Related papers: A Random Matrix Model of Adiabatic Quantum Computi…
Adiabatic quantum computing is a universal model for quantum computing whose implementation using a gate-based quantum computer requires depths that are unreachable in the early fault-tolerant era. To mitigate the limitations of near-term…
Discerning chaos in quantum systems is an important problem as the usual route of Lyapunov exponents in classical systems is not straightforward in quantum systems. A standard route is the comparison of statistics derived from model…
We study the eigenlevel spectrum of quantum adiabatic algorithm for 3-satisfiability problem, focusing on single-solution instances. The properties of the ground state and the associated gap, crucial for determining the running time of the…
We discuss the application of the adiabatic perturbation theory to analyze the dynamics in various systems in the limit of slow parametric changes of the Hamiltonian. We first consider a two-level system and give an elementary derivation of…
Two recent preprints [B. Altshuler, H. Krovi, and J. Roland, "Quantum adiabatic optimization fails for random instances of NP-complete problems", arXiv:0908.2782 and "Anderson localization casts clouds over adiabatic quantum optimization",…
In the continuum limit (large number of qubits), adiabatic quantum algorithms display a remarkable similarity to sweeps through quantum phase transitions. We find that transitions of second or higher order are advantageous in comparison to…
In quantum adiabatic evolution algorithms, the quantum computer follows the ground state of a slowly varying Hamiltonian. The ground state of the initial Hamiltonian is easy to construct; the ground state of the final Hamiltonian encodes…
Background: Solving nuclear many-body problems with an ab initio approach is widely recognized as a computationally challenging problem. Quantum computers offer a promising path to address this challenge. There are urgent needs to develop…
Adiabatic quantum computing and optimization have garnered much attention recently as possible models for achieving a quantum advantage over classical approaches to optimization and other special purpose computations. Both techniques are…
The Hungarian physicist Eugene Wigner introduced random matrix models in physics to describe the energy spectra of atomic nuclei. As such, the main goal of Random Matrix Theory (RMT) has been to derive the eigenvalue statistics of matrices…
We present experimental and theoretical results for the fluctuation properties in the incomplete spectra of quantum systems with symplectic symmetry and a chaotic dynamics in the classical limit. To obtain theoretical predictions, we extend…
Alongside the effort underway to build quantum computers, it is important to better understand which classes of problems they will find easy and which others even they will find intractable. We study random ensembles of the QMA$_1$-complete…
We numerically simulate the effects of noise-induced sampling of alternative Hamiltonian paths on the ability of quantum adiabatic search (QuAdS) to solve randomly generated instances of the NP-Complete problem N-bit Exact Cover 3. The…
Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement…
Many quantum algorithms, such as adiabatic algorithms (e.g. AQC) and phase randomisation, require simulating Hamiltonian evolution. In addition, the simulation of physical systems is an important objective in its own right. In many cases,…
Random Matrix Theory (RMT) is a powerful statistical tool to model spectral fluctuations. This approach has also found fruitful application in Quantum Chromodynamics (QCD). Importantly, RMT provides very efficient means to separate…
We propose and analyze a robust implementation of Rydberg antiblockade based on rapid adiabatic passage. Although Rydberg antiblockade offers key opportunities in quantum information processing and sensing, its sensitivity to position…
Adiabatic quantum computing~(AQC) is based on the adiabatic principle, where a quantum system remains in an instantaneous eigenstate of the driving Hamiltonian. The final state of the Hamiltonian encodes solution to the problem of interest.…
We investigate the symmetry breaking role of noise in adiabatic quantum computing using the example of the CNOT gate. In particular, we analyse situations where the choice of initial configuration leads to symmetries in the Hamiltonian and…
We introduce and study the adiabatic dynamics of free-fermion models subject to a local Lindblad bath and in the presence of a time-dependent Hamiltonian. The merit of these models is that they can be solved exactly, and will help us to…