Quantum Computer Succeeds Where a Classical Algorithm Fails
upstart writes:
Quantum computer succeeds where a classical algorithm fails:
[...] Google's quantum computing group [...] used a quantum computer as part of a system that can help us understand quantum systems in general, rather than the quantum computer. And they show that, even on today's error-prone hardware, the system can outperform classical computers on the same problem.
To understand what the new work involves, it helps to step back and think about how we typically understand quantum systems. Since the behavior of these systems is probabilistic, we typically need to measure them repeatedly. The results of these measurements are then imported into a classical computer, which processes them to generate a statistical understanding of the system's behavior. With a quantum computer, by contrast, it can be possible to mirror a quantum state using the qubits themselves, reproduce it as often as needed, and manipulate it as necessary. This method has the potential to provide a route to a more direct understanding of the quantum system at issue.
[...] The first of these ideas describes some property of a quantum system involving an arbitrary number of items-like a quantum computer with n qubits. This is exactly the circumstance described above, where repeated measurements need to be made before a classical computer can reliably identify a property. By contrast, a quantum computer can store a copy of the system in its memory, allowing it to be repeatedly duplicated and processed.
These problems, the authors show, can be solved on a quantum computer in what's called polynomial time, where the number of qubits is raised to a constant power (denoted nk). Using classical hardware, by contrast, the time scales as a constant raised to the power related to the number of qubits. As the number of qubits increases, the time needed for classical hardware rises much faster.
[...] The second task they identify is a quantum principal component analysis, where computers are used to identify the property that has the largest influence on the quantum system's behavior. This was chosen in part because this analysis is thought to be relatively insensitive to the noise introduced by errors in today's quantum processors. Mathematically, the team shows that the number of times you'd need to repeat the measurements for analysis on a classical system grows exponentially with the number of qubits. Using a quantum system, the analysis can be done with a constant number of repeats.
Journal Reference:
Hsin-Yuan Huang et al., Quantum advantage in learning from experiments, Science, 376, 6598, 2022. DOI: 10.1126/science.abn7293
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