Quantum computers, technologies that perform computations leveraging quantum mechanical phenomena, could eventually outperform classical computers on many complex computational and optimization problems. While some quantum computers have attained remarkable results on some tasks, their advantage over classical computers is yet to be conclusively and consistently demonstrated. Nature Physics , mathematically shows that simulating random quantum circuits and estimating their outputs is so-called #P-hard for classical computers (i.e., meaning that is highly difficult).
“A key question in the field of quantum computation is: Are quantum computers exponentially more powerful than classical ones?” Ramis Movassagh, who carried out the study, told Phys.org.”Quantum supremacy conjecture (which we renamed to Quantum Primacy conjecture) says yes. However, mathematically it’s been a major open problem to establish rigorously.”
Researchers have recently been trying to demonstrate the advantages of quantum computers over classical computers in various ways, both via theoretical and experimental studies. A key to demonstrating this mathematically would be to prove that it is hard for classical computers to achieve the results of quantum computers with high precision and small margins of error.
“In 2018 a colleague gave a talk at MIT on, at the time, a recent result which tried to provide evidence for the hardness of random circuit sampling (RCS),” Movassagh explained.
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