Related papers: Broken Promises and Quantum Algorithms
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
The potential of the exact quantum information processing is an interesting, important and intriguing issue. For examples, it has been believed that quantum tools can provide significant, that is larger than polynomial, advantages in the…
One of the key obstacles in traditional deep learning is the reduction in model transparency caused by increasingly intricate model functions, which can lead to problems such as overfitting and excessive confidence in predictions. With the…
We exhibit two black-box problems, both of which have an efficient quantum algorithm with zero-error, yet whose composition does not have an efficient quantum algorithm with zero-error. This shows that quantum zero-error algorithms cannot…
Besides the superior efficiency compared to their classical counterparts, quantum algorithms known so far are basically task-dependent, and scarcely any common features are shared between them. In this work, however, we show that the…
In this paper, we present a generalisation of the Phase Kick-Back technique, which is central to some of the classical algorithms in quantum computing, such as the Deutsch--Jozsa algorithm, Simon's algorithm or Grover's algorithm. We will…
Quantum computers may achieve speedups over their classical counterparts for solving linear algebra problems. However, in some cases -- such as for low-rank matrices -- dequantized algorithms demonstrate that there cannot be an exponential…
The oracle chooses a function out of a known set of functions and gives to the player a black box that, given an argument, evaluates the function. The player should find out a certain character of the function through function evaluation.…
We study the practical performance of quantum-inspired algorithms for recommendation systems and linear systems of equations. These algorithms were shown to have an exponential asymptotic speedup compared to previously known classical…
Nuclear magnetic resonance (NMR) has been widely used as a demonstrative medium for showcasing the ability for quantum computations to outperform classical ones. A large number of such experiments performed have been implementations of the…
The query model has generated considerable interest in both classical and quantum computing communities. Typically, quantum advantages are demonstrated by showcasing a quantum algorithm with a better query complexity compared to its…
Equality and disjointness are two of the most studied problems in communication complexity. They have been studied for both classical and also quantum communication and for various models and modes of communication. Buhrman et al. [Buh98]…
It is generally believed that entanglement is essential for quantum computing. We present here a few simple examples in which quantum computing without entanglement is better than anything classically achievable, in terms of the reliability…
We investigate the power of quantum computers when they are required to return an answer that is guaranteed to be correct after a time that is upper-bounded by a polynomial in the worst case. We show that a natural generalization of Simon's…
Quantum algorithms have the potential to provide exponential speedups over some of the best known classical algorithms. These speedups may enable quantum devices to solve currently intractable problems such as those in the fields of…
In the {\em distributed Deutsch-Jozsa promise problem}, two parties are to determine whether their respective strings $x,y\in\{0,1\}^n$ are at the {\em Hamming distance} $H(x,y)=0$ or $H(x,y)=\frac{n}{2}$. Buhrman et al. (STOC' 98) proved…
The technique of combining multiple votes to enhance the quality of a decision is the core of boosting algorithms in machine learning. In particular, boosting provably increases decision quality by combining multiple weak…
In this letter, by establishing the Schr\"odinger equation of the optimization problem, the optimization problem is transformed into a constrained state quantum problem with the objective function as the potential energy. The mathematical…
Is there a general theorem that tells us when we can hope for exponential speedups from quantum algorithms, and when we cannot? In this paper, we make two advances toward such a theorem, in the black-box model where most quantum algorithms…
Unstructured search remains as one of the significant challenges in computer science, as classical search algorithms become increasingly impractical for large-scale systems due to their linear time complexity. Quantum algorithms, notably…