Building the quantum internet

Do you remember your first computer? And your first internet connection?  Sure, they were not as powerful as today’s technology but it was something completely new and opened many possibilities. A quantum computer, ideally connected to quantum internet, must then be even more remarkable. Although it is true that algorithms for quantum computers focus on abstract mathematical tasks such as factoring large numbers, everyday life applications will certainly come as well. After all, classical computers were also originally seen solely as calculators.

We have now pretty good idea what the quantum internet could look like. Because quantum systems are very sensitive to disturbances and quantum features do not survive for long, the ideal medium for transmitting quantum signals is light. It travels fast and almost does not interact with the surrounding environment so quantum effects can survive a long-distance transfer.

Quantum computers, on the other hand, can in principle be built in many different ways. Some scientists trap ions in electric fields and use them as the basic building blocks. Others try to build the whole quantum computer from a single molecule and use different parts of this molecule as quantum bits that store information. Some try to use light to perform quantum computations since such quantum computers are then easily connected via quantum internet. There are also those who use superconducting systems.

In a way, superconducting systems are, in their form, most similar to classical computers. You can build a chip from the right material, similarly to an integrated circuit in a normal computer. Then you cool the chip down to temperature of a few Kelvin (around -270 degrees Celsius) and it becomes superconducting — it starts to transmit current without any resistance. Quantum bits can then be represented by superconducting currents of various strength, similar to normal computers.

There is just one problem with superconducting quantum computers — it is not possible to connect them to optical quantum internet. Energy of superconducting qubits is much smaller than that of an optical photon so they do not interact well. Superconducting systems can interact with microwave fields but those cannot be transmitted as easily as light because they require low temperatures (just like superconducting systems) to overcome noise.

The solution is simple: We let the superconducting qubits interact with microwave photons which can then be converted to light using mechanical oscillators. Or we can even skip the microwave field and couple superconducting qubits directly to mechanical oscillators. That is possible because superconducting qubits are built using capacitors and some other elements. If one of the capacitor plates can vibrate, its position will affect the state of the qubit and the state of the qubit, in turn, determines the position of the vibrating plate.

Because we do not have quantum computers just yet, we can start with a smaller task — we can try to entangle two superconducting qubits that sit on two different chips. That would be a first step towards building quantum internet with superconducting systems.

Measurement of the number of excitations
Number of excitations of two qubits can be measured if the signal from the first qubit (the sphere with arrow) is converted using a transducer (blackbox), transmitted and converted back.

The approach I like is based on measurement feedback and there are two options how to use it. The first one uses entanglement swapping where each of the qubits interacts with a microwave field in a way that generates entanglement between them. The microwave field is then converted to light and travels to a detector where both the fields are measured together. In this way, the entangled state is teleported from a microwave field to a qubit and both qubits become entangled.

Entanglement swapping with two qubits
Entangling qubits with their transducers locally and then performing joint measurement on the light fields, one can entangle the two qubits.

Another option is to engineer the system in such a way that we perform a measurement of the number of excitations of the two qubits. Each qubit has two levels — denoted by 0 and 1 and thus showing the number of excitations in the qubit. If we prepare the qubits in a suitable state and the measurement reveals that one qubit is excited but we do not know which one, they become entangled. That is commonly done with superconducting qubits (without coupling to light, though). With the optical link, this can be done in the following way: we let one qubit interact with a microwave field which then gets converted to light. The light gets transmitted to the second qubit where it is converted back to microwave frequency, interacts with the second qubit, and is measured.

So far it seems that such tasks can be performed with mechanical oscillators that need not be much better that what is available currently. We thus might see the first steps towards quantum networks with superconducting qubits in the near future. But it will still be a long way to go if we want to build quantum computers connected by quantum internet.

This post is loosely based on talk I held at the Spring meeting of the German Physical Society in Heidelberg, March 2015.

Is nature scared of emptiness?

There can never be a truly empty space. That was the opinion of many scholars from the times of ancient Greece up to the beginning of the twentieth century. When the idea of aether as a medium in which light can travel has been refuted, the existence of vacuum became widely accepted. But then the quantum revolution came, and nothing is ever simple with quantum physics.

The main obstacle in achieving space that is entirely empty is the Heisenberg uncertainty principle. It states that the position and momentum of an object can never be known exactly. This is, furthermore, not just due to technical imperfections in measuring these quantities; the object itself does not know them exactly.

Let us now take a glass cell and pump all air out. If we also leave it in complete darkness, there will be no light and, therefore, no electromagnetic field and no atoms or molecules inside, right?

Not quite. Light is an oscillating electromagnetic field and as such can be mathematically described as a harmonic oscillator, similar to a pendulum. And a harmonic oscillator has a position and momentum which, even at ground state (i.e., with no light), cannot be exactly zero but have some uncertainty. So there still is some electromagnetic field present, even in complete darkness!

But things can get even weirder because in quantum physics, virtually everything can be described as a harmonic oscillator. For every kind of particles, there can be defined a field whose excitations are the respective particles. For light, there is the electromagnetic field and the particles are photons, electrons are excitations in an electron field, and so on. And each harmonic oscillator has to follow the uncertainty principle. In our glass cell, we thus have a small bit of fluctuations of the electromagnetic field but also fluctuations for electrons and other particles. Vacuum is an endlessly boiling soup where every now and then an electron pops out and disappears again, then a quark, then something else.

