Related papers: Adiabatic Quantum Computation with a 1D projector …

It is known that for multi-level time-dependent quantum systems one can construct superadiabatic representations in which the coupling between separated levels is exponentially small in the adiabatic limit. For a family of two-state systems…

The adiabatic theorem has been recently used to design quantum algorithms of a new kind, where the quantum computer evolves slowly enough so that it remains near its instantaneous ground state which tends to the solution [Farhi et al.,…

Quantum annealing is a promising algorithm for solving combinatorial optimization problems. It searches for the ground state of the Ising model, which corresponds to the optimal solution of a given combinatorial optimization problem. The…

Adiabatic quantum computing (AQC) started as an approach to solving optimization problems, and has evolved into an important universal alternative to the standard circuit model of quantum computing, with deep connections to both classical…

We prove the equivalence between adiabatic quantum computation and quantum computation in the circuit model. An explicit adiabatic computation procedure is given that generates a ground state from which the answer can be extracted. The…

Adiabatic quantum control is a powerful tool for quantum engineering and a key component in some quantum computation models, where accurate control over the timing of the involved pulses is not needed. However, the adiabatic condition…

We present a general method for studying coupled qubits driven by adiabatically changing external parameters. Extended calculations are provided for a two-bit Hamiltonian whose eigenstates can be used as logical states for a quantum CNOT…

We introduce a simple framework for estimating lower bounds on the runtime of a broad class of adiabatic quantum algorithms. The central formula consists of calculating the variance of the final Hamiltonian with respect to the initial…

Adiabatic quantum computing is a framework for quantum computing that is superficially very different to the standard circuit model. However, it can be shown that the two models are computationally equivalent. The key to the proof is a…

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.

Continuous-time quantum walks and adiabatic quantum evolution are two general techniques for quantum computing, both of which are described by Hamiltonians that govern their evolutions by Schr\"odinger's equation. In the former, the…

We show that the quasi-adiabatic evolution of a system governed by the Dicke Hamiltonian can be described in terms of a self-induced quantum many-body metrological protocol. This effect relies on the sensitivity of the ground state to a…

We present numerical calculations, and simulations performed on a Rydberg atom quantum simulator, of the adiabatic evolution of many-body quantum systems around a quantum phase transition. We demonstrate that the end-to-end transfer error,…

Adiabatic quantum computing enables the preparation of many-body ground states. This is key for applications in chemistry, materials science, and beyond. Realisation poses major experimental challenges: Direct analog implementation requires…

In his famous 1981 talk, Feynman proposed that unlike classical computers, which would presumably experience an exponential slowdown when simulating quantum phenomena, a universal quantum simulator would not. An ideal quantum simulator…

We discuss in this chapter the basics of adiabatic computation, as well as some physical implementations. After a short introduction of the quantum circuit model, we describe quantum adiabatic computation, quantum annealing, and the strong…

The quantum adiabatic algorithm is a Hamiltonian based quantum algorithm designed to find the minimum of a classical cost function whose domain has size N. We show that poor choices for the Hamiltonian can guarantee that the algorithm will…

We introduce a shortcut to the adiabatic gate teleportation model of quantum computation. More specifically, we determine fast local counterdiabatic Hamiltonians able to implement teleportation as a universal computational primitive. In…

Quantum phase transitions materialize as level crossings in the ground-state energy when the parameters of the Hamiltonian are varied. The resulting ground-state phase diagrams are straightforward to determine by exact diagonalization on…

Computing using a continuous-time evolution, based on the natural interaction Hamiltonian of the quantum computer hardware, is a promising route to building useful quantum computers in the near-term. Adiabatic quantum computing, quantum…