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Quantum error correction research yields unexpected quantum gravity insights
- Researchers have discovered that developing a framework understanding of the subsystem variance parameter described in approximate quantum error correction (AQEC) codes, will help build reliable quantum computers. The resulting threshold creates a generalised method of evaluating AQEC codes, establishing a boundary between good, or non-trivial AQEC codes and bad ones, enabling broader error correction schemes. Researchers noted that the dividing line between trivial and non-trivial AQEC codes in quantum computing also arises as a universal threshold in other physical scenarios, and has revealed unexpected insight into quantum gravity including new approaches to spacetime revealing links to anti-de Sitter/conformal field theory correspondence (AdS/CFT) that could help reconcile quantum mechanics with Einstein's general theory of relativity. They hope to explore AQEC's applications in other interesting physical systems.
- AQEC codes help quantum computers produce consistent errors by allowing mild degrees of approximation that cannot be achieved by exact QEC codes that aim for perfect error correction where errors will become negligible as the system size increases. The performance of AQEC codes and its characteristics remains unclear, raising questions on what separates good, non-trivial AQEC codes from bad ones.
- Researchers have developed a framework by establishing a subsystem variance parameter, which describes the fluctuation of subsystems of states within the code space, linking the effectiveness of AQEC codes to a property known as quantum circuit complexity.
- If the subsystem variance falls below a certain threshold, any code within this regime is considered a non-trivial AQEC code and subject to a lower bound of circuit complexity.
- The threshold creates a more unified framework for evaluating and using AQEC codes enabling broader error correction schemes, essential for building reliable quantum computers.
- The researchers found that the threshold is not arbitrary but rooted in elementary laws of nature and is universal, arising in other physical scenarios, including the study of topological order in condensed matter physics.
- The new framework clarifies the connection between entanglement conditions and topological quantum order, allowing researchers to better understand these exotic phases of matter.
- The new AQEC theory also carries implications beyond quantum computing and shows that their AQEC threshold may be useful for probing certain symmetries in quantum gravity, and could even lead to new approaches to spacetime and gravity, helping to bridge the divide between quantum mechanics and general relativity.
- Researchers plan to explore scenarios where AQEC codes could outperform exact codes, and make the implications for quantum gravity more rigorous. They hope their study will inspire further explorations of AQEC’s applications to other interesting physical systems.
- The research is described in Nature Physics.
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