We analyze the computational power and limitations of the recently proposed ‘quantum adiabatic evolution algorithm’.

The concept of quasiresonance was introduced in connection with inelastic collisions between one atom and a vibro-rotationally excited diatomic molecule. In its original form, the collisions induce quasiresonant transfer of energy between the internal degrees of freedom of the diatom: there is a surprisingly accurate low order rational value for the ratio of the changes in the vibrational and r...

This mostly expository paper shows how weak convergence methods provide simple, elegant proofs of (i) the stabilization of an inverted pendulum under fast vertical oscillations, (ii) the existence of particle traps induced by rapidly varying electric fields and (iii) the adiabatic invariance of ∫ Γ p dx for slowing varying planar Hamiltonian dynamics. Under an appropriate, but very restrictive,...

D X : A(X) = Sym (H0(X)⊕H2(X)) → C, where w ∈ H(X ;Z). As for the grading of A(X), the elements in H2(X) have degree 2 and the point x ∈ H0(X) has degree 4. Let d0 = −w 2 − 32 (1 + b ), so that for homogeneous z ∈ A(X), D X(z) is non-zero only if 1 2 deg z ≡ d0 (mod 4). Set ℘ = x−4 ∈ A(X) as in [12]. By definition, X is of simple type if the condition D X(℘z) = 0 is satisfied for any z ∈ A(X). ...

Granada oscillation code (GraCo) is a software constructed to compute adiabatic and non-adiabatic oscillation eigenfunctions and eigenvalues. The adiabatic version gives the standard numerical resolution, and also the Richardson extrapolation, different sets of eigenfunctions, different outer mechanical boundary conditions or different integration variables. The non-adiabatic version can includ...

This paper presents low-power characteristics of adiabatic complementary pass-transistor logic (ACPL) using four-phase AC power supply. Adiabatic CPL circuits consist of pure NMOS transistors, use CPL blocks for evaluation and bootstrapped NMOS switches to eliminate non-adiabatic loss of output loads. In this paper, combinational circuit (4-bit ripple carry adder) and sequential circuit (4-bit ...

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 theorem holds for the ground state of atoms in quantized radiation field. The general result we prove gives no information on the rate at which the adi...

The basic adiabatic theorems of classical and quantum mechanics are overviewed and an adiabatic theorem in quantum mechanics without a gap condition is described. 1 Classical Adiabatic Invariants Consider a (mathematical) pendulum whose period is slowly modulated, for example by shortening the length of the pendulum, fig 1, [1, 18]. Figure 1: An adiabatic pendulum The Hamiltonian describing the...

For a many-body system of arbitrary dimension, we consider fermionic ground states non-interacting Hamiltonians invariant under $C_2$ cyclic group. The absolute difference $\Delta$ between the number occupied symmetric and anti-symmetric single-particle is an adiabatic invariant. We prove lower bounds on configurational entropy based this In band insulators, topological can be directly determin...

Analog models of quantum information processing, such as adiabatic quantum computation and analog quantum simulation, require the ability to subject a system to precisely specified Hamiltonians. Unfortunately, the hardware used to implement these Hamiltonians will be imperfect and limited in its precision. Even small perturbations and imprecisions can have profound effects on the nature of the ...