Temporal entropy: The clock puzzle limiting the future of quantum computing

Quantum computing is increasingly easier to use to perform calculations. However, research shows that quantum computing has inherent limitations, particularly related to the quality of the clocks used.

People have different ideas about how to build a quantum computer. But they all have one thing in common: taking a quantum physical system - such as a single atom - and subjecting it to very specific forces for a specific period of time, thereby changing its state. However, this means that in order to be able to rely on quantum computing operations to provide correct results, you need a clock that is as accurate as possible.

But here's the problem: perfect time measurement is impossible. Every clock has two basic characteristics: a certain accuracy and a certain time resolution. Temporal resolution represents how small a measurable time interval is, i.e. how fast a clock ticks. Accuracy indicates the error of each scale.

The team was able to show that since no clock has an infinite amount of available energy (or produces an infinite amount of entropy), it can never have perfect resolution and perfect accuracy at the same time. This fundamentally limits the possibilities of quantum computers.

In our classical world, perfect arithmetic operations are no problem. For example, you could use an abacus by threading wooden beads on a stick and pushing them back and forth. Wooden beads have a well-defined state. Each wooden bead is in a very specific position. If you do nothing, the wooden beads will stay in their original position.

Whether you move the wooden beads quickly or slowly will not affect the results. But in quantum physics, the situation is much more complicated.

"Mathematically speaking, changing the quantum state in a quantum computer is equivalent to rotating in a higher dimension. In order to finally reach the desired state, the rotation must last for a very specific period of time. Otherwise, you will turn the state too short or too far."

Entropy: time makes everything more chaotic

Markus Huber and his team investigated which laws must always apply to every conceivable clock. He explains: "The measurement of time is always related to entropy. In every closed physical system, entropy increases and becomes more and more disordered. It is this development that determines the direction of time: the future is a place of higher entropy, and the past is a place of lower entropy."

As shown in the figure, every measurement of time is inevitably accompanied by an increase in entropy: for example, a clock requires a battery, and the energy of the battery is eventually converted by the clock's mechanism into frictional heat and ticking sound - in the process, a rather ordered state of the battery is transformed into a rather disordered state of thermal radiation and sound.

Based on this, the team created a mathematical model that essentially every imaginable clock must adhere to. Florian Meier, lead author of the second paper, said: "At a certain increase in entropy, there is a trade-off between time resolution and accuracy. This means: the clock either works quickly or it works accurately - it is impossible to do both at the same time."

The limits of quantum computers

This realization creates a natural limit for quantum computers: the resolution and precision a clock can achieve limits the speed and reliability a quantum computer can achieve. "This is not yet a problem," says Markus Huber. "The accuracy of quantum computers is still limited by other factors, such as the accuracy of the components used or the electromagnetic field. But our calculations also show that today we are not far away from a mechanism in which the fundamental limits of time measurement play a decisive role."

Therefore, if quantum information processing technology is further improved, people will inevitably face the problem of non-optimal time measurement. But who knows: maybe this is an interesting way for us to understand the quantum world.