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**1 - 3**of**3**### c ○ Rinton Press HIGH-FIDELITY 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 two-dimensional 9Be + ion crystals for experimental tests of quantum control techniques. Our primary qubit is the 124 GHz ground-state 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 Pauli-randomized π/2 and π pulse pair) of 8±1×10−4. Ramsey interferometry and spin-locking [14] measurements are used to elucidate the limits of qubit coherence in the system, yielding a typical free-induction 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 error-suppressing capabilities of dynamical

### An Investigation of . . . Trapped-Ion Quantum Simulators

, 2009

"... Quantum simulation offers the possibility of using a controllable quantum-mechanical 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 quantum-mechanical 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 three-qubit nuclear spin system to calculate the low-lying 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

### Creation of two-dimensional coulomb crystals of ions in oblate Paul traps for quantum simulations

"... Full list of author information is available at the end of the article We develop the theory to describe the equilibrium ion positions and phonon modes for a trapped ion quantum simulator in an oblate Paul trap that creates two-dimensional Coulomb crystals in a triangular lattice. By coupling the in ..."

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Full list of author information is available at the end of the article We develop the theory to describe the equilibrium ion positions and phonon modes for a trapped ion quantum simulator in an oblate Paul trap that creates two-dimensional Coulomb crystals in a triangular lattice. By coupling the internal states of the ions to laser beams propagating along the symmetry axis, we study the effective Ising spin-spin interactions that are mediated via the axial phonons and are less sensitive to ion micromotion. We find that the axial mode frequencies permit the programming of Ising interactions with inverse power law spin-spin couplings that can be tuned from uniform to r−3 with DC voltages. Such a trap could allow for interesting new geometrical configurations for quantum simulations on moderately sized systems including frustrated magnetism on triangular lattices or Aharonov-Bohm effects on ion tunneling. The trap also incorporates periodic boundary conditions around loops which could be employed to examine time crystals.