Related papers: Characterization of exact one-query quantum algori…
Quantum computation holds promise for the solution of many intractable problems. However, since many quantum algorithms are stochastic in nature they can only find the solution of hard problems probabilistically. Thus the efficiency of the…
Consider the model of computation where we start with two halves of a $2n$-qubit maximally entangled state. We get to apply a universal quantum computation on one half, measure both halves at the end, and perform classical postprocessing.…
A new methodology is proposed to solve classical Boolean problems as Hamiltonians, using the quantum approximate optimization algorithm (QAOA). Our methodology successfully finds all optimized approximated solutions for Boolean problems,…
Quantum computing, leveraging quantum phenomena like superposition and entanglement, is emerging as a transformative force in computing technology, promising unparalleled computational speed and efficiency crucial for engineering…
Here we revisit the quantum algorithms for obtaining Forrelation [Aaronson et al, 2015] values to evaluate some of the well-known cryptographically significant spectra of Boolean functions, namely the Walsh spectrum, the cross-correlation…
Practical challenges in simulating quantum systems on classical computers have been widely recognized in the quantum physics and quantum chemistry communities over the past century. Although many approximation methods have been introduced,…
We study classical query algorithms with post-selection, and find that they are closely connected to rational functions with nonnegative coefficients. We show that the post-selected classical query complexity of a Boolean function is equal…
We build a quantum algorithm which uses the Grover quantum search procedure in order to sample the exact equilibrium distribution of a wide range of classical statistical mechanics systems. The algorithm is based on recently developed exact…
In this paper we review our current results concerning the computational power of quantum read-once branching programs. First of all, based on the circuit presentation of quantum branching programs and our variant of quantum fingerprinting…
The ability to extract relevant information is critical to learning. An ingenious approach as such is the information bottleneck, an optimisation problem whose solution corresponds to a faithful and memory-efficient representation of…
Quantum algorithms are known for providing more efficient solutions to certain computational tasks than any corresponding classical algorithm. Here we show that a single qudit is sufficient to implement an oracle based quantum algorithm,…
Quantum computing promises to provide the next step up in computational power for diverse application areas. In this review, we examine the science behind the quantum hype, and the breakthroughs required to achieve true quantum advantage in…
Quantum search algorithms offer a remarkable advantage of quadratic reduction in query complexity using quantum superposition principle. However, how an actual architecture may access and handle the database in a quantum superposed state…
We assess the potential of quantum computing to accelerate computation of central tasks in genomics, focusing on often-neglected theoretical limitations. We discuss state-of-the-art challenges of quantum search, optimization, and machine…
We develop a classical model of computation (the S model) which captures some important features of quantum computation, and which allows to design fast algorithms for solving specific problems. In particular, we show that Deutsch's problem…
Simon's problem is an essential example demonstrating the faster speed of quantum computers than classical computers for solving some problems. The optimal separation between exact quantum and classical query complexities for Simon's…
Given a blackbox for f, a smooth real scalar function of d real variables, one wants to estimate the gradient of f at a given point with n bits of precision. On a classical computer this requires a minimum of d+1 blackbox queries, whereas…
Recent technological developments have focused the interest of the quantum computing community on investigating how near-term devices could outperform classical computers for practical applications. A central question that remains open is…
We use the benefits and components of classical computers every day. However, there are many types of problems which, as they grow in size, their computational complexity grows larger than classical computers will ever be able to solve.…
We investigate the entanglement features of the quantum states employed in quantum algorithms. In particular, we analyse the multipartite entanglement properties in the Deutsch-Jozsa, Grover and Simon algorithms. Our results show that for…