Related papers: Nonlinear Hamiltonians and Boolean satisfiability
We propose a method for exact circuit synthesis using a discrete gate set, as required for fault-tolerant quantum computing. Our approach translates the problem of synthesizing a gate specified by its unitary matrix into a boolean…
The Boolean SATisfiability problem (SAT) is of central importance in computer science. Although SAT is known to be NP-complete, progress on the engineering side, especially that of Conflict-Driven Clause Learning (CDCL) and Local Search SAT…
We study several problems related to properties of non-negative matrices that arise at the boundary between quantum and classical probabilistic computation. Our results are twofold. First, we identify a large class of quantum Hamiltonians…
Satisfiability filters, introduced by S. A. Weaver et al. in 2014, are a new and promising type of filters to address set membership testing. In order to construct satisfiability filters, it is necessary to find disparate solutions to hard…
The problem 2-quantum-satisfiability (2-QSAT) is the generalisation of the 2-CNF-SAT problem to quantum bits, and is equivalent to determining whether or not a spin-1/2 Hamiltonian with two-body terms is frustration-free. Similarly to the…
Satisfiability (SAT) is a central problem in computer science, and advances in SAT-solving algorithms have a far-reaching impact across many fields. Recent works have proposed quantum SAT solvers based on Grover's algorithm, a quantum…
Efficient solutions to NP-complete problems would significantly benefit both science and industry. However, such problems are intractable on digital computers based on the von Neumann architecture, thus creating the need for alternative…
In the article \The State of SAT", the authors asked whether a procedure dramatically different from DPLL can be found for handling unsatisfiable instances. This study proposes a new linear programming approach to address this issue…
We present a new approach to quantum computation involving the geometric phase. In this approach, an entire computation is performed by adiabatically evolving a suitably chosen quantum system in a closed circuit in parameter space. The…
In this work, using a NISQ framework, we obtain the gap of a BCS Hamiltonian. This could lead to interesting implications for superconductivity research. For such task, we choose to use the Variational Quantum Deflation and analyze the…
Exactly-solvable Hamiltonians that can be diagonalized using relatively simple unitary transformations are of great use in quantum computing. They can be employed for decomposition of interacting Hamiltonians either in Trotter-Suzuki…
We reduce the extra qubits needed for two fault-tolerant quantum computing protocols: error correction, specifically syndrome bit measurement, and cat state preparation. For distance-three fault-tolerant syndrome extraction, we show an…
Digital quantum simulators are among the most appealing applications of a quantum computer. Here we propose a universal, scalable, and integrated quantum computing platform based on tunable nonlinear electromechanical nano-oscillators. It…
The boolean satisfiability (SAT) problem asks whether there exists an assignment of boolean values to the variables of an arbitrary boolean formula making the formula evaluate to True. It is well-known that all NP-problems can be coded as…
DNA computation could in principle solve the satisfiability (SAT) problem due to the operations in parallel on extremely large numbers of strands. We demonstrate some quantum gates corresponding to the DNA ones, based on which an…
We describe a quantum algorithm for preparing states that encode solutions of non-homogeneous linear partial differential equations. The algorithm is a continuous-variable version of matrix inversion: it efficiently inverts differential…
A frustration-free local Hamiltonian has the property that its ground state minimises the energy of all local terms simultaneously. In general, even deciding whether a Hamiltonian is frustration-free is a hard task, as it is closely related…
This paper reviews the recent literature on solving the Boolean satisfiability problem (SAT), an archetypal NP-complete problem, with the help of machine learning techniques. Despite the great success of modern SAT solvers to solve large…
As the nascent field of quantum computing develops, an increasing number of quantum hardware modalities, such as superconducting electronic circuits, semiconducting spins, trapped ions, and neutral atoms, have become available for…
We give a quantum algorithm for solving instances of the satisfiability problem, based on adiabatic evolution. The evolution of the quantum state is governed by a time-dependent Hamiltonian that interpolates between an initial Hamiltonian,…