Tangible reduction in learning sample complexity with large classical samples and small quantum system

Communication Complexity Reduction from Globally Uncorrelated States

Bell inequality violating entangled states are the working horse for many potential quantum information processing applications, including secret sharing, cryptographic key distribution and communication complexity reduction in distributed computing. Here we explicitly demonstrate the power of certain multi-qubit states to improve the efficiency of partners in joint computation of some multi-qubit function, despite the fact that there could be no correlations between all distributed particles. It is important to stress that the class of functions that can be computed more efficiently is widene…

Super-exponential query complexity reduction via noise-resistant quantum search

In the SEARCH WITH ADVICE problem, a single entry of interest within a database of N entries is to be found assuming that an ordering of the entries, from that with the highest probability of being the entry of interest (as determined by a so-called advice distribution) to that with the lowest, is provided. We present a quantum algorithm that, in the presence of significant levels of quantum noise, solves SEARCH WITH ADVICE for a power law advice distribution with average-case query complexity O(1) as N tends to infinity. Since as we also show the best classical algorithms for this problem exh…

Quantum Go: Designing a Proof-of-Concept on Quantum Computer

The strategic Go game, known for the tedious mathematical complexities, has been used as a theme in many fiction, movies, and books. Here, we introduce the Go game and provide a new version of quantum Go in which the boxes are initially in a superposition of quantum states |0> and |1> and the players have two kinds of moves (classical and quantum) to mark each box. The mark on each box depends on the state to which the qubit collapses after the measurement. All other rules remain the same, except for here, we capture only one stone and not chains. Due to the enormous power and exponential spee…

通过量子算法实现不可知学习样本复杂度的二次方缩减

A Quadratic Sample Complexity Reduction for Agnostic Learning via Quantum Algorithms

本文利用量子算法，在有限假设类的一般不可知学习模型中，将样本复杂度从经典算法的 $Θ(\log(1/δ)/ε^2)$ 二次方缩减至 $O(\log(1/δ)/ε)$，实现了量子加速。

Preparing thermal states of quantum systems by dimension reduction

We present an algorithm that prepares thermal Gibbs states of one dimensional quantum systems on a quantum computer without any memory overhead, and in a time significantly shorter than other known alternatives. Specifically, the time complexity is dominated by the quantity $N^{\|h\|/ T}$, where $N$ is the size of the system, $\|h\|$ is a bound on the operator norm of the local terms of the Hamiltonian (coupling energy), and $T$ is the temperature. Given other results on the complexity of thermalization, this overall scaling is likely optimal. For higher dimensions, our algorithm lowers the kn…

量子态合成：与决策复杂性类的关系及合成误差缩减的不可能性

Quantum State Synthesis: Relation with Decision Complexity Classes and Impossibility of Synthesis Error Reduction

本文研究量子态合成复杂性类与决策复杂性类的关系，证明高误差下合成类坍缩导致决策类坍缩，并揭示合成误差在任意计算能力下均不可缩减。