27

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 ...


26

Firstly, a classical computer does basic maths at the hardware level in the arithmetic and logic unit (ALU). The logic gates take low and high input voltages and uses CMOS to implement logic gates allowing for individual gates to be performed and built up to perform larger, more complicated operations. In this sense, typing on a keyboard is sending ...


19

Is a dilution refrigerator the only way to cool superconducting qubits down to 10 millikelvin? There's another type of refrigerator that can get to 10 mK: the adiabatic demagnetization refrigerator (ADR).$^{[a]}$ why is dilution refrigeration the primary method? To understand that, let's talk about one of the main limitations of the ADR. How an ADR ...


15

Here is my process for doing arithmetic on a quantum computer. Step 1: Find a classical circuit that does the thing you're interested in. In this example, a full adder. Step 2: Convert each classical gate into a reversible gate. Have your output bits present from the start, and initialize them with CNOTs, CCNOTs, etc. Step 3: Use temporary outputs. If ...


12

The transmon is a Josephson junction and capacitor in parallel. Originally, transmons were differential circuits, i.e. two transmons on the same chip were not galvanically connected in any way. In other words, transmons didn't share a ground reference. Furthermore, in the early days, transmons were almost always embedded into the middle of a harmonic ...


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 ...


7

Disclosure: while I am not an experimental physicist, I am part of the NQIT project, which is aiming to develop quantum hardware which is suitable to realise scalable quantum computers. The architecture that we're investing most heavily in is optically linked ion traps. Ions represent some of the physically best understood systems to experimental and ...


7

Getting enough capacitance and maintaining coherence essentially set the size limit. A superconducting qubit, for the purposes of answering this question, can be imagined as an oscillator consisting of an inductor and a capacitor. The frequency of the oscillator can't be too high otherwise controlling the qubit becomes difficult. At Google, we typically work ...


6

It think the (very) short answer is that there is not a preferred platform yet. This is why there are very active research communities around each of these technologies. Often if someone says otherwise they are probably working on one of the platforms :)


6

Kirchhoff to Lagrangian Let's approximate the transmon as a parallel LC resonant circuit. Suppose we connect a voltage source through a coupling capacitor $C_d$ (d for "drive") to a transmon qubit. If the voltage of the source is $V_d(t)$, then Kirchhoff's equations for the circuit are $$\frac{1}{C/C_d} \dot{V}_d(t) = \ddot{\Phi}(t) + \frac{\omega_0^2}{1 + ...


5

What does "obtaining samples" mean in this context? The same thing it means in a more classical context. Consider the probability distribution of the possible outcomes of a (possibly biased) coin flip. Sampling from this probability distributions means to flip the coin once and record the result (head or tail). If you sample many times, you can retrieve ...


5

TL/DR: The two-qubit gates are going by the moniker "Sycamore gates" in the paper, and it appears that they would ideally want to explore more of the $(\phi, \theta)$ phase-space but for their purposes (of quantum supremacy) their current Sycamore gate is sufficient. The pattern of gates $\mathrm{ABCDCDAB}$ was chosen to avoid "wedges" and maximize/optimize ...


5

What follows turned out to be a rather technical explanation, so I'll start with the main point: The qubit state can change the resonator's state, and the resonator's state can be easily measured only if there is a large different in frequencies between the qubit and the resonator. Let's model a qubit as a two-level system and a resonator as a harmonic ...


5

Here's a paper comparing Trapped Ion and Superconducting (the main competitors right now) from the group at UMD which compares their trapped ion system with IBM's transmon (superconducting) system. If you want to look at a more algorithm-focused line of thought. If you are looking for a more general summary of the strengths and weaknesses this paper seems ...


5

The resonance frequencies of TLS fluctuate due to their interaction with neighboring TLS, which occurs through electric dipole interaction or the local mechanical strain in the material. If a TLS at low energy (below kB*T) is involved, this one may change its state randomly due to thermal activation. The resulting change in local electric field or strain can ...


