Related papers: Adiabatic preparation without Quantum Phase Transi…
Quantum computing has the potential to transform simulations of quantum many-body problems at the heart of electronic structure theory. Efficient quantum algorithms to compute the eigenstates of fermionic Hamiltonians, such as quantum phase…
The parametric deformations of quasienergies and eigenvectors of unitary operators are applied to the design of quantum adiabatic algorithms. The conventional, standard adiabatic quantum computation proceeds along eigenenergies of…
Whether one is interested in quantum state preparation or in the design of efficient heat engines, adiabatic (reversible) transformations play a pivotal role in minimizing computational complexity and energy losses. Understanding the…
The discrete formulation of adiabatic quantum computing is compared with other search methods, classical and quantum, for random satisfiability (SAT) problems. With the number of steps growing only as the cube of the number of variables,…
We present straightforward proofs of estimates used in the adiabatic approximation. The gap dependence is analyzed explicitly. We apply the result to interpolating Hamiltonians of interest in quantum computing.
The adiabatic theorem states that when the time evolution of the Hamiltonian is "infinitely slow", a system, when started in the ground state, remains in the instantaneous ground state at all times. This, however, does not mean that the…
Adiabatic state engineering is a powerful technique in quantum information and quantum control. However, its performance is limited by the adiabatic theorem of quantum mechanics. In this scenario, shortcuts to adiabaticity, such as provided…
We prove the adiabatic theorem for quantum evolution without the traditional gap condition. All that this adiabatic theorem needs is a (piecewise) twice differentiable finite dimensional spectral projection. The result implies that the…
Adiabatic transformation can be approximated as alternating unitary operators of a Hamiltonian and its parameter derivative as proposed in a gate-based approach to counterdiabatic driving (van Vreumingen, arXiv:2406.08064). In this paper,…
Adiabatic preparation of the ground states of many-body Hamiltonians in the closed system limit is at the heart of adiabatic quantum computation, but in reality systems are always open. This motivates a natural comparison between, on the…
Transition amplitudes between instantaneous eigenstates of quantum two-level system are evaluated analytically on the basis of a new parametrization of its evolution operator, which has recently been proposed to construct exact solutions.…
Ising spin Hamiltonians are often used to encode a computational problem in their ground states. Quantum Annealing (QA) computing searches for such a state by implementing a slow time-dependent evolution from an easy-to-prepare initial…
In this thesis, it is presented a set of results in adiabatic dynamics (closed and open system) and transitionless quantum driving that promote some advances in our understanding on quantum control and Hamiltonian inverse engineering. In…
We give a careful proof that a parallelized version of adiabatic quantum computation can efficiently simulate universal gate model quantum computation. The proof specifies an explicit parameter-dependent Hamiltonian $H({\lambda})$ that is…
We present a method for accelerating adiabatic protocols for systems involving a coupling to a continuum, one that cancels both non-adiabatic errors as well as errors due to dissipation. We focus on applications to a generic quantum state…
We propose a protocol for quantum adiabatic optimization, whereby an intermediary Hamiltonian that is diagonal in the computational basis is turned on and off during the interpolation. This `diagonal catalyst' serves to bias the energy…
We describe a many-body quantum system which can be made to quantum compute by the adiabatic application of a large applied field to the system. Prior to the application of the field quantum information is localized on one boundary of the…
We introduce a quantum algorithm to efficiently prepare states with a small energy variance at the target energy. We achieve it by filtering a product state at the given energy with a Lorentzian filter of width $\delta$. Given a local…
Adiabatic quantum computation (AQC) is a universal model for quantum computation which seeks to transform the initial ground state of a quantum system into a final ground state encoding the answer to a computational problem. AQC initial…
We study state conversion in parity-time (PT) symmetry broken non-Hermitian two level system. We construct a theory and explain underlying mechanism for state conversion and define adiabatic evolutions in non-Hermitian systems. The…