The study identifies limits on the efficiency of techniques for reducing noise in quantum resources

A drawing representing distillation — a fundamental subroutine for quantum technologies. Credit: Fang and Liu.

Quantum computers, such as quantum computers, quantum sensing devices, and quantum memory, have often been found to improve traditional electronics in speed and performance, and thus may soon help humans deal with a wide variety of problems. Despite their vast potential, most quantum systems are inherently susceptible to errors and noise, which is a serious challenge to implement and use them in real-world settings.

To enable large-scale implementation of quantum technologies, researchers are trying to develop techniques that can make them more flexible for noise and less prone to errors. While some of these methods, such as quantum error correction and fault tolerance, have proved useful and are now cornerstones of quantum informatics, the factors limiting the performance of quantum systems in real-world applications are still poorly understood.

Researchers from the University of Cambridge in the UK and the Perimetical Institute for Theoretical Physics in Canada have recently tried to gain a theoretical understanding of the limitations of techniques for “noisy” resources. In a letter published in Physical review letter, He mathematically proved the existence of a series of universal limits on the accuracy and efficiency of methods for purifying various types of quantum resources associated with practical applications, which play an important role in the functioning of quantum technologies.

“The ideas and techniques discussed in our paper originate from general ‘one-shot quantum resource theory, which we outlined in one of our earlier PRL papers,” Xi-Wen Liu, study One of the researchers, told “The main idea is to analyze an information-theory quantity called a quantum hypothesis test relative entropy, which has been shown to induce universal limits on the noise-state for pure-state transformations.”

The study identifies limits on the efficiency of techniques for reducing noise in quantum resources

Credit: Fang and Liu.

Using mathematical theorems, Liu and his colleagues proved a series of fundamental limitations to the extent to which general noise resources can be purified, which stems from the laws of quantum mechanics. The calculations he performed apply to almost all types of quantum resources.

“More explicitly, we obtain the nontrivial lower limit on the error of converting any target net-resource state to a full-rank noise state by any complete protocol (including probabilistic ones) – and find that this completeness It is impossible to achieve purification, even potentially, ”Liu explained. “In particular, there is a nontrivial tradeoff bound between the probability of success and the accuracy of the protocol, which is similar to the ‘indefinite relationship’.

Mathematical theorems initiated by this team of researchers exist strong limitations to the efficiency of distillation, a technique for purifying quantum resources that outlines a range of blueprint quantum technologies. More specifically, these theorems introduce the first clear lower limit on the costs of magic state distillation, which is considered a pioneering scheme for realizing scalable and fault-tolerant quantum calculations.

“Remarkably, our theorems allowed us to establish the first rigorous understanding of the required resource costs of large-scale quantum computing and other quantum technologies,” Liu said. “We expect our results to serve as important guidelines and find broader applications in practical scenarios. In addition, we are writing a follow-up work on extending the no-purification theorems to quantum channels, directly leading to critical dynamic scenarios. Applied to. To make the theory more complete, like quantum channel simulation and circuit synthesis. ”

In addition to shedding light on the costs and limitations of quantum technologies, the findings improve understanding of the fundamentals of quantum mechanics. Like the well-known no-go theorems, the no-cloning theorem and the uncertainty principle, the new “no-purification” theorems introduced by them are expected to play an important role in the scientific and practical development of quantum physics. In the future, they may pursue research on how well these limitations can be achieved, eventually paving the way for more efficient quantum technologies for practical real-world applications.

Noise pulsation through superposition of order

more information:
Kun Phang et al. No-Go Theory for Quantum Resource Refining, Physical review letter (2020). DOI: 10.1103 / PhysRevLett.125.060405
Xie-Wen Liu et al. One-Shot Operational Quantum Resource Theory, Physical review letter (2019). DOI: 10.1103 / PhysRevLett.123.020401

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