Related papers: Fast digital methods for adiabatic state preparati…
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…
Holonomic quantum computation exploits the geometric evolution of eigenspaces of a degenerate Hamiltonian to implement unitary evolution of computational states. In this work we introduce a framework for performing scalable quantum…
Let $H(t)=(1-t/T)H_0 + (t/T)H_1$, $t\in [0,T]$, be the Hamiltonian governing an adiabatic quantum algorithm, where $H_0$ is diagonal in the Hadamard basis and $H_1$ is diagonal in the computational basis. We prove that $H_0$ and $H_1$ must…
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…
Adiabatic quantum computation has recently attracted attention in the physics and computer science communities, but its computational power was unknown. We describe an efficient adiabatic simulation of any given quantum algorithm, which…
Nonadiabatic holonomic quantum computation (NHQC) provides a method to implement error resilient gates and that has attracted considerable attention recently. Since it was proposed, three-level {\Lambda} systems have become the typical…
Adiabatic quantum algorithms are characterized by their run time and accuracy. The relation between the two is essential for quantifying adiabatic algorithmic performance, yet is often poorly understood. We study the dynamics of a…
Adiabatic quantum computation is based on the adiabatic evolution of quantum systems. We analyse a particular class of qauntum adiabatic evolutions where either the initial or final Hamiltonian is a one-dimensional projector Hamiltonian on…
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…
We analyze the ground state entanglement in a quantum adiabatic evolution algorithm designed to solve the NP-complete Exact Cover problem. The entropy of entanglement seems to obey linear and universal scaling at the point where the mass…
Recently, nonadiabatic geometric quantum computation has been received great attentions, due to its fast operation and intrinsic error resilience. However, compared with the corresponding dynamical gates, the robustness of implemented…
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.…
Adiabatic passage employs a slowly varying time-dependent Hamiltonian to control the evolution of a quantum system along the Hamiltonian eigenstates. For processes of finite duration, the exact time evolving state may deviate from the…
Recently a method for adiabatic quantum computation has been proposed and there has been considerable speculation about its efficiency for NP-complete problems. Heuristic arguments in its favor are based on the unproven assumption of an…
We provide a theoretical study of the quantum adiabatic evolution algorithm with different evolution paths proposed in [E. Farhi, et al., arXiv:quant-ph/0208135]. The algorithm is applied to a random binary optimization problem (a version…
Determining Hamiltonian ground states and energies is a challenging task with many possible approaches on quantum computers. While variational quantum eigensolvers are popular approaches for near term hardware, adiabatic state preparation…
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…
A numerical method is proposed for simulation of composite open quantum systems. It is based on Lindblad master equations and adiabatic elimination. Each subsystem is assumed to converge exponentially towards a stationary subspace, slightly…
For adiabatic controls of quantum systems, the non-adiabatic transitions are reduced by increasing the operation time of processes. Perfect quantum adiabaticity usually requires the infinitely slow variation of control parameters. In this…
We present a coherent counter-diabatic quantum protocol to prepare ground states in the lattice gauge mapping of all-to-all Ising models (LHZ) with considerably enhanced final ground state fidelity compared to a quantum annealing protocol.…