A Quasicrystal for Quantum Simulations

Quantum critical state in a magnetic quasicrystal.

Quasicrystals are metallic alloys that possess long-range, aperiodic structures with diffraction symmetries forbidden to conventional crystals. Since the discovery of quasicrystals by Schechtman et al. in 1984, there has been considerable progress in resolving their geometric structure. For example, it is well known that the golden ratio of mathematics and art occurs over and over again in thei...

Quantum Simulations on a Quantum Computer

In 1982, Richard Feynman proposed that a quantum system would be more efficiently simulated by a computer based on the principles of quantum mechanics rather than by one based on classical mechanics [1]. Recently, it has been pointed out that it should be possible to efficiently approximate any desired Hamiltonian within the standard model of a quantum computer by a sparsely coupled array of tw...

Quantum Physics: A Case for Anti-Realism?

Quantum Algorithms for Fermionic Simulations

We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to be of exponential complexity into one of polynomial complexity. The key to our demonstration is the spin-particle connection (or generalized Jordan-Wigner tra...

Matching-pursuit for simulations of quantum processes

The matching-pursuit algorithm is implemented to develop an extension of the split-operator Fourier transform method to a nonorthogonal, nonuniform and dynamically adaptive coherent-state representation. The accuracy and efficiency of the computational approach are demonstrated in simulations of deep tunneling and long time dynamics by comparing our simulation results with the corresponding ben...