Quantum simulations with cold trapped ions

Johanning, M.; Varòn, Andrès; Wunderlich, Christof

doi:10.1088/0953-4075/42/15/154009

Cited by 191 publications

(227 citation statements)

References 172 publications

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“…Thanks to impressive progress on the experimental side, many small-and medium-scale quantum devices are now ready for applications ranging from quantum metrology [1][2][3][4] to quantum simulation [5][6][7][8][9]. With quantum information processing as one of the driving but longterm goals (e.g., [10][11][12]), one of the pressing questions is, what can one do with these devices now ?…”

Section: Introductionmentioning

confidence: 99%

Symmetry criteria for quantum simulability of effective interactions

et al. 2015

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What can one do with a given tunable quantum device? We provide complete symmetry criteria deciding whether some effective target interaction(s) can be simulated by a set of given interactions. Symmetries lead to a better understanding of simulation and permit a reasoning beyond the limitations of the usual explicit Lie closure. Conserved quantities induced by symmetries pave the way to a resource theory for simulability. On a general level, one can now decide equality for any pair of compact Lie algebras just given by their generators without determining the algebras explicitly. Several physical examples are illustrated, including entanglement invariants, the relation to unitary gate membership problems, as well as the central-spin model.

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Section: Introductionmentioning

confidence: 99%

Symmetry criteria for quantum simulability of effective interactions

et al. 2015

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“…Usually, one imposes the constraint of vanishing total magnetization, which can be realized by mean-field-like interactions (α (2) …”

Section: Np-complete Models Realizable With Available Trapped-ion Tecmentioning

confidence: 99%

“…This procedure is sketched in Figure 1. It is in spirit very similar to adiabatic state preparation, where one seeks to reach the ground state of a quantum many-body Hamiltonian via a ramp as Equation (2). First steps in this direction have already been done in a trapped-ion setup [11].…”

Section: Introductionmentioning

confidence: 99%

Probing entanglement in adiabatic quantum optimization with trapped ions

et al. 2015

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Adiabatic quantum optimization has been proposed as a route to solve NP-complete problems, with a possible quantum speedup compared to classical algorithms. However, the precise role of quantum effects, such as entanglement, in these optimization protocols is still unclear. We propose a setup of cold trapped ions that allows one to quantitatively characterize, in a controlled experiment, the interplay of entanglement, decoherence, and non-adiabaticity in adiabatic quantum optimization. We show that, in this way, a broad class of NP-complete problems becomes accessible for quantum simulations, including the knapsack problem, number partitioning, and instances of the max-cut problem. Moreover, a general theoretical study reveals correlations of the success probability with entanglement at the end of the protocol. From exact numerical simulations for small systems and linear ramps, however, we find no substantial correlations with the entanglement during the optimization. For the final state, we derive analytically a universal upper bound for the success probability as a function of entanglement, which can be measured in experiment. The proposed trapped-ion setups and the presented study of entanglement address pertinent questions of adiabatic quantum optimization, which may be of general interest across experimental platforms.

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“…When N ions are placed in a linear Paul trap [9,10,20] with harmonic trapping potentials, they form a nonuniform (Wigner) lattice, with increasing interparticle spacing as one moves from the center to the edge of the chain. The ions vibrate in all three spatial dimensions about these equilibrium positions [21] with 3N normal modes.…”

Section: Theory a Microscopic Hamiltonianmentioning

confidence: 99%

Intrinsic phonon effects on analog quantum simulators with ultracold trapped ions

Wang

Freericks

2012

Phys. Rev. A

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Linear Paul traps have been used recently to simulate the transverse field Ising model with longrange spin-spin couplings. We study the intrinsic effects of phonon creation (from the initial phonon ground state) on the spin-state probability and spin entanglement for such quantum spin simulators. While it has often been assumed that phonon effects are benign because they play no role in the pure Ising model, they can play a significant role when a transverse field is added to the model. We use a many-body factorization of the quantum time-evolution operator of the system, adiabatic perturbation theory and exact numerical integration of the Schrödinger equation in a truncated spin-phonon Hilbert space followed by a tracing out of the phonon degrees of freedom to study this problem. We find that moderate phonon creation often makes the probabilities of different spin states behave differently from the static spin Hamiltonian. In circumstances in which phonon creation is minor, the spin dynamics state probabilities converge to the static spin Hamiltonian prediction at the cost of reducing the spin entanglement. We show how phonon creation can severely impede the observation of kink transitions in frustrated spin systems when the number of ions increases. Many of our results also have implications for quantum simulation in a Penning trap.

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Quantum simulations with cold trapped ions

Cited by 191 publications

References 172 publications

Symmetry criteria for quantum simulability of effective interactions

Symmetry criteria for quantum simulability of effective interactions

Probing entanglement in adiabatic quantum optimization with trapped ions

Intrinsic phonon effects on analog quantum simulators with ultracold trapped ions

