Related papers: Exponential Quantum Speedup on Structured Hard Ins…
We present a theoretical analysis of the DIC-DAC-DOA algorithm, a non-stoquastic quantum algorithm for solving the Maximum Independent Set (MIS) problem. The algorithm runs in polynomial time and achieves exponential speedup over both…
Designing quantum algorithms with a speedup over their classical analogs is a central challenge in quantum information science. Motivated by recent experimental observations of a superlinear quantum speedup in solving the Maximum…
One of the distinct features of quantum mechanics is that the probability amplitude can have both positive and negative signs, which has no classical counterpart as the classical probability must be positive. Consequently, one possible way…
The Maximum Independent Set (MIS) problem is a fundamental combinatorial optimization task that can be naturally mapped onto the Ising Hamiltonian of neutral atom quantum processors. Given its connection to NP-hard problems and real-world…
Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally…
A quadratic speedup of the quantum adiabatic algorithm (QAA) for finding independent sets (ISs) in a graph is proven analytically. In comparison to the best classical algorithm with $O(n^2)$ scaling, where $n$ is the number of vertexes, our…
Tunneling is often claimed to be the key mechanism underlying possible speedups in quantum optimization via quantum annealing (QA), especially for problems featuring a cost function with tall and thin barriers. We present and analyze…
Quantum computation provides exponential speedup for solving certain mathematical problems against classical computers. Motivated by current rapid experimental progress on quantum computing devices, various models of quantum computation…
Quantum algorithms have been widely studied in the context of combinatorial optimization problems. While this endeavor can often analytically and practically achieve quadratic speedups, theoretical and numeric studies remain limited,…
We demonstrate the possibility of (sub)exponential quantum speedup via a quantum algorithm that follows an adiabatic path of a gapped Hamiltonian with no sign problem. This strengthens the superpolynomial separation recently proved by…
Along with the development of quantum technology, finding useful applications of quantum computers has been a central pursuit. Despite various quantum algorithms have been developed, many of them often require strong input assumptions,…
Non-stoquastic Hamiltonians have both positive and negative signs in off-diagonal elements in their matrix representation in the standard computational basis and thus cannot be simulated efficiently by the standard quantum Monte Carlo…
We present new theoretical mechanisms for quantum speedup in the global optimization of nonconvex functions, expanding the scope of quantum advantage beyond traditional tunneling-based explanations. As our main building-block, we…
A central roadblock to analyzing quantum algorithms on quantum states is the lack of a comparable input model for classical algorithms. Inspired by recent work of the author [E. Tang, STOC'19], we introduce such a model, where we assume we…
Research in quantum information science aims to surpass the scaling limitations of classical information processing. From a physicist's perspective, performance improvement involves a physical speedup in the quantum domain, achieved by…
The simulation of many industrially relevant physical processes can be executed up to exponentially faster using quantum algorithms. However, this speedup can only be leveraged if the data input and output of the simulation can be…
The simulation of large-scale classical systems in exponentially small space on quantum computers has gained attention. The prior work demonstrated that a quantum algorithm offers an exponential speedup over any classical algorithm in…
Classical optimization problems can be solved by adiabatically preparing the ground state of a quantum Hamiltonian that encodes the problem. The performance of this approach is determined by the smallest gap encountered during the…
Classical algorithms are often not effective for solving nonconvex optimization problems where local minima are separated by high barriers. In this paper, we explore possible quantum speedups for nonconvex optimization by leveraging the…
We describe and analyze an architecture for quantum optimization to solve maximum independent set (MIS) problems using neutral atom arrays trapped in optical tweezers. Optimizing independent sets is one of the paradigmatic, NP-hard problems…