Zobrazeno 1 - 10
of 13 517
pro vyhledávání: '"Aaronson A"'
This paper furthers existing evidence that quantum computers are capable of computations beyond classical computers. Specifically, we strengthen the collapse of the polynomial hierarchy to the second level if: (i) Quantum computers with postselection
Externí odkaz:
http://arxiv.org/abs/2410.20935
Autor:
Aaronson, Jon., Nakada, Hitoshi
For an invariant probability measure for the Gauss map, almost all numbers are Diophantine if the log of the partial quotent function is integrable. We show that with respect to a ``Renyi measure'' for the Gauss map with the log of the partial quoten
Externí odkaz:
http://arxiv.org/abs/2409.19393
We study the complexity of testing properties of quantum channels. First, we show that testing identity to any channel $\mathcal N: \mathbb C^{d_{\mathrm{in}} \times d_{\mathrm{in}}} \to \mathbb C^{d_{\mathrm{out}} \times d_{\mathrm{out}}}$ in diamon
Externí odkaz:
http://arxiv.org/abs/2409.12566
Autor:
Aaronson, Scott, Zhang, Yuxuan
Over a decade after its proposal, the idea of using quantum computers to sample hard distributions has remained a key path to demonstrating quantum advantage. Yet a severe drawback remains: verification seems to require classical computation exponent
Externí odkaz:
http://arxiv.org/abs/2404.14493
We define and study a variant of QMA (Quantum Merlin Arthur) in which Arthur can make multiple non-collapsing measurements to Merlin's witness state, in addition to ordinary collapsing measurements. By analogy to the class PDQP defined by Aaronson, B
Externí odkaz:
http://arxiv.org/abs/2403.02543
Autor:
Aaronson, Jon., Sera, Toru
We establish a conditional limit theorem for occupation times of infinite ergodic transformations under a tied-down condition, that is, the condition that the orbit returns to a reference set with finite measure at the final observation time. The cla
Externí odkaz:
http://arxiv.org/abs/2308.09406
Motivated by the fact that input distributions are often unknown in advance, distribution-free property testing considers a setting where the algorithmic task is to accept functions $f : [n] \to \{0,1\}$ with a certain property P and reject functions
Externí odkaz:
http://arxiv.org/abs/2308.08874
Autor:
Davis, Ernest, Aaronson, Scott
This report describes a test of the large language model GPT-4 with the Wolfram Alpha and the Code Interpreter plug-ins on 105 original problems in science and math, at the high school and college levels, carried out in June-August 2023. Our tests su
Externí odkaz:
http://arxiv.org/abs/2308.05713
Autor:
Aaronson, Jon, Nadkarni, Mahendra
We study the circle restrictions of inner functions of the unit disc showing that the local invertibility of a restriction is independent of its singularity set and proving a local characterization of analytic conditional expectations. We establish c
Externí odkaz:
http://arxiv.org/abs/2305.15278
Autor:
Aaronson, Scott, Hung, Shih-Han
We propose an application for near-term quantum devices: namely, generating cryptographically certified random bits, to use (for example) in proof-of-stake cryptocurrencies. Our protocol repurposes the existing "quantum supremacy" experiments, based
Externí odkaz:
http://arxiv.org/abs/2303.01625