Related papers: Necessary Condition for the Quantum Adiabatic Appr…
Models of quantum computation are important because they change the physical requirements for achieving universal quantum computation (QC). For example, one-way QC requires the preparation of an entangled "cluster" state followed by…
We present a rigorous proof that quantum circuit algorithm can be transformed into quantum adiabatic algorithm with the exact same time complexity. This means that from a quantum circuit algorithm of $L$ gates we can construct a quantum…
We study quantum adiabatic dynamics, where the slowly moving field is influenced by system's state (feedback). The information for the feedback is gained from non-disturbating measurements done on an ensemble of identical non-interacting…
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…
The viability of adiabatic quantum computation depends on the slow evolution of the Hamiltonian. The adiabatic switching theorem provides an asymptotic series for error estimates in $1/T$, based on the lowest non-zero derivative of the…
We review our work on the interplay between non-resonant gates and solid state environment in various solid state quantum computer architectures and the resulting gate errors. Particular, we show that adiabatic condition can be satisfied in…
A sweep through a quantum phase transition by means of a time-dependent external parameter (e.g., pressure) entails non-equilibrium phenomena associated with a break-down of adiabaticity: At the critical point, the energy gap vanishes and…
We introduce an adiabatic perturbation theory for quantum systems with degenerate energy spectra. This perturbative series enables one to rigorously establish conditions for the validity of the adiabatic theorem of quantum mechanics for…
A computation in adiabatic quantum computing is implemented by traversing a path of nondegenerate eigenstates of a continuous family of Hamiltonians. We introduce a method that traverses a discretized form of the path: At each step we apply…
Quantum annealing (QA) is a method for solving combinatorial optimization problems. We can estimate the computational time for QA using the adiabatic condition. The adiabatic condition consists of two parts: an energy gap and a transition…
Envariance is a symmetry exhibited by correlated quantum systems. Inspired by this "quantum fact of life," we propose a novel method for shortcuts to adiabaticity which enables the system to evolve through the adiabatic manifold at all…
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. Based on results from [BeTe1] for special…
We present two quantum algorithms based on evolution randomization, a simple variant of adiabatic quantum computing, to prepare a quantum state $\vert x \rangle$ that is proportional to the solution of the system of linear equations $A…
The consistency of quantum adiabatic theorem has been doubted recently. It is shown in the present paper that the difference between the adiabatic solution and the exact solution to the Schrodinger equation with a slowly changing driving…
In this paper we analyze the performance of the Quantum Adiabatic Evolution algorithm on a variant of Satisfiability problem for an ensemble of random graphs parametrized by the ratio of clauses to variables, $\gamma=M/N$. We introduce a…
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…
The necessary and sufficient conditions for the stability of adiabatic states in three-level quantum systems are investigated analytically and numerically. Various possible configurations of three-level systems under exact two-photon…
This paper explores several aspects of the adiabatic quantum computation model. We first show a way that directly maps any arbitrary circuit in the standard quantum computing model to an adiabatic algorithm of the same depth. Specifically,…
We consider a time-dependent two-level quantum system interacting with a free Boson reservoir. The coupling is energy conserving and depends slowly on time, as does the system Hamiltonian, with a common adiabatic parameter $\varepsilon$.…
We prove an analytical expression for the size of the gap between the ground and the first excited state of quantum adiabatic algorithm for the 3-satisfiability, where the initial Hamiltonian is a projector on the subspace complementary to…