Related papers: Solving k-SAT problems with generalized quantum me…
Quantum Zeno dragging enables the preparation of common eigenstates of a set of observables by frequent measurement and adiabatic-like modulation of the measurement basis. In this work, we present a deeper analysis of multi-channel Zeno…
We investigate the performance of a quantum algorithm for solving classical 3-SAT problems. A cycle of post-selected measurements drives the computer's register monotonically toward a steady state which is correlated to the classical…
The Boolean satisfiability problem (SAT) is of central importance in both theory and practice. Yet, most provable guarantees for quantum algorithms rely exclusively on Grover-type methods that cap the possible advantage at only quadratic…
Constrained optimization problems are ubiquitous in science and industry. Quantum algorithms have shown promise in solving optimization problems, yet none of the current algorithms can effectively handle arbitrary constraints. We introduce…
Boolean satisfiability [1] (k-SAT) is one of the most studied optimization problems, as an efficient (that is, polynomial-time) solution to k-SAT (for $k\geq 3$) implies efficient solutions to a large number of hard optimization problems…
Quantum k-SAT is the problem of deciding whether there is a n-qubit state which is perpendicular to a set of vectors, each of which lies in the Hilbert space of k qubits. Equivalently, the problem is to decide whether a particular type of…
We give a nearly linear-time algorithm to approximately sample satisfying assignments in the random $k$-SAT model when the density of the formula scales exponentially with $k$. The best previously known sampling algorithm for the random…
Quantum optimization algorithms promise advantages for difficult problems but are costly to simulate and analyze on classical machines. Recently, constrained quantum optimization has been investigated through the lens of Quantum Zeno…
We report a cluster of results regarding the difficulty of finding approximate ground states to typical instances of the quantum satisfiability problem $k$-QSAT on large random graphs. As an approximation strategy, we optimize the solution…
The quantum Zeno effect is the suppression of Hamiltonian evolution by repeated observation, resulting in the pinning of the state to an eigenstate of the measurement observable. Using measurement only, control of the state can be achieved…
I describe one quantum approach to solving 3-satisfiability (3-SAT), the well known problem in computer science. The approach is based on repeatedly measuring the truth value of the clauses forming the 3-SAT proposition using a…
The constraint satisfaction problems k-SAT and Quantum k-SAT (k-QSAT) are canonical NP-complete and QMA_1-complete problems (for k>=3), respectively, where QMA_1 is a quantum generalization of NP with one-sided error. Whereas k-SAT has been…
The quantum Zeno effect asserts that quantum measurements inhibit simultaneous unitary dynamics when the "collapse" events are sufficiently strong and frequent. This applies in the limit of strong continuous measurement or dissipation. It…
Complexity of a quantum analogue of the satisfiability problem is studied. Quantum k-SAT is a problem of verifying whether there exists n-qubit pure state such that its k-qubit reduced density matrices have support on prescribed subspaces.…
A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for…
We present a quantum adiabatic algorithm for a set of quantum 2-satisfiability (Q2SAT) problem, which is a generalization of 2-satisfiability (2SAT) problem. For a Q2SAT problem, we construct the Hamiltonian which is similar to that of a…
The quantum Zeno effect is the prediction, going back to Alan Turing, that the decay of an unstable system can be slowed down by measuring it frequently enough. It was also noticed later that the opposite effect, i.e., enhancement of the…
The random k-SAT instances undergo a "phase transition" from being generally satisfiable to unsatisfiable as the clause number m passes a critical threshold, $r_k n$. This causes a drastic reduction in the number of satisfying assignments,…
The Boolean constraint satisfaction problem 3-SAT is arguably the canonical NP-complete problem. In contrast, 2-SAT can not only be decided in polynomial time, but in fact in deterministic linear time. In 2006, Bravyi proposed a physically…
A complete suppression of the exponential decay in a qubit (interacting with a squeezed vacuum reservoir) can be achieved by frequent measurements of adequately chosen observables. The observables and initial states (Zeno subspace) for…