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How Many Qubits Are Needed for Quantum Computational Supremacy? by Dalzell, Alexander M.; Harrow, Aram W.; Koh, Dax Enshan; La Placa, Rolando L. is a scholarly article available to read on EtoBox.

What is How Many Qubits Are Needed for Quantum Computational Supremacy? about?

Quantum computational supremacy arguments, which describe a way for a quantum computer to perform a task that cannot also be done by a classical computer, typically require some sort of computational assumption related to the limitations of classical computation. One common assumption is that the polynomial hierarchy (PH) does not collapse, a stronger version of the statement that P $\neq$ NP, which leads to the conclusion that any classical simulation of certain families of quantum circuits requires time scaling worse than any polynomial in the size of the circuits. However, the asymptotic nature of this conclusion prevents us from calculating exactly how many qubits these quantum circuits must have for their classical simulation to be intractable on modern classical supercomputers. We refine these quantum computational supremacy arguments and perform such a calculation by imposing fine-grained versions of the non-collapse assumption. Each version is parameterized by a constant $a$ and asserts that certain specific computational problems with input size $n$ require $2^{an}$ time steps to be solved by a non-deterministic algorithm. Then, we choose a specific value of $a$ for each v

Author

Dalzell, Alexander M.; Harrow, Aram W.; Koh, Dax Enshan; La Placa, Rolando L.

Published

2018

Language

EN