Variational Quantum Algorithms (VQAs) rely upon the iterative optimization of a parameterized unitary circuit with respect to an objective function. Since quantum machines are noisy and expensive resources, it is imperative to choose a VQA's ansatz appropriately and its initial parameters to be close to optimal. This work tackles the problem of finding initial ansatz parameters by proposing CAFQA, a Clifford ansatz for quantum accuracy. The CAFQA ansatz is a hardwareefficient circuit built with only Clifford gates. In this ansatz, the initial parameters for the tunable gates are chosen by searching efficiently through the Clifford parameter space via classical simulation,more »
How many qubits are needed for quantum computational supremacy?
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 ( P H ) does not collapse, a stronger version of the statement that P ≠ N P , 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 finegrained versions of the noncollapse conjecture. Our first two conjectures poly3NSETH( a ) and perintNSETH( b ) take specific classical counting problems related to the number of zeros of a degree3 polynomial in n variables over F 2 or the permanent of an n × n integervalued matrix, and assert that any nondeterministic algorithm that solves them requires 2 c n more »
 Publication Date:
 NSFPAR ID:
 10212758
 Journal Name:
 Quantum
 Volume:
 4
 Page Range or eLocationID:
 264
 ISSN:
 2521327X
 Sponsoring Org:
 National Science Foundation
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