Related papers: Solving k-SAT problems with generalized quantum me…
Photonic quantum computers, programmed within the framework of the measurement-based quantum computing (MBQC), currently concur with gate-based platforms in the race towards useful quantum advantage, and some algorithms emerged as main…
We establish the satisfiability threshold for random $k$-SAT for all $k\ge k_0$, with $k_0$ an absolute constant. That is, there exists a limiting density $\alpha_*(k)$ such that a random $k$-SAT formula of clause density $\alpha$ is with…
This dissertation studies the statistics and modeling of a quantum system probed by a coherent laser field. We focus on an ensemble of qubits dispersively coupled to a traveling wave light field. The first research topic explores the…
We introduce an algorithm to compute Hamiltonian dynamics on digital quantum computers that requires only a finite circuit depth to reach an arbitrary precision, i.e. achieves zero discretization error with finite depth. This finite number…
Quantum state tomography is a core task in quantum system identification. Real experimental conditions often deviate from nominal designs, introducing errors in both the measurement devices and the Hamiltonian governing the system's…
Randomized algorithms for deciding satisfiability were shown to be effective in solving problems with thousands of variables. However, these algorithms are not complete. That is, they provide no guarantee that a satisfying assignment, if…
In this paper we present a search algorithm that finds useful optical quantum states which can be created with current technology. We apply the algorithm to the field of quantum metrology with the goal of finding states that can measure a…
As contemporary quantum computers do not possess error correction, any calculation performed by these devices can be considered an involuntary approximation. To solve a problem on a quantum annealer, it has to be expressed as an instance of…
In the ideal quantum Zeno effect, repeated quantum projective measurements can freeze the coherent dynamics of a quantum system. However, in the weak quantum Zeno regime, measurement back-actions can allow the sensing of semi-classical…
A pivotal task for quantum computing is to speed up solving problems that are both classically intractable and practically valuable. Among these, combinatorial optimization problems have attracted tremendous attention due to their broad…
The quantum Zeno effect (QZE) reveals that frequent measurements can suppress quantum evolution, but the detailed dynamics of the system under finite-duration measurements in experiments remain insufficiently explored. Here, we employ an…
We give a simpler derandomization of the best known $k$-SAT algorithm PPSZ [FOCS'97, JACM'05] for $k$-SAT with \emph{sub-exponential} number of solutions. The existing derandomization uses a complicated construction of small sample space,…
Quantum computing is seeking to realize hardware-optimized algorithms for application-related computational tasks. NP (nondeterministic-polynomial-time) is a complexity class containing many important but intractable problems like the…
The random k-SAT model is the most important and well-studied distribution over k-SAT instances. It is closely connected to statistical physics; it is used as a testbench for satisfiability algorithms, and average-case hardness over this…
Despite significant advances in characterizing the highly nonconvex landscapes of constraint satisfaction problems, the good performance of certain algorithms in solving hard combinatorial optimization tasks remains poorly understood. This…
Critical decision-making issues in science, engineering, and industry are based on combinatorial optimization; however, its application is inherently limited by the NP-hard nature of the problem. A specialized paradigm of analogue quantum…
We theoretically investigate the stochastic dynamics of two qubits subject to one- and two-site correlated continuous weak measurements. When measurements dominate over the local unitary evolution, the system's dynamics is constrained and…
The quantum Zeno effect is a striking feature of quantum mechanics with foundational implications and practical applications in quantum control, error suppression, and error correction. In recent years, the effect has branched off into a…
Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. [Suba\c{s}i et al., Phys. Rev. Lett.…
We optimize fault-tolerant quantum error correction to reduce the number of syndrome bit measurements. Speeding up error correction will also speed up an encoded quantum computation, and should reduce its effective error rate. We give both…