On the Quantum versus Classical Learnability of Discrete Distributions

Quantum versus Classical Learnability

We consider quantum versions of two well-studied classical learning models: Angluin's model of exact learning from membership queries and Valiant's Probably Approximately Correct (PAC) model of learning from random examples. We give positive and negative results for quantum versus classical learnability. For each of the two learning models described above, we show that any concept class is information-theoretically learnable from polynomially many quantum examples if and only if it is information-theoretically learnable from polynomially many classical examples. In contrast to this information…

观测量子测量坍缩作为可学习性相变

Observing quantum measurement collapse as a learnability phase transition

本研究在离子阱量子处理器上实验观测到测量诱导的相变，表现为可观测量的量子不确定性与可学习信息量随测量强度尖锐变化，并设计了高效算法以观测该相变并抑制噪声影响。

Quantum versus classical effects in the chirped-drive discrete nonlinear Schrodinger equation

A chirped parametrically driven discrete nonlinear Schrodinger equation is discussed. It is shown that the system allows two resonant excitation mechanisms, i.e., successive two-level transitions (ladder climbing) or a continuous classical-like nonlinear phase-locking (autoresonance). Two-level arguments are used to study the ladder-climbing process, and semiclassical theory describes the autoresonance effect. The regimes of efficient excitation in the problem are identified and characterized in terms of three dimensionless parameters describing the driving strength, the dispersion nonlinearit…

Laplacian versus Adjacency Matrix in Quantum Walk Search

A quantum particle evolving by Schrödinger's equation contains, from the kinetic energy of the particle, a term in its Hamiltonian proportional to Laplace's operator. In discrete space, this is replaced by the discrete or graph Laplacian, which gives rise to a continuous-time quantum walk. Besides this natural definition, some quantum walk algorithms instead use the adjacency matrix to effect the walk. While this is equivalent to the Laplacian for regular graphs, it is different for non-regular graphs, and is thus an inequivalent quantum walk. We algorithmically explore this distinction by ana…

MDI-QKD: Continuous- versus discrete-variables at metropolitan distances

In a comment, Xu, Curty, Qi, Qian, and Lo claimed that discrete-variable (DV) measurement device independent (MDI) quantum key distribution (QKD) would compete with its continuous-variable (CV) counterpart at metropolitan distances. Actually, Xu et al.'s analysis supports exactly the opposite by showing that the experimental rate of our CV protocol (achieved with practical room-temperature devices) remains one order of magnitude higher than their purely-numerical and over-optimistic extrapolation for qubits, based on nearly-ideal parameters and cryogenic detectors (unsuitable solutions for a r…

On a digital quantum description of physical space versus the continuum description

The continuum of real numbers has served well as a model for physical space in mechanics and field theories. However it is a well-motivated and popular idea that at the fundamental Planck scale the combination of gravitational and quantum effects forces us to re-evaluate the concept of space (and time), and some sort of discreteness or granularity is expected. Here we study a cubic grid of points representing fundamental volumes of space and derive the spectra of momenta and wave number, which are not generally proportional to each other. The momentum is bounded and discrete for a finite grid.…