Related papers: Approximation algorithms for QMA-complete problems
The quantum k-Local Hamiltonian problem is a natural generalization of classical constraint satisfaction problems (k-CSP) and is complete for QMA, a quantum analog of NP. Although the complexity of k-Local Hamiltonian problems has been well…
This thesis studies three topics in quantum computation and information: The approximability of quantum problems, quantum proof systems, and non-classical correlations in quantum systems. In the first area, we demonstrate a polynomial-time…
The polynomial hierarchy plays a central role in classical complexity theory. Here, we define a quantum generalization of the polynomial hierarchy, and initiate its study. We show that not only are there natural complete problems for the…
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…
We establish efficient approximate counting algorithms for several natural problems in local lemma regimes. In particular, we consider the probability of intersection of events and the dimension of intersection of subspaces. Our approach is…
The classical work of (Arora et al., 1999) provides a scheme that gives, for any $\epsilon>0$, a polynomial time $1-\epsilon$ approximation algorithm for dense instances of a family of $\mathcal{NP}$-hard problems, such as Max-CUT and…
Quantum algorithms can deliver asymptotic speedups over their classical counterparts. However, there are few cases where a substantial quantum speedup has been worked out in detail for reasonably-sized problems, when compared with the best…
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…
We consider constraint satisfaction problems of bounded degree, with a good notion of "typicality", e.g. the negation of the variables in each constraint is taken independently at random. Using the quantum approximate optimization algorithm…
The k-local Hamiltonian problem is a natural complete problem for the complexity class QMA, the quantum analog of NP. It is similar in spirit to MAX-k-SAT, which is NP-complete for k<=2. It was known that the problem is QMA-complete for any…
Recent successes in producing rigorous approximation algorithms for local Hamiltonian problems such as Quantum Max Cut have exploited connections to unconstrained classical discrete optimization problems. We initiate the study of…
We initiate a systematic study of utilizing predictions to improve over approximation guarantees of classic algorithms, without increasing the running time. We propose a systematic method for a wide class of optimization problems that ask…
A quantum constraint problem is a frustration-free Hamiltonian problem: given a collection of local operators, is there a state that is in the ground state of each operator simultaneously? It has previously been shown that these problems…
Building on the blueprint from Goemans and Williamson (1995) for the Max-Cut problem, we construct a polynomial-time approximation algorithm for orthogonally constrained quadratic optimization problems. First, we derive a semidefinite…
In this work we develop theoretical techniques for analysing the performance of the quantum approximate optimization algorithm (QAOA) when applied to random boolean constraint satisfaction problems (CSPs), and use these techniques to…
Approximation algorithms for constraint satisfaction problems (CSPs) are a central direction of study in theoretical computer science. In this work, we study classical product state approximation algorithms for a physically motivated…
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…
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…
It is well-known in physics that the limit of large quantum spin $S$ should be understood as a semiclassical limit. This raises the question of whether such emergent classicality facilitates the approximation of computationally hard quantum…
Simulating the time-evolution of quantum mechanical systems is BQP-hard and expected to be one of the foremost applications of quantum computers. We consider classical algorithms for the approximation of Hamiltonian dynamics using…