5

In one sense, the Xmon qubit is a transmon qubit, in that they both operate in the $E_J>>E_c$ regime of the CPB Hamiltonian and take advantage of the exponentially suppressed charge noise vs. polynomial decrease in anharmonicity effect discussed in (Koch, 2007). You could work out the dynamics of a superconducting qubit-resonator system without ever ...


4

Yes, they use $\require{\mhchem}\ce{^3He}$ and $\ce{^4He}$. No, they do not use compounds of these but instead a solution of these two (at the operating temperature) liquid nobel gases. The details can be found in the wikipedia article on dilution refrigerators.


3

By coincidence, this article just came out on Ars Technica which might answer some of your questions. (This is not an endorsement of everything written in that article. But the author basically asked, and researched, the same question that you're asking.) The TL;DR answer is that superconducting qubits are manufactured and allow for better control over ...


3

There's a superconducting circuit element called Josephson junction, which is roughly a nonlinear inductor. The inductance of a Josephson junction depends on current via the relation $$L(I) = \frac{L_0}{\sqrt{1 - (I/I_c)^2}}$$ where $L_0$ is the inductance of the junction with no bias current and $I_c$ is the so-called "critical current" which is the maximum ...


3

While a follow-up question asks for the motivation behind the two-qubit gates used in Sycamore, this question focuses on the random nature of the single qubit operations used in Sycamore, that is, the gates $\{\sqrt{X},\sqrt{Y},\sqrt{W}=(X+Y)/\sqrt{2}\}$ applied to each of the $53$ qubits between each of the two-qubit gates. Although I agree with @Marsl ...


3

For superconducting qubits, x and y rotations are usually both done with microwave pulses, and as you said the phase of the pulse determines the rotation axis. See mathematical details in this Physics Stack Exchange post: How do we perform transverse measurements in a two level system? Rotations about the z axis are quite different; they are done by ...


3

Each of the two spins, $q\in\{L,R\}$, has a bunch of energy levels $\{|n\rangle_q\}$, each at energy $\omega_{n}^q$. In other words, the basic Hamiltonian of the spins is: $$ H=\sum_{n=0}^{N}\omega_{n}^L|n\rangle\langle n|_L+\omega_{n}^R|n\rangle\langle n|_R $$ Written like this, the two spins are not interacting, so we won't get a two-qubit gatewithout ...


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

Whilst we normally talk about $\left|0\right>$ and $\left|1\right>$ as unchanging states in quantum computing, this is not usually the case in a physical realization where there tends to be an energy difference $\Delta E$ between these states such that $\left|1\right>_\mathrm{logical} = e^{-it \Delta E / \hbar} \left|1\right>_\mathrm{physical}$. ...


2

This answer only addresses the part about the necessity of the randomness of the circuit because I am by no means familiar with the physical implementation of the qubits at Google and what kind of constraints these impose on the implementation of certain gates. Now, for the randomness: Consider the problem of sampling from the output distribution of a ...


2

I think the subject matter of supercondcuting qubits is rather broad and diverse, making it challenging to accurately capture it in a 'brief explanation'. With that said, this recent review (Krantz et al., Applied Physics Reviews 6, 021318 (2019)) - "A Quantum Engineer's Guide to Superconducting Qubits" (arXiv:1904.06560) from the MIT group may be a good ...


1

They are resources to help people get started with learning about quantum computing. They are also useful to help further research as services such as IBM Q Experience provide access to real quantum computers, and so people can conduct research using them.


1

Not sure if this answers your question directly, but Docplex, which is IBM's Decision Optimization CPLEX Modeling for Python is capable of generating an Ising hamiltonian from a cost function. Take a look at this qiskit tutorial.


1

According to [1]: Readout error is the error in measuring qubits. You read the figure correctly (44 out of 1000 measurements fail on reading). Note there is yet another, though minor, error there: gate error. It is about errors in quantum gate operation, and is one 10th less than the error of measurement. So, actually there may occur more erroreus ...


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