Two metallic plates placed in vacuum will attract or repel each other due to vacuum fluctuations.
Two metallic plates placed in vacuum will attract or repel each other due to vacuum fluctuations.

Does all that sound ridiculous? It turns out that these phenomena have observable effects. Take, for instance, two metallic plates placed in vacuum. One would naively expect that nothing will happen to them since they are in vacuum. But we know better — there are always fluctuations, and these will be smaller in the space between the plates than everywhere around. As a result, the plates will attract each other; in a different configuration than parallel, they could even repel. This behaviour is known as Casimir effect (though I am stretching things a bit here — only the fluctuations of the electromagnetic field are important for the Casimir effect) and has already been observed in an experiment.

Another, even more important evidence of fluctuations of the vacuum is the existence of spontaneous emission. If you excite an atom (for example by shining light on it) it will eventually radiate the energy it absorbed and end up in its ground state. But from the point of view of classical physics, this happens only when there is electromagnetic field around the atom. This means that an excited atom in utter darkness should stay excited — but it does not! This can only be explained by quantum physics; fluctuations in the vacuum are strong enough to kick the atom to its ground state while emitting a photon, similarly to the presence of electromagnetic field in the classical picture.

So remember — vacuum (for instance the vast empty space between you and the nearest star when watching the skies at night) is not empty. It is alive with many particles that we can never directly see, swirling around. And nature maybe, after all, really is scared of emptiness.

Wi-Fi for a quantum computer

The basic picture of an optomechanical system, that even many scientists keep in mind, is that of a cavity with one movable mirror. But that is not the only way to achieve coupling between light and mechanical vibrations. Every time light is strong enough (and the mechanical oscillator light enough), the light can be used to control the vibrational state of the mechanical system.

Optomechanical systems can take on various forms, such as a vibrating mirror inside a cavity or a vibrating microdisk.
Optomechanical systems can take on various forms, such as a vibrating mirror inside a cavity or a vibrating microdisk.

People have studied all sorts of different systems this way. One option is to use a cavity (with both mirrors fixed) and put a vibrating membrane inside. Other scientists work with microdisks where light travels around thanks to total internal reflection; if the disk can vibrate, strong light will excite mechanical vibrations of the disk. And there are optomechanical platforms that are more exotic than these examples.

The beauty of the theoretical description of such systems lies in the fact that they are all described by the same mathematics. This stays true even if we do not use visible light but a microwave field which cannot be trapped in a cavity using two simple mirrors. Instead, microwave cavities have the form of LC circuits — basic electrical circuits with an inductor (basically a coil) and a capacitor (two conducting plates separated by a thin layer of a dielectric material) that have been used in electronics for decades.

Optomechanics can be studied even in microwave systems, where the role of the optical cavity is taken by an LC circuit and vibrating mirror is replaced by an oscillating capacitor plate.
Optomechanics can be studied even in microwave systems, where the role of the optical cavity is taken by an LC circuit and vibrating mirror is replaced by an oscillating capacitor plate.

If such a circuit is to be used in the quantum regime, though, it is not that simple. The circuit has to be built from a superconducting material (and cooled down for the experiments) so that the electrical signals can travel through the circuit many times without being absorbed. If we now make one of the capacitor plates vibrating, usually by making it from a membrane, the following happens:

The microwave field acts as a varying electric field across the capacitor. Since the membrane can freely vibrate, it will move in accordance with the electric field. But that results in varying distance between the capacitor plates which affects the resonance of the LC circuit in a way similar to a moving mirror in an optical cavity. The whole system is then described in the same way as other optomechanical systems — even though we now use a microwave field, instead of visible light!

Imagine that we now take such an LC circuit with a vibrating membrane and put the membrane in an optical cavity (either by making it an end mirror or putting it inside a closed cavity). The microwaves as well as the visible light can now swap state with the vibrating membrane. Using such a system, we can, for example, swap the state of the microwave field and the membrane and then swap the state of the membrane and the visible light. Any signal that was initially encoded in the microwave field has now been converted to light.

Combining microwave and optical cavity with a vibrating membrane, we get a system that is capable of converting microwaves to visible light and vice versa.
Combining microwave and optical cavity with a vibrating membrane, we get a system that is capable of converting microwaves to visible light and vice versa.

Such a conversion is commonly done in the classical world — Wi-Fi uses microwaves to send signals between your computer and router and light is used in optical fibres to transmit these signals over long distances to a server. This is done by the router measuring the microwave signal, transmitting it to a modem via a cable where it is measured again, sent in the form of light to the other end where the process is repeated in reverse. That is something you cannot do in the quantum world where every measurement destroys the quantum nature of the signal. This is why more sophisticated methods — such as swapping the state with a mechanical oscillator — have to be used.

There is one immediate application for these opto-electromechanical systems (i.e., systems comprising an optical cavity, an LC circuit, and a mechanical oscillator). The conversion of microwave signals to visible light can be used to improve detection efficiency of weak microwave fields. That is a task that is very difficult to do. But if you could efficiently convert these signals to light, you would need to measure weak light pulses instead, which is easier. Radio astronomers, for instance, can then use these systems to detect weaker sources of radio waves in the universe. Magnetic resonance imaging can profit by reaching better accuracy than with current detection strategies, which could lead to earlier diagnoses of serious illnesses. But we still have to wait for these applications — there is a long way between a successful experimental demonstration and a practical use of an effect.