54 votes

Why is Google's quantum supremacy experiment impressive?

To elaborate on my intuition here, the thing I consider "impressive" about classical computers is their ability to simulate other systems, not just themselves. When setting up a classical ...
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48 votes
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Why is Google's quantum supremacy experiment impressive?

The big difference between the quantum supremacy experiment and your pudding experiment is that the quantum supremacy experiment solved an unambiguous, well-posed mathematical problem. While people ...
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47 votes
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Could quantum computers break any cipher?

No, it is not. Quantum computers can factor large numbers efficiently, which would allow to break many of the commonly used public key cryptosystems such as RSA, which are based on the hardness of ...
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33 votes
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Canonical examples of quantum channels

The following is a list of channels you can use to test your conjecture. (Some are special cases of subsequent ones -- it makes more sense to first test the special cases.) Here, $d$ is the dimension ...
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33 votes

Why not implement quantum circuits on classical computers?

Matrix multiplication is polynomial in the number of matrix elements. In quantum computing the number of matrix elements is basically the number of elements in the quantum state vector, which is ...
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30 votes

Why is Google's quantum supremacy experiment impressive?

I co-run an experimental research group in which, among other things, we develop the ability to control quantum bits so as to do (one day) quantum computing. In our lab we have the most precise ...
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22 votes
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Does "natural" superposition of particles exist?

One of the common misconceptions that people starting out with QM often have is to think that a system is either in a superposition state or it is not. Actually superposition is only defined relative ...
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18 votes

Could quantum computers break any cipher?

There is actually an entire complexity class devoted to the answer, which is "no, it cannot break any code." The class is known as BQP, or "bounded error quantum polynomial time." It is the class of ...
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17 votes

Why not implement quantum circuits on classical computers?

The false point in the premise is that a composition of single-qubit and two-qubit gates will be represented by some sort of composition of 2×2 and 4×4 matrices. In fact, if a single-qubit gate (for ...
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  • 1,255
16 votes

Quantum and classical physics are reversible, yet quantum gates have to be reversible, whereas classical gates need not. Why?

Though your language is vague and handwavy, I would say you pretty much got it right. Classical physics is reversible at a microscopic level when you look at ALL degrees of freedom. However, we don’t ...
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14 votes

To what extent is it true that quantum computation cannot be simulated on classical computers, and how can we prove it?

The statement is either false or unproven, depending on how you take it. Scenario 1: "Quantum Computers Cannot Be Simulated, Even Given Infinite Time and Space" This statement would be one in which ...
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13 votes

How do $|1⟩$ and $-|1⟩$ represent the same state?

$\def\ket#1{\left|#1\right\rangle}\def\bra#1{\left\langle#1\right|}\def\braket#1#2{\left\langle#1|#2\right\rangle}$In quantum mechanics, the overall phase of the wavefunction is not physical. So $e^{...
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11 votes

Why is Google's quantum supremacy experiment impressive?

It is (in isolation) no different from you pudding computer. However, the context is very important. Their are certain useful problems that we know how to solve much faster on a quantum computer than ...
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11 votes
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Why can photons be used as qubits?

A photon is a massless spin-1 particle. This means that a photon has exactly two spin states, just like an electron.
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10 votes
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What is the difference between a bit and a qubit?

After several discussions on that topic, I came to think that it is more appropriate to separate those different types of "bits" into four instead of two classes: A deterministic classical bit is an ...
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10 votes
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Why is a transmon a charge qubit?

There are two things to consider: What does the potential look like? Is the wave function of the qubit narrow in the flux or charge basis? Potential shape The Hamiltonian of the transmon (a ...
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10 votes
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Why do quantum gates have to be reversible?

Quantum gates have to be reversible because quantum mechanics is reversible (and even more specifically it is unitary). It's just an observed fact about the universe. (Even measurement can be modeled ...
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10 votes

Why not implement quantum circuits on classical computers?

To put slightly differently the Hilbert Space (H) for your quantum circuit is growing exponentially ($ \text{dim H} = 2^n$) where n is the number of qubits. There are a class of quantum circuits that ...
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10 votes

Quantum circuit for a $3$-qubit $|W \rangle$ state

Given a gate schema $G(p) = \begin{bmatrix} \sqrt{1-p} & -\sqrt{p} \\ \sqrt{p} & \sqrt{1-p} \end{bmatrix}$, you can use $G(1/3)$ to make a circuit that does the trick. First you make a ...
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9 votes
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How can I derive fusion rules for anyons?

Naively, the collection of data which describes a model of anyons is not its fusion rules, but rather its modular data - that is, a pair of matrices $S$ and $T$ which generate a representation of the (...
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9 votes

How do we imagine a Hadamard gate acting on the Bloch Sphere?

The Hadamard gate is a 180 degree rotation around the diagonal X+Z axis of the Bloch sphere. Terrible picture (from a blog post): In the diagram the |0> state ...
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9 votes

How are quantum qubits implemented?

(This post has a bias toward superconducting qubits because that's what I know best. I encourage edits to add more information for the other qubit types) There are many realized and proposed physical ...
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9 votes

How does non-commutativity of observables lead to quantum speedup in solving algorithms in quantum computing?

tl;dr It's not just about observables not commuting. That states can be superposed, entangled etc. is also crucial. Some computational problems can exist at different scales, such as sorting $n$ items,...
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8 votes

Finding the ground state of the toric code Hamiltonian

The $A$ operators and the $B$s all commute with each other because they always share an even number of sites and therefore an even number of Pauli matrices. Therefore, these are all conserved ...
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8 votes
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Quantum Error Correction: Surface code vs. color code

The color code and surface code are very similar. They are stabilizer codes composed of qubits arranged in two dimensions, requiring only geometrically local stabilizer measurements. From the theory ...
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8 votes
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Characterisation of the generalised Bloch space in spherical coordinates

$\newcommand{\bs}[1]{\boldsymbol{#1}}\newcommand{\on}[1]{\operatorname{#1}}$Let $f:\mathbb R^{d^2-1}\to\mathscr B(\mathscr H)$ be the mapping from points in $\mathbb R^{d^2-1}$ to bounded operators on ...
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8 votes
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How does non-commutativity of observables lead to quantum speedup in solving algorithms in quantum computing?

A few thoughts: The "non-commuting observables" aspect of quantum mechanics is essentially equivalent to the possibility of having superpositions, and therefore interference effects etc. ...
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7 votes

Output of a beamsplitter with photon number (Fock) state inputs

The transformation equations you specify are not correct since they do not respect unitarity. The condition of unitarity (or energy conservation) for the action of the beam-splitter gives the ...
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7 votes
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What's the Cause of Quantum Entanglement?

I.The cause of the quantum entanglement is that the wave-function (w.f.) of the involved particles doesn't have the form of the w.f. of independent particles. So, let's begin by defining what is the ...
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