7

About the need of boson sampling verification First of all, let me point out that it is not a strict necessity to verify the output of a boson sampler. By this, I don't mean to say that it is not useful or interesting to try and do so, but rather that it is in some sense more of a practical than a fundamental necessity. I think you yourself put up a good ...


7

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, ...


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 ...


5

What is non-classicality? I'm not sure if there's a universally accepted definition, but the way that I'd define it is: if all possible outcomes of experiments on a particular quantum system can be described by a probability distribution, then the system is classical. Otherwise, it is non-classical. In alternative terminology, for a classical system, people ...


5

Quantum computers are, unfortunately, quite hard to build. Experiments with polarizing filters or beam splitters would be able to demonstrate quantum effects, but I know of no way to make simple quantum circuits for multiple qubits unless you have single photon sources and detectors. Alternatively, you could use current cloud-based devices. The IBM Q ...


5

You can get the sort of optical bench that is typically used for classrooms. For a couple examples: 3B Scientific School Speciality I think the one I have taught with before was from 3B, but I don't know about any of the others so research them yourself rather than taking a product recommendation from me. There are several options and this choice will be ...


5

We may simulate the three-polarising-filter experiment as a circuit, in the following way, using qutrits. I will start by describing this as a sequence of transformations (a channel) on qutrits, and then give a circuit which simulates this using qubits. $\def\ket#1{\left\lvert#1\right\rangle} \def\bra#1{\left\langle#1\right\rvert}$ The three-polarising-...


4

Firstly, that sphere that you've pictured is convenient for thinking about what's going on, but remember that it is not what is actually happening. So the fact that you don't visualise light as having a little arrow pointing somewhere doesn't matter. The fact of that matter is that for an electron spin, having the two possible states "up" and "down", we ...


4

In quantum theory, the pure states are associated with the unit vectors of the Hilbert space. A pure state of a quantum bit can be represented as $$| \psi \rangle = \alpha | 0 \rangle + \beta | 1 \rangle$$ where $|\alpha|^2 + |\beta|^2 = 1$. The basis $| 0 \rangle$ and $| 1 \rangle$ can be viewed as two orthogonal polarization directions. Bloch sphere is ...


4

Here are a couple of contributions related to your question: 1- Very recently, Chris Ferrie created an open-source card game based on a toy version of quantum mechanics, called $<B|racket|S>$. 2- The company Phase Space Computing markets electronic kits that simulate quantum gates and simple quantum algorithms.


3

Start in $$ a_0 | 01 \rangle + a_1 | 10 \rangle $$ Then apply $P \otimes I$ to get $$ a_0 * 1 | 01 \rangle + a_1*e^{i \Delta} | 10 \rangle $$ But that is the same up to phase as $$ e^{-i \Delta /2} (a_0 * 1 | 01 \rangle + a_1*e^{i \Delta} | 10 \rangle) $$ which simplifies to $$ a_0 e^{-i \Delta /2} | 01 \rangle + a_1 e^{i \Delta /2} | 10 \rangle $$


3

I am glad you enjoyed my experiments! :) I'd be happy to talk more about how I ran that project --- dm me at twitter.com/crazy4pi314. To your question, I don't know of any good papers or articles on the setup, but you can get a pretty reasonable demo of polarization-encoded BB84 with a few pretty common components: polarized laser pointer some half wave ...


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.


3

Consider a sequence of 3 measurement devices, applied sequentially to the same qubit, which starts in the 0 state. The first and last devices measure in the Z basis. The second measures in the X basis. Now you ask what the probability of getting the outcome 1 from the final measurement, depending on whether or not the second measurement device is present.


3

Just a small complement to @gIS excellent answer: I know of several people (including myself) interested on the public verification aspect. As far as I know, all attempts have failed, hence the lack of literature on the subject: as soon as one can prove the Boson sampler acted correctly, it is indeed a regime where the Boson sampler can be efficiently ...


2

To answer your first, general question: Optical circuits are usually drawn with a selection of conventional symbols, a directory of which to draw them can be found here. With respect to that specific circuit, if a single photon was input, the output would produce a state in a decaying superposition of subsequent time bins. If you choose a temporal basis for ...


2

There is a number of groups using time-bin encoding to realise computation/communication protocols. One example is Furusawa's group in Japan, which among other things works on measurement-based QC with time-bin encoding (e.g. 1706.06312). Another example that comes to mind is Silberhorn's group in Paderborn. They use time-bin encoding for various things, a ...


2

Yes! The first application of time bin photonic qudits that comes to mind is for quantum key distribution. Here's an example: https://arxiv.org/abs/1611.01139. I am sure there are more references out there though!


2

It looks like the only relation they say is $\text{IdentityMatrix}[3^2]=\sum P_{k,l}$. You get a linear combination of $P_{k,l}$. Those are vertices of a $d^2-1$ simplex so the coefficents $c_{k,l}$ are baryocentric coordinates. You can then match with the previous more general definition of $\rho_d$ term by term on each of the $c_{k,l}$. The inequalities ...


2

You seem to be thinking about "quantum memory" like it is one specific thing and there is only one specific way it can happen. In reality, what you describe is a valid notion of quantum memory. Another popular one, involving the element Yb, is this one: https://arxiv.org/abs/1701.04195.


2

Your understanding is correct. In the theory of photon polarization, the parametrization of the Bloch sphere (or its surfave) has traditionally another name. On the wikipedia page for the Jones calculus (the parametrization of the Bloch sphere surface), you'll find a table for the correspondence between kets and polarizations. To summarize, eigenstates ...


1

I see the heart of your question. I'd like to clarify a bit, before answering your question though. Matrices (aka operators) do not measure quantum states--they operate on them. Specifically, they project the state into the matrix's eigenvectors. We can then measure that projected state in a particular basis that may be the same or different than what the ...


1

A photon can be thought of as a tiny piece of a circularly polarized wave. In this sense, all polarization states of EM waves are a superposition of photons, each with a circular (left or right) polarization. Linearly polarized light could then be constructed as a pair of photons with left and right polarization (or spin). Maybe your question is whether ...


1

For the former part: Even a simple slab of glass can act as a phase shift quantum gate. The difference in path covered is $(n-n_0)L \equiv \delta L$ and the time difference is $\delta L/c_0$ and then the phase shift is proportional to this time shift. Or just divide this time phase difference by some time $T$ taken by the light in a vacuum to travel the same ...


1

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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