Related papers: Adiabatic Condition and Quantum Geometric Potentia…
The time-evolution operator for an explicitly time-dependent Hamiltonian is expressed as the product of a sequence of unitary operators. These are obtained by successive time-dependent unitary transformations of the Hilbert space followed…
Adiabatic invariants are introduced and shown to provide an approximate second integral of motion for the non-integrable Dicke model, in the energy region where the system exhibits a regular dynamics. This low-energy region is always…
A major challenge facing adiabatic quantum computing is that algorithm design and error correction can be difficult for adiabatic quantum computing. Recent work has considered addressing his challenge by using coherently controlled…
The adiabatic quantum computation is a universal and robust method of quantum computing. In this architecture, the problem can be solved by adiabatically evolving the quantum processor from the ground state of a simple initial Hamiltonian…
We generalize the adiabatic approximation to the case of open quantum systems, in the joint limit of slow change and weak open system disturbances. We show that the approximation is ``physically reasonable'' as under wide conditions it…
The theoretical analysis of the Adiabatic Quantum Computation protocol presents several challenges resulting from the difficulty of simulating, with classical resources, the unitary dynamics of a large quantum device. We present here a…
A quantum system will stay near its instantaneous ground state if the Hamiltonian that governs its evolution varies slowly enough. This quantum adiabatic behavior is the basis of a new class of algorithms for quantum computing. We test one…
A proof of the adiabatic theorem for quantum systems whose time evolution proceeds along discrete time, e.g., quantum maps and quantum circuits, is shown.
We discuss a toy model for adiabatic quantum computation which displays some phenomenological properties expected in more realistic implementations. This model has two free parameters: the adiabatic evolution parameter $s$ and the $\alpha$…
A general quantum adiabatic theorem with and without the time-dependent orthogonalization is proven, which can be applied to understand the origin of activation energies in chemical reactions. Further proofs are also developed for the…
The preparation of a given quantum state on a quantum computing register is a typically demanding operation, requiring a number of elementary gates that scales exponentially with the size of the problem. Using the adiabatic theorem for…
Preparing the ground state of a Hamiltonian is a problem of great significance in physics with deep implications in the field of combinatorial optimization. The adiabatic algorithm is known to return the ground state for sufficiently long…
In a recent Letter [Phys. Rev. Lett. {\bf 95}, 080502 (2005)], an interesting scheme was proposed to implement a type of conditional quantum phase gates with built-in fault-tolerant feature via adiabatic evolution of dark eigenstates. In…
Counterdiabatic (CD) driving has the potential to speed up adiabatic quantum state preparation by suppressing unwanted excitations. However, existing approaches either require intractable classical computations or are based on…
Different techniques to speed up quantum adiabatic processes are currently being explored for applications in atomic, molecular and optical physics, such as transport, cooling and expansions, wavepacket splitting, or internal state control.…
We discuss dynamics of periodically-driven open quantum systems. The time evolution of the quantum state is described by the quantum master equation and the form of the dissipator is chosen so that the instantaneous stationary state is…
We simulate the quantum adiabatic algorithm (QAA) for the exact cover problem for sizes up to N=256 using quantum Monte Carlo simulations incorporating parallel tempering. At large N we find that some instances have a discontinuous (first…
We review the proposal of a quantum algorithm for Hilbert's tenth problem and provide further arguments towards the proof that: (i) the algorithm terminates after a finite time for any input of Diophantine equation; (ii) the final ground…
Adiabatic quantum computing is a powerful framework for state preparation, while its evolution time often scales quadratically in the inverse Hamiltonian spectral gap, leading to sub-optimal computational complexity. In this work, we…
On-the-fly quantum nonadiabatic dynamics for large systems greatly benefits from the adiabatic representation readily available from the electronic structure programs. However, frequently occurring in this representation conical…