arXiv subjects

R. Somma

Publications and source records attributed to R. Somma.

5 recordsLinked to original sources

arXiv2007

Quantum Simulated Annealing

We develop a quantum algorithm to solve combinatorial optimization problems through quantum simulation of a classical annealing process. Our algorithm combines techniques from quantum walks, quantum phase estimation, and quantum Zeno effect. It can be viewed as a quantum analogue of the discrete-time Markov chain Monte Carlo implementation of classical simulated annealing. Our implementation scales with the inverse of the square root of the minimum spectral gap of the stochastic matrix used in the classical simulation. The quantum algorithm outperforms the classical one, which scales with the inverse of the gap.

quant-ph↗

arXiv2004

Liquid state NMR simulations of quantum many-body problems

Recently developed quantum algorithms suggest that in principle, quantum computers can solve problems such as simulation of physical systems more efficiently than classical computers. Much remains to be done to implement these conceptual ideas into actual quantum computers. As a small-scale demonstration of their capability, we simulate a simple many-fermion problem, the Fano-Anderson model, using liquid state Nuclear Magnetic Resonance (NMR). We carefully designed our experiment so that the resource requirement would scale up polynomially with the size of the quantum system to be simulated. The experimental results allow us to assess the limits of the degree of quantum control attained in these kinds of experiments. The simulation of other physical systems, with different particle statistics, is also discussed.

quant-ph↗

arXiv2004

Exactly-Solvable Models Derived from a Generalized Gaudin Algebra

We introduce a generalized Gaudin Lie algebra and a complete set of mutually commuting quantum invariants allowing the derivation of several families of exactly solvable Hamiltonians. Different Hamiltonians correspond to different representations of the generators of the algebra. The derived exactly-solvable generalized Gaudin models include the Bardeen-Cooper-Schrieffer, Suhl-Matthias-Walker, the Lipkin-Meshkov-Glick, generalized Dicke, the Nuclear Interacting Boson Model, a new exactly-solvable Kondo-like impurity model, and many more that have not been exploited in the physics literature yet.

cond-mat.supr-con↗

arXiv2002

Introduction to NMR Quantum Information Processing

After a general introduction to nuclear magnetic resonance (NMR), we give the basics of implementing quantum algorithms. We describe how qubits are realized and controlled with RF pulses, their internal interactions, and gradient fields. A peculiarity of NMR is that the internal interactions (given by the internal Hamiltonian) are always on. We discuss how they can be effectively turned off with the help of a standard NMR method called ``refocusing''. Liquid state NMR experiments are done at room temperature, leading to an extremely mixed (that is, nearly random) initial state. Despite this high degree of randomness, it is possible to investigate QIP because the relaxation time (the time scale over which useful signal from a computation is lost) is sufficiently long. We explain how this feature leads to the crucial ability of simulating a pure (non-random) state by using ``pseudopure'' states. We discuss how the ``answer'' provided by a computation is obtained by measurement and how this measurement differs from the ideal, projective measurement of QIP. We then give implementations of some simple quantum algorithms with a typical experimental result. We conclude with a discussion of what we have learned from NMR QIP so far and what the prospects for future NMR QIP experiments are.

quant-ph↗

arXiv2001

Simulating Physical Phenomena by Quantum Networks

Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by means of the algebra generated by the usual fermionic creation and annihilation operators, or by using the algebra of Pauli (spin-1/2) operators. The correspondence between the two algebras is given by the Jordan-Wigner isomorphism. As we previously noted similar one-to-one mappings enable one to represent any physical system in a quantum computer. In this paper we evolve and exploit this fundamental concept in quantum information processing to simulate generic physical phenomena by quantum networks. We give quantum circuits useful for the efficient evaluation of the physical properties (e.g, spectrum of observables or relevant correlation functions) of an arbitrary system with Hamiltonian $H$.

quant-ph↗