Quantum mechanics as a representation of classical conditional
... 1. and representing the three pairs of measurement outcomes by three orthogonal pairs of projections in M2 ; 2. the state of the system by a matrix Ws in M2 ; 3. requiring that the conditional probabilities of the measurement outcomes be given by the Born rule; 4. requiring that the projection postu ...
... 1. and representing the three pairs of measurement outcomes by three orthogonal pairs of projections in M2 ; 2. the state of the system by a matrix Ws in M2 ; 3. requiring that the conditional probabilities of the measurement outcomes be given by the Born rule; 4. requiring that the projection postu ...
Introduction to Differential Equations
... y = C1 sin 3t + C2 cos 3t y0 = 3C1 cos 3t − 3C2 sin 3t y00 = −9C1 sin 3t − 9C2 cos 3t Substituting into the differential equation, we get y00 + 9y = (−9C1 sin 3t − 9C2 cos 3t) + 9 (C1 sin 3t + C2 cos 3t) = 0. Thus y(t) = C1 sin 3t + C2 cos 3t is the general solution. (b) Applying the initial conditi ...
... y = C1 sin 3t + C2 cos 3t y0 = 3C1 cos 3t − 3C2 sin 3t y00 = −9C1 sin 3t − 9C2 cos 3t Substituting into the differential equation, we get y00 + 9y = (−9C1 sin 3t − 9C2 cos 3t) + 9 (C1 sin 3t + C2 cos 3t) = 0. Thus y(t) = C1 sin 3t + C2 cos 3t is the general solution. (b) Applying the initial conditi ...
ABSTRACT ADIABATIC QUANTUM COMPUTATION: NOISE IN THE ADIABATIC THEOREM AND USING THE JORDAN-WIGNER
... ground-state energy gap can be found analytically. These Hamiltonian evolutions are more complex than (1.3) in that they allow terms with interactions between qubits with non-adjacent indices (“non-nearest-neighbor interactions”). We then identify ...
... ground-state energy gap can be found analytically. These Hamiltonian evolutions are more complex than (1.3) in that they allow terms with interactions between qubits with non-adjacent indices (“non-nearest-neighbor interactions”). We then identify ...
Extremal eigenvalues of local Hamiltonians
... Theorem 1 are based on the use of a correspondence between local quantum Hamiltonians and lowdegree polynomials, which allows us to apply classical approximation algorithms for constraint satisfaction problems. This correspondence uses a qubit 2design [5, 13] to convert arbitrary qubit Hamiltonians ...
... Theorem 1 are based on the use of a correspondence between local quantum Hamiltonians and lowdegree polynomials, which allows us to apply classical approximation algorithms for constraint satisfaction problems. This correspondence uses a qubit 2design [5, 13] to convert arbitrary qubit Hamiltonians ...
Quantum Critical Systems from ADS/CFT
... The AdS/CFT (anti-de Sitter/conformal field theory) correspondence enables us to construct some strongly coupled quantum field theories by means of general relativity, and this approach provides new universality classes of condensed matter systems. In this dissertation, we will consider three system ...
... The AdS/CFT (anti-de Sitter/conformal field theory) correspondence enables us to construct some strongly coupled quantum field theories by means of general relativity, and this approach provides new universality classes of condensed matter systems. In this dissertation, we will consider three system ...
Multiphoton adiabatic rapid passage: classical transition induced by separatrix crossing
... photons are absorbed/emitted during the transition. It is more appropriate to say that the transition occurs by chirping through a 10-photon resonance condition. We also performed classical calculations for this system. To our great surprise, we found that the classical system also evolved from a sp ...
... photons are absorbed/emitted during the transition. It is more appropriate to say that the transition occurs by chirping through a 10-photon resonance condition. We also performed classical calculations for this system. To our great surprise, we found that the classical system also evolved from a sp ...
3 The Fundamental Postulate - Princeton University Press
... The aim of statistical mechanics is to describe the thermodynamic properties of complex systems, composed of a large number of particles. The characteristic evolution times of these systems are microscopic, and for this reason, measuring mechanical quantities in an experiment of reasonable length is ...
... The aim of statistical mechanics is to describe the thermodynamic properties of complex systems, composed of a large number of particles. The characteristic evolution times of these systems are microscopic, and for this reason, measuring mechanical quantities in an experiment of reasonable length is ...