From University of Cambridge and Perimeter Institute via phys.org: “Study identifies limits on the efficiency of techniques for reducing noise in quantum resources”

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From University of Cambridge

Perimeter Institute
Perimeter Institute

via


phys.org

September 7, 2020
Ingrid Fadelli

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

Quantum technologies, such as quantum computers, quantum sensing devices and quantum memory, have often been found to outperform traditional electronics in speed and performance, and could thus soon help humans to tackle a variety of problems more efficiently. Despite their huge potential, most quantum systems are inherently susceptible to errors and noise, which poses a serious challenge to implementing and using them in real-world settings.

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

Researchers at University of Cambridge in the U.K. and Perimeter Institute for Theoretical Physics in Canada have recently tried to gain a theoretical understanding of the limitations of techniques for “purifying” noisy quantum resources. In a paper published in Physical Review Letters, they mathematically proved the existence of a series of universal limits on the accuracy and efficiency of methods to purify different types of quantum resources associated with practical applications, which play a key role in the functioning of quantum technologies.

“The ideas and techniques discussed in our paper originate from the general ‘one-shot quantum resource theory,’ which we outlined in one of our earlier Physical Review Letters papers,” Zi-Wen Liu, one of the researchers who carried out the study, told Phys.org. “The key idea is to analyze an information-theoretic quantity called the quantum hypothesis testing relative entropy, which is shown to induce universal limitations on noisy-state to pure-state transformations.”

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Credit: Fang & Liu.

Using mathematical theorems, Liu and his colleagues proved a series of fundamental limitations on the extent to which generic noisy resources can be purified, which stem from the laws of quantum mechanics. The calculations they carried out apply to virtually all types of quantum resources.

“More explicitly, we derive nontrivial lower bounds on the error of converting any full-rank noisy state to any target pure-resource state by any free protocol (including probabilistic ones)—and find that it is impossible to achieve perfect resource purification, even probabilistically,” Liu explained. “In particular, there is a nontrivial tradeoff bound between the success probability and the accuracy of the protocol, which is akin to an ‘uncertainty relation.'”

The mathematical theorems introduced by this team of researchers imply the existence of strong limits to the efficiency of distillation, a technique to purify quantum resources that underpins a wide variety of blueprinted quantum technologies. More specifically, these theorems introduce the first explicit lower bounds on the costs of magic state distillation, which is considered to be a leading scheme for realizing scalable and fault-tolerant quantum computation.

“Remarkably, our theorems allowed us to establish the first rigorous understanding of the necessary resource costs of large-scale quantum computing and other quantum technologies,” Liu said. “We expect that our results will serve as important guidelines and find wide-ranging applications in practical scenarios. Moreover, we are writing a follow-up work on extending the no-purification theorems to quantum channels, which are directly applicable to important dynamical scenarios like quantum channel simulation and circuit synthesis, to make the theory more complete.”

In addition to shedding light on the costs and limitations of quantum technologies, the findings improve the understanding of the fundamental principles of quantum mechanics. Like the celebrated no-go theorems, the no-cloning theorem and the uncertainty principle, the new “no-purification” theorems they have introduced are expected to play critical roles in the scientific and practical development of quantum physics. In the future, they could spark further research into how well these limits can be achieved, ultimately paving the way to more efficient quantum technologies for practical real-world applications.

See the full article here .

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Perimeter Institute is a leading centre for scientific research, training and educational outreach in foundational theoretical physics. Founded in 1999 in Waterloo, Ontario, Canada, its mission is to advance our understanding of the universe at the most fundamental level, stimulating the breakthroughs that could transform our future. Perimeter also trains the next generation of physicists through innovative programs, and shares the excitement and wonder of science with students, teachers and the general public.

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The University of Cambridge (abbreviated as Cantab in post-nominal letters) is a collegiate public research university in Cambridge, England. Founded in 1209, Cambridge is the second-oldest university in the English-speaking world and the world’s fourth-oldest surviving university. It grew out of an association of scholars who left the University of Oxford after a dispute with townsfolk. The two ancient universities share many common features and are often jointly referred to as “Oxbridge”.

Cambridge is formed from a variety of institutions which include 31 constituent colleges and over 100 academic departments organised into six schools. The university occupies buildings throughout the town, many of which are of historical importance. The colleges are self-governing institutions founded as integral parts of the university. In the year ended 31 July 2014, the university had a total income of £1.51 billion, of which £371 million was from research grants and contracts. The central university and colleges have a combined endowment of around £4.9 billion, the largest of any university outside the United States. Cambridge is a member of many associations and forms part of the “golden triangle” of leading English universities and Cambridge University Health Partners, an academic health science centre. The university is closely linked with the development of the high-tech business cluster known as “Silicon Fen”.