Multiparty hierarchical quantum-information splitting

We propose a scheme for multiparty hierarchical quantum-information splitting (QIS) with a multipartite entangled state, where a boss distributes a secret quantum state to two grades of agents asymmetrically. The agents who belong to different grades have different authorities for recovering boss's secret. Except for boss's Bell-state measurement, no nonlocal operation is involved. The presented scheme is also shown to be secure against eavesdropping. Such a hierarchical QIS is expected to find useful applications in the field of modern multipartite quantum cryptography.Comment: 6 pages, 2 table

Shared computational principles for language processing in humans and deep language models

Departing from traditional linguistic models, advances in deep learning have resulted in a new type of predictive (autoregressive) deep language models (DLMs). Using a self-supervised next-word prediction task, these models generate appropriate linguistic responses in a given context. In the current study, nine participants listened to a 30-min podcast while their brain responses were recorded using electrocorticography (ECoG). We provide empirical evidence that the human brain and autoregressive DLMs share three fundamental computational principles as they process the same natural narrative: (1) both are engaged in continuous next-word prediction before word onset; (2) both match their pre-onset predictions to the incoming word to calculate post-onset surprise; (3) both rely on contextual embeddings to represent words in natural contexts. Together, our findings suggest that autoregressive DLMs provide a new and biologically feasible computational framework for studying the neural basis of language

Quantum Algorithm for Linear Systems of Equations

Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b⃗, find a vector x⃗ such that Ax⃗=b⃗. We consider the case where one does not need to know the solution x⃗ itself, but rather an approximation of the expectation value of some operator associated with x⃗, e.g., x⃗†Mx⃗ for some matrix M. In this case, when A is sparse, N×N and has condition number κ, the fastest known classical algorithms can find x⃗ and estimate x⃗†Mx⃗ in time scaling roughly as N√κ. Here, we exhibit a quantum algorithm for estimating x⃗†Mx⃗ whose runtime is a polynomial of log(N) and κ. Indeed, for small values of κ [i.e., polylog(N)], we prove (using some common complexity-theoretic assumptions) that any classical algorithm for this problem generically requires exponentially more time than our quantum algorithm.W. M. Keck Foundation Center for Extreme Quantum Information Theor