Absolute zero is the temperature at which all matter reaches its lowest possible energy state. In a quantum computer, achieving temperatures near absolute zero is essential to ensure that quantum bits, or qubits, remain in a stable state and do not suffer from unwanted interference.

Absolute zero cannot be reached – unless you have an infinite amount of energy or an infinite amount of time. Scientists in Vienna (Austria) studying the connection between thermodynamics and quantum physics have now found out that there is a third option: Infinite complexity. It turns out that reaching absolute zero is in a way equivalent to perfectly erasing information in a quantum computer, for which an infinetly complex quantum computer would be required.

The absolute lowest temperature possible is -273.15 degrees Celsius. It is never possible to cool any object exactly to this temperature – one can only approach absolute zero. This is the third law of thermodynamics.

A research team at TU Wien (Vienna) has now investigated the question: How can this law be reconciled with the rules of quantum physics? They succeeded in developing a “quantum version” of the third law of thermodynamics: Theoretically, absolute zero is attainable. But for any conceivable recipe for it, you need three ingredients: Energy, time and complexity. And only if you have an infinite amount of one of these ingredients can you reach absolute zero.

From information theory, we know the so-called Landauer principle. It says that a very specific minimum amount of energy is required to delete one bit of information.

Prof. Marcus Huber

**Information and thermodynamics: an apparent contradiction**

When quantum particles reach absolute zero, their state is precisely known: They are guaranteed to be in the state with the lowest energy. The particles then no longer contain any information about what state they were in before. Everything that may have happened to the particle before is perfectly erased. From a quantum physics point of view, cooling and deleting information are thus closely related.

At this point, two important physical theories meet: Information theory and thermodynamics. But the two seem to contradict each other: “From information theory, we know the so-called Landauer principle. It says that a very specific minimum amount of energy is required to delete one bit of information,” explains Prof. Marcus Huber from the Atomic Institute of TU Wien. Thermodynamics, however, says that you need an infinite amount of energy to cool anything down exactly to absolute zero. But if deleting information and cooling to absolute zero are the same thing – how does that fit together?

**Energy, time and complexity**

The problem stems from the fact that thermodynamics was developed in the nineteenth century for classical objects such as steam engines, refrigerators, and glowing pieces of coal. People had no idea about quantum theory at the time. To understand the thermodynamics of individual particles, we must first examine how thermodynamics and quantum physics interact – exactly what Marcus Huber and his colleagues did.

“We quickly realized that you don’t have to use infinite energy to achieve absolute zero,” Marcus Huber says. “It is also possible with finite energy, but it takes an infinitely long time.” Considerations are still compatible with classical thermodynamics as we know it from textbooks up to this point. But then the team came across an additional detail of crucial importance:

“We found that quantum systems can be defined that allow the absolute ground state to be reached even at finite energy and in finite time – none of us had expected that,” says Marcus Huber. “But these special quantum systems have another important property: they are infinitely complex.” So you would need infinitely precise control over infinitely many details of the quantum system – then you could cool a quantum object to absolute zero in finite time with finite energy. In practice, of course, this is just as unattainable as infinitely high energy or infinitely long time.

**Erasing data in the quantum computer**

“So if you want to perfectly erase quantum information in a quantum computer, and in the process transfer a qubit to a perfectly pure ground state, then theoretically you would need an infinitely complex quantum computer that can perfectly control an infinite number of particles,” says Marcus Huber. In practice, however, perfection is not necessary – no machine is ever perfect. It is enough for a quantum computer to do its job fairly well. So the new results are not an obstacle in principle to the development of quantum computers.

In practical applications of quantum technologies, temperature plays a key role today – the higher the temperature, the easier it is for quantum states to break and become unusable for any technical use. “This is precisely why it is so important to better understand the connection between quantum theory and thermodynamics,” says Marcus Huber. “There is a lot of interesting progress in this area at the moment. It is slowly becoming possible to see how these two important parts of physics intertwine.”