Related papers: Quantum and Classical Algorithms for Bounded Dista…
We give a quantum speedup for solving the canonical semidefinite programming relaxation for binary quadratic optimization. This class of relaxations for combinatorial optimization has so far eluded quantum speedups. Our methods combine…
In this work, we present a quantum neighborhood preserving embedding and a quantum local discriminant embedding for dimensionality reduction and classification. We demonstrate that these two algorithms have an exponential speedup over their…
Quantum computers have the potential of solving certain problems exponentially faster than classical computers. Recently, Harrow, Hassidim and Lloyd proposed a quantum algorithm for solving linear systems of equations: given an $N\times{N}$…
Quantum error-correcting codes (QECCs) is at the heart of fault-tolerant quantum computing. As the size of quantum platforms is expected to grow, one of the open questions is to design new optimal codes of ever-increasing size. A related…
A quantum algorithm to solve the parity problem is better than its most efficient classical counter- part with a separation that is polynomial in the number of queries. This was shown by E. Bernstein and U. Vazirani and was one of the…
In this work, we consider the performance of using a quantum algorithm to predict a result for a binary classification problem if a machine learning model is an ensemble from any simple classifiers. Such an approach is faster than classical…
We show that in quantum logic of closed subspaces of Hilbert space one cannot substitute quantum operations for classical (standard Hilbert space) ones and treat them as primitive operations. We consider two possible ways of such a…
The general classical solution of the 3D electromagnetic pp-wave spacetime has been obtained. The relevant line element contains an arbitrary essential function providing an infinite number of in-equivalent geometries as solutions. A…
Time-dependent linear differential equations are a common type of problem that needs to be solved in classical physics. Here we provide a quantum algorithm for solving time-dependent linear differential equations with logarithmic dependence…
We consider the characterization as well as the construction of quantum codes that allow to transmit both quantum and classical information, which we refer to as `hybrid codes'. We construct hybrid codes $[\![n,k{: }m,d]\!]_q$ with length…
We prove that certain classical cyclic redundancy check codes can be used for classical error correction and not just classical error detection. We extend the idea of classical cyclic redundancy check codes to quantum cyclic redundancy…
We study quantum algorithms working on classical probability distributions. We formulate four different models for accessing a classical probability distribution on a quantum computer, which are derived from previous work on the topic, and…
A quantum computer needs the assistance of a classical algorithm to detect and identify errors that affect encoded quantum information. At this interface of classical and quantum computing the technique of machine learning has appeared as a…
Computing the unit group and solving the principal ideal problem for a number field are two of the main tasks in computational algebraic number theory. This paper proposes efficient quantum algorithms for these two problems when the number…
In this paper, we identify a family of nonconvex continuous optimization instances, each $d$-dimensional instance with $2^d$ local minima, to demonstrate a quantum-classical performance separation. Specifically, we prove that the recently…
Attempts to separate the power of classical and quantum models of computation have a long history. The ultimate goal is to find exponential separations for computational problems. However, such separations do not come a dime a dozen: while…
Simulation of realistic classical mechanical systems is of great importance to many areas of engineering such as robotics, dynamics of rotating machinery and control theory. In this work, we develop quantum algorithms to estimate quantities…
We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm…
This work revisits quantum algorithms for the well-known welded tree problem, proposing a very succinct quantum algorithm based on the simplest coined quantum walks. It simply iterates the naturally defined coined quantum walk operator for…
We present classical and quantum algorithms based on spectral methods for a problem in tensor principal component analysis. The quantum algorithm achieves a quartic speedup while using exponentially smaller space than the fastest classical…