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This paper talk about the complexity of computation by Turing Machine. I take attention to the relation of symmetry and order structure of the data, and I think about the limitation of computation time. First, I make general problem named…
The operational formulations of quantum theory are drastically time oriented. However, to the best of our knowledge, microscopic physics is time-symmetric. We address this tension by showing that the asymmetry of the operational…
There exists a stark tension among different formulations of quantum theory as some are inherently time-symmetric while others are time-asymmetric. This tension is crisply captured when considering physical theories as theories of…
Blind quantum computation is a new secure quantum computing protocol which enables Alice who does not have sufficient quantum technology to delegate her quantum computation to Bob who has a fully-fledged quantum computer in such a way that…
Systems of linear equations are used to model a wide array of problems in all fields of science and engineering. Recently, it has been shown that quantum computers could solve linear systems exponentially faster than classical computers,…
These notes discuss the quantum algorithms we know of that can solve problems significantly faster than the corresponding classical algorithms. So far, we have only discovered a few techniques which can produce speed up versus classical…
Finding a good approximation of the top eigenvector of a given $d\times d$ matrix $A$ is a basic and important computational problem, with many applications. We give two different quantum algorithms that, given query access to the entries…
Time continues to be an intriguing physical property in the modern era. On the one hand, we have the Classical and Relativistic notion of time, where space and time have the same hierarchy, which is essential in describing events in…
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…
Quantum tomography is an essential method of the photonic technology toolbox and is routinely used for evaluation of experimentally prepared states of light and characterization of devices transforming such states. The tomography procedure…
A central roadblock to analyzing quantum algorithms on quantum states is the lack of a comparable input model for classical algorithms. Inspired by recent work of the author [E. Tang, STOC'19], we introduce such a model, where we assume we…
We study supervised learning algorithms in which a quantum device is used to perform a computational subroutine - either for prediction via probability estimation, or to compute a kernel via estimation of quantum states overlap. We design…
Our computers today, from sophisticated servers to small smartphones, operate based on the same computing model, which requires running a sequence of discrete instructions, specified as an algorithm. This sequential computing paradigm has…
We present and experimentally realize a quantum algorithm for efficiently solving the following problem: given an $N\times N$ matrix $\mathcal{M}$, an $N$-dimensional vector $\textbf{\emph{b}}$, and an initial vector $\textbf{\emph{x}}(0)$,…
Symmetry is a unifying concept in physics. In quantum information and beyond, it is known that quantum states possessing symmetry are not useful for certain information-processing tasks. For example, states that commute with a Hamiltonian…
We characterize the conditions under which a multi-time quantum process with a finite temporal resolution can be approximately described by an equilibrium one. By providing a generalization of the notion of equilibration on average, where a…
Demonstrating quantum advantage has been a pressing challenge in the field. Most claimed quantum speedups rely on a subroutine in which classical information can be accessed in a coherent quantum manner, which imposes a crucial constraint…
Assume that Alice can do only classical probabilistic polynomial-time computing while Bob can do quantum polynomial-time computing. Alice and Bob communicate over only classical channels, and finally Bob gets a state…
Recently developed quantum algorithms suggest that quantum computers can solve certain problems and perform certain tasks more efficiently than conventional computers. Among other reasons, this is due to the possibility of creating…
We study prepare-and-measure experiments where the sender (Alice) receives trusted quantum inputs but has an untrusted state-preparation device and the receiver (Bob) has a fully-untrusted measurement device. A distributed-sampling task…