox's "Quantum Optics -- An Introduction" and a more ...


2

Here's some relevant work in Optimizing type-I polarization-entangled photons-Radhika Rangarajan, Michael Goggin, Paul Kwiat. Abstract: Optical quantum information processing needs ultra-bright sources of entangled photons, especially from synchronizable femtosecond lasers and low-cost cw-diode lasers. Decoherence due to timing information and ...


2

DanielSank is correct, but I think the answer is actually even more subtle. If there was no loss there would also be no way the background radiation leaking into your quantum device. Even if it was initially thermally excited, one could actively reset the state of the qubits. Thus, in addition to thermal excitations of microwave qubits, the fundamental ...


2

Strictly, what you have to calculate is that for all $i$ and $j$ $$ \langle 0_L|U_iU_j|1_L\rangle=0 $$ and $$ \langle 0_L|U_iU_j|0_L\rangle=\langle 1_L|U_iU_j|1_L\rangle. $$ (I've ignored the Hermitian conjugate because all the single-qubit errors are Hermitian.) Obviously there's a lot of work involved in calculating all $28^2$ cases of $i,j$. You can at ...


2

While the Pauli-$Z$ matrix is a 2 x 2 matrix, there are more basis states that need to be considered, namely the vacuum. The atomic basis states are $\left|0\right>$ and $\left|1\right>$, representing the number of excitations in the atom (as it's only a two-level atom, there can't be more than 1 excitation) and this is what $Z$ acts on. Similarly, the ...


2

Here is a handful of Linear Optical Quantum Computation (LOQC) resources I have found useful in the past: "Linear Optical Quantum Computing" (2005) by Kok et. al.: this is probably the best review paper that came out after Knill, Laflamme, and Milburn's 2001 discovery that theoretically-efficient LOQC was possible. It's a pretty thorough but very accessible ...


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a good stater i would say is the paper of Knill and Laflamme about LOQC (Linear Optical Quantum computing) from 2001, that says that quantum computing can be achieved with linear optic. Photons are really good as they can be used in many way to create qubits (polarisation of course, but also time, frequency, OAM). A Ph.D Thesis of Laurent Olislager is ...


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In QuTiP, one can construct generalized dissipators with the lindblad_dissipator function listed under "Superoperators and Liouvillians" here. You can pass in separate operators to act from the left and right: \begin{align} D[a,b] = a\rho b^\dagger - \frac{1}{2}a^\dagger b \rho - \frac{1}{2} \rho a b^\dagger \end{align} Then, in the master ...


1

The Hilbert space of the environment part of the state must have at least as many dimensions as the minimum number of Kraus operators $N$ used to describe the local state's evolution: $$|\psi\rangle\langle\psi|\to\mathrm{Tr}_E[U(|\psi\rangle\langle\psi|\otimes |0\rangle_E\langle 0|)U^\dagger]=\sum_{k=1}^N K_k|\psi\rangle\langle\psi| K_k^\dagger.$$ For the ...


1

With polarizers you can implement projections. The Pauli Z oerator has an eigenvalue $-1$, so no, you cannot implement $U_a$ with only polarizers.


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This is very much possible. And is a very general technique of how product systems in composite states are coupled. Here of the form $|n_1\rangle |n_2\rangle$. This kind of general ket is a solution of the Hamiltonian interaction/coupling terms like $V\sim (a_1^\dagger a_2 +h.c)$ which describe the exchange of one quanta (between the two optical cavities ...


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