相关论文: BQP, meet NP: Search-to-decision reductions and ap…
A canonical feature of the constraint satisfaction problems in NP is approximation hardness, where in the worst case, finding sufficient-quality approximate solutions is exponentially hard for all known methods. Fundamentally, the lack of…
One can fix the randomness used by a randomized algorithm, but there is no analogous notion of fixing the quantumness used by a quantum algorithm. Underscoring this fundamental difference, we show that, in the black-box setting, the…
We propose a quantum algorithm (in the form of a quantum oracle) that estimates the closeness of a given Boolean function to one that satisfies the ``strict avalanche criterion'' (SAC). This algorithm requires $n$ queries of the Boolean…
In this note we study the power of so called query-limited computers. We compare the strength of a classical computer that is allowed to ask two questions to an NP-oracle with the strength of a quantum computer that is allowed only one such…
The quantum approximate optimization algorithm (QAOA) is one of the most prominent proposed applications for near-term quantum computing. Here we study the ability of QAOA to solve hard constraint satisfaction problems, as opposed to…
Grover's algorithm can solve NP-complete problems on quantum computers faster than all the known algorithms on classical computers. However, Grover's algorithm still needs exponential time. Due to the BBBV theorem, Grover's algorithm is…
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…
In order to qualify quantum algorithms for industrial NP-Hard problems, comparing them to available polynomial approximate classical algorithms and not only to exact ones -- exponential by nature -- , is necessary. This is a great challenge…
Boolean satisfiability ({\SAT}) has played a key role in diverse areas spanning testing, formal verification, planning, optimization, inferencing and the like. Apart from the classical problem of checking boolean satisfiability, the…
In the exact quantum query model a successful algorithm must always output the correct function value. We investigate the function that is true if exactly $k$ or $l$ of the $n$ input bits given by an oracle are 1. We find an optimal…
The approximate degree of a Boolean function f is the least degree of a real polynomial that approximates f pointwise to error at most 1/3. Approximate degree is known to be a lower bound on quantum query complexity. We resolve or nearly…
We develop a complexity theory for approximate real computations. We first produce a theory for exact computations but with condition numbers. The input size depends on a condition number, which is not assumed known by the machine. The…
Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…
If one modifies the laws of Quantum Mechanics to allow nonlinear evolution of quantum states, this paper shows that NP-complete problems would be efficiently solvable in polynomial time with bounded probability (NP in BQP). With that…
Quantum Approximate Optimization algorithm (QAOA) aims to search for approximate solutions to discrete optimization problems with near-term quantum computers. As there are no algorithmic guarantee possible for QAOA to outperform classical…
The problem of P vs. NP is very serious, and solutions to the problem can help save lives. This article is an attempt at solving the problem using a computer algorithm. It is presented in a fashion that will hopefully allow for easy…
This is the latest in a series of articles aimed at exploring the relationship between the complexity classes of P and NP. In the previous papers, we have proved that the sat CNF problem is polynomially reduced to the problem of finding a…
The computational equivalence between approximate counting and sampling is well established for polynomial-time algorithms. The most efficient general reduction from counting to sampling is achieved via simulated annealing, where the…
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…
Many problems of industrial interest are NP-complete, and quickly exhaust resources of computational devices with increasing input sizes. Quantum annealers (QA) are physical devices that aim at this class of problems by exploiting quantum…