The fundamental quantum theorem now applies to finite temperatures and not only to absolute zero

Absolute zero – the most suitable temperature for both quantum experiments and quantum computers – makes it easier to describe a system by relying on a number of fundamental statements. One of them, the quantum adiabatic theorem, provides for easier dynamics of quantum systems when external parameters change smoothly enough. Since absolute zero is physically inaccessible, expanding the range of theoretical research instruments for finite temperatures is a hot topic. A team of Russian physicists took an important step in this direction by proving the adiabatic theorem at finite temperature and identifying quantitative conditions for the adiabatic dynamics. Your results will be of great interest to next-generation quantum device developers who require fine-tuning of the properties of quantum superpositions with hundreds or thousands of elements. This study was published in Physical verification A.

Quantum effects can help develop ultra-fast computers, ultra-precise measuring devices, and absolutely secure communications, which often require very specific environments in order to function properly. The most comfortable temperature for quantum experiments is absolute zero or -273.15 degrees Celsius. At the same time, the quantum superposition principle, which enables some unimaginable things, such as the famous Schrödinger cat, which can be dead and alive at the same time, can develop its full power. In addition, absolute zero makes the theoretical description of quantum processes somewhat easier and provides physicists and engineers with rigorous suggestions that will help predict the results of quantum experiments and develop quantum devices.

“The third law of thermodynamics says that absolute zero is inaccessible and is just a useful abstraction. In real life, temperatures are always finite and can destroy the underlying fragile quantum overlays, so controlling the fine processes at a finite temperature is the main goal. of quantum technologies, “says Oleg Lychkovskiy, Ph.D. in physics and mathematics and senior scientist at the Skolkovo Institute of Science and Technology (Skoltech), the Moscow Institute of Physics and Technology (MIPT), and the Steklov Mathematical Institute of RAS.

The state of a quantum system is defined by a complex mathematical object called the density operator. As the system’s external control parameters, such as electric or magnetic fields, change over time, the operator will evolve too. The complexity of this evolution, which constitutes the enormous potential of a quantum computer, far exceeds the capabilities of modern supercomputers, even for systems with only hundreds of qubits. However, we should learn to “tame” this complexity in order to develop quantum computers and other quantum devices of the new generation. A fairly simple idea based on adiabatic evolution, one of the fundamental concepts in physics, is that the quantum state could be made a little more predictable by gently varying external parameters.

The adiabatic theorem – a fundamental achievement of quantum mechanics – was first formulated by Max Born and Vladimir Fock at the beginning of quantum mechanics. The theorem ensures that the evolving quantum state always remains close to the so-called momentary eigenstate if external parameters change slowly enough. In a way, adiabatic evolution is like walking a museum with a class of first graders: you should guide your class carefully and in no hurry to make sure that by the end of the tour no one is missing and all of the exhibits are intact.

Although the adiabatic theorem has been refined and improved since the time of Born and Fock, its main limitation was that it only worked for the so-called pure states, but not for all quantum states. This means that it could only be applied to systems at absolute zero, but never at finite temperatures. In our museum example, the tour could only go smoothly if the class consisted of well-behaved A-class students, which is hardly possible in real life. Just as there can be no class without naughty children, there can be no strict zero temperature.

Researchers from Skoltech, Steklov Mathematical Institute of RAS, and MIPT extended the adiabatic theorem to finite temperature systems and obtained quantitative conditions that guarantee the adiabaticity of evolution with a certain accuracy. To illustrate, the team applied these conditions to several modeled systems and discovered that in some, the adiabatic dynamics were even more stable at finite temperature than at absolute zero.

The team’s results contribute to the collection of theoretical research tools used by quantum scientists and engineers. There is a fairly wide variety of adiabatic protocols for creating quantum states with specific properties.

“The adiabatic quantum computer, which is based entirely on the adiabatic theorem, is perhaps the most popular example. D-Wave Systems Inc. in Canada is currently working on this type of device. In addition, the adiabatic preparation of quantum states is a first or additional step in other quantum designs as well as simulations and measurements. Our results will help select the optimal operating modes for adiabatic protocols while also taking into account that quantum devices operate at finite temperatures, “concludes Lychkovskiy.