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A quantum computer is a remarkable device. While, at current, it's still limited in its application, we now know that it can be faster than the fastest computers we currently have access to. As Scientific American reminds us, quantum primacy (also known as quantum supremacy) is the point at which a quantum machine outstrips a classical computer. Computers have helped advance civilization and increased our ability to process data many times over. Even so, there are some problems that not even they can solve. The more answers we find, the more questions we have. Quantum computing was built to multiply computing power by tapping into what we know about quantum states. While a traditional computer is limited by bits, quantum computers aren't, allowing them to perform calculations many times faster. Or so it's assumed. There's still much debate as to whether we've gotten to the point of quantum primacy or not. Are quantum computers faster than regular computers, or aren't they?

When we compare different classical computers, we use the clock speed of their processors to figure out how "fast" they are. For example, a 3GHz processor can perform two billion compute cycles per second. With quantum computers, it's a little more challenging to determine how fast it's doing its processes. Quantum computers use a system known as quantum bits or qubits. Classical computers contain binary bits that can either be a 1 or a 0. Qubits, by comparison, can be any of a set of quantum states and are sometimes superpositioned over one another. The physics behind it deals with the quantum particle's spin and considers that quantum states only collapse when they are observed. Because of these things, it can be challenging to put a value on a quantum computer's processing speed. Still, it's assumed that they will be many times faster than traditional computers using the same resources.

So why would we say that we've gotten to quantum primacy while some experts are still skeptical? The heart of the matter lies in how we do tests to verify the difference in processing speed between a quantum computer and a traditional one. In practice, when comparing a conventional system to a quantum computer, the go-to method is using sampling problems. Sampling problems are computational problems with solutions that are random instances of a given probability distribution. However, the question arises from a computing standpoint as to whether the best possible algorithm was used. Traditional computing places a lot of stock in the efficiency of algorithms, and by not using the best case for the random generation, experts argue that the quantum computer has an unfair advantage.

In a paper published in Physical Review Letters, a team from the University of Science and Technology of China has sought to challenge the limitations of testing. The team set up a case where they would use a superconducting system to demonstrate that a quantum computer could deliver accurate results in situations where classical computing cannot simulate anything similar. The non-specialist may find this description challenging to break down, but the easiest way to think about it is that the research team increased the number of sequential calculations within the system so that it would be impossible to have the same physical clock speed on a traditional computer. In this sense, raw processing power seems to be the metric by which the quantum computer is establishing its dominance.

The superconducting experiment takes a quantum processor and tasks it with a sampling problem. The problem is to produce random instances of measurements for experimental data, outputting in qubits. The logic behind this experiment is that this should be almost impossible for a traditional computer but feasible for a quantum machine. The only way that true quantum primacy can be established is by using large-scale sampling problems. In this experiment, the number of circuits used was large enough to guarantee a massive sample size but small enough to still be feasible to implement. However, the superconductor test was only one of two tests the team used to prove quantum primacy. The establishment of the investigation still has some detractors, but it's a step in the right direction.

The second test was known as the photonic experiment, seeking to solve the problem of boson sampling. The methodology for boson sampling requires a lot of processing for a traditional computing system, but theoretically, it should be a simple process for a quantum machine. While boson sampling has an ideal mathematical formula, it's difficult to realize experimentally. As a result, generalizations would need to be made, resulting in "Gaussian" boson sampling. While Gaussian boson sampling is experimentally viable, the results are much more challenging to prove quantum primacy with. However, given the assumptions made on classical systems and increasing the time scale to match what would be expected, the quantum computer managed to deliver results in a fraction of the calculated time. This result suggests that quantum machines are, indeed, "faster" than traditional computers.

Quantum computers are still a way off from being commercially viable machines. However, their power and the ability to deal with complex problems offer them a solution to questions in other areas of physics that need this type of computational system. When quantum primacy is mentioned, the issue that constantly comes up is whether classical computers can spoof results that "seem" right enough. These complex problems decrease the chance of spoofing, establishing a baseline that can be used to determine whether quantum computers are as fast as we assume they are. Can these samplers be used to solve complex physics problems? The possibility of using these systems to solve computationally difficult problems is one of the biggest questions of our time, but the initial results suggest that it can. On the other hand, researchers claim that, to date, there aren't any real, meaningful questions that the system can be used to test, leaving interpretation open. These two experiments are a great leap forward in putting quantum sampling to practical use in the field.

Link:

Understanding Quantum Primacy And How We Got There - Science 2.0