Related papers: Essentiality of the Non-stoquastic Hamiltonians an…
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…
Quantum annealing (QA) is a heuristic algorithm for finding low-energy configurations of a system, with applications in optimization, machine learning, and quantum simulation. Up to now, all implementations of QA have been limited to qubits…
Quantum annealing (QA) is a promising method for solving combinatorial optimization problems whose solutions are embedded into a ground state of the Ising Hamiltonian. This method employs two types of Hamiltonians: a driver Hamiltonian and…
Establishing quantum speedup for computationally hard problems of practical relevance, particularly combinatorial optimization problems, remains a central challenge in quantum computation. In this work, we identify a structurally defined…
Quantum annealing (QA) is a promising approach for not only solving combinatorial optimization problems but also simulating quantum many-body systems such as those in condensed matter physics. However, non-adiabatic transitions constitute a…
We argue that a complete description of quantum annealing (QA) implemented with continuous variables must take into account the non-adiabatic Aharonov-Anandan geometric phase that arises when the system Hamiltonian changes during the…
We assess the prospects for algorithms within the general framework of quantum annealing (QA) to achieve a quantum speedup relative to classical state of the art methods in combinatorial optimization and related sampling tasks. We argue for…
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 annealing is a computational approach designed to leverage quantum fluctuations for solving large-scale classical optimization problems. Although incorporating standard transverse field (TF) terms in the annealing process can help…
Quantum annealing is a generic solver of the optimization problem that uses fictitious quantum fluctuation. Its simulation in classical computing is often performed using the quantum Monte Carlo simulation via the Suzuki--Trotter…
Quantum annealing (QA) is a generic method for solving optimization problems using fictitious quantum fluctuation. The current device performing QA involves controlling the transverse field; it is classically simulatable by using the…
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…
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…
Simulated Quantum Annealing (SQA) is a Markov Chain Monte-Carlo algorithm that samples the equilibrium thermal state of a Quantum Annealing (QA) Hamiltonian. In addition to simulating quantum systems, SQA has also been proposed as another…
Quantum Annealing, or Quantum Stochastic Optimization, is a classical randomized algorithm which provides good heuristics for the solution of hard optimization problems. The algorithm, suggested by the behaviour of quantum systems, is an…
Perturbative anticrossings have long been identified as a potential computational bottleneck for quantum annealing. This bottleneck can appear, for example, when a uniform transverse driver Hamiltonian is applied to each qubit. Previous…
The viability of non-stoquastic catalyst Hamiltonians to deliver consistent quantum speedups in quantum adiabatic optimization remains an open question. The infinite-range ferromagnetic $p$-spin model is a rare example exhibiting an…
We analyze the behavior of stoquastic transverse-field quantum annealing (TFQA) on a structured class of Maximum Independent Set (MIS) instances, using the same decomposition framework developed in our companion work on the DIC-DAC-DOA…
Quantum annealing is a proposed combinatorial optimization technique meant to exploit quantum mechanical effects such as tunneling and entanglement. Real-world quantum annealing-based solvers require a combination of annealing and classical…
Quantum fluctuations driven by non-stoquastic Hamiltonians have been conjectured to be an important and perhaps essential missing ingredient for achieving a quantum advantage with adiabatic optimization. We introduce a transformation that…