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Classical Simulation of Quantum Adiabatic Algorithms using Mathematica on GPUs
, 2011
"... In this paper we present a simulation environment enhanced with parallel processing which can be used on personal computers, based on a highlevel user interface developed on Mathematica c© which is connected to C++ code in order to make our platform capable of communicating with a Graphics Processi ..."
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In this paper we present a simulation environment enhanced with parallel processing which can be used on personal computers, based on a highlevel user interface developed on Mathematica c© which is connected to C++ code in order to make our platform capable of communicating with a Graphics Processing Unit. We introduce the reader to the behavior of our proposal by simulating a quantum adiabatic algorithm designed for solving hard instances of the 3SAT problem. We show that our simulator is capable of significantly increasing the number of qubits that can be simulated using classical hardware. Finally, we present a review of currently available classical simulators of quantum systems together with some justifications, based on our willingness to further understand processing properties of Nature, for devoting resources to building more powerful simulators. Key words: classical simulation of quantum algorithms, adiabatic quantum computation, GPU, Mathematica, symbolic computation, natural and artificial parallel processes.
c ○ Rinton Press HIGHFIDELITY QUANTUM CONTROL USING ION CRYSTALS IN A PENNING TRAP
, 2009
"... We provide an introduction to the use of ion crystals in a Penning trap [1, 2, 3, 4] for experiments in quantum information. Macroscopic Penning traps allow for the containment of a few to a few million atomic ions whose internal states may be used in quantum information experiments. Ions are laser ..."
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We provide an introduction to the use of ion crystals in a Penning trap [1, 2, 3, 4] for experiments in quantum information. Macroscopic Penning traps allow for the containment of a few to a few million atomic ions whose internal states may be used in quantum information experiments. Ions are laser Doppler cooled [1], and the mutual Coulomb repulsion of the ions leads to the formation of crystalline arrays [5, 6, 7, 8]. The structure and dimensionality of the resulting ion crystals may be tuned using a combination of control laser beams and external potentials [9, 10]. We discuss the use of twodimensional 9Be + ion crystals for experimental tests of quantum control techniques. Our primary qubit is the 124 GHz groundstate electron spin flip transition, which we drive using microwaves [11, 12]. An ion crystal represents a spatial ensemble of qubits, but the effects of inhomogeneities across a typical crystal are small, and as such we treat the ensemble as a single effective spin. We are able to initialize the qubits in a simple state and perform a projective measurement [1] on the system. We demonstrate full control of the qubit Bloch vector, performing arbitrary highfidelity rotations (τπ ∼200 µs). Randomized Benchmarking [13] demonstrates an error per gate (a Paulirandomized π/2 and π pulse pair) of 8±1×10−4. Ramsey interferometry and spinlocking [14] measurements are used to elucidate the limits of qubit coherence in the system, yielding a typical freeinduction decay coherence time of T2 ∼2 ms, and a limiting T1ρ ∼688 ms. These experimental specifications make ion crystals in a Penning trap ideal candidates for novel experiments in quantum control. As such, we briefly describe recent efforts aimed at studying the errorsuppressing capabilities of dynamical
An Investigation of . . . TrappedIon Quantum Simulators
, 2009
"... Quantum simulation offers the possibility of using a controllable quantummechanical system to implement the dynamics of another quantum system, performing calculations that are intractable on classical computers for all but the smallest systems. This great possibility carries with it great challeng ..."
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Quantum simulation offers the possibility of using a controllable quantummechanical system to implement the dynamics of another quantum system, performing calculations that are intractable on classical computers for all but the smallest systems. This great possibility carries with it great challenges, two of which motivate the experiments with nuclear spins and trapped ions presented in this thesis. The first challenge is determining the bounds on the precision of quantities that are calculated using a digital quantum simulator. As a specific example, we use a threequbit nuclear spin system to calculate the lowlying spectrum of a pairing Hamiltonian. We find that the simulation time scales poorly with the precision, and increases further if error correction is employed. In addition, control errors lead to yet more stringent limits on the precision. These results indicate that quantum simulation is more efficient than classical computation only when a limited precision is acceptable and when no efficient classical
c ○ Rinton Press EXPERIMENTAL AND THEORETICAL CHALLENGES FOR THE TRAPPED ELECTRON QUANTUM COMPUTER
, 810
"... We discuss quantum information processing with trapped electrons. After recalling the operation principle of planar Penning traps we sketch the experimental conditions to load, cool and detect single electrons. Here we present a detailed investigation of a scalable scheme including feasibility studi ..."
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We discuss quantum information processing with trapped electrons. After recalling the operation principle of planar Penning traps we sketch the experimental conditions to load, cool and detect single electrons. Here we present a detailed investigation of a scalable scheme including feasibility studies and the analysis of all important elements, relevant for the experimental stage. On the theoretical side, we discuss different methods to couple electron qubits. We estimate the relevant qubit coherence times and draw implications for the experimental setting. A critical assessment of quantum information processing with trapped electrons is concluding the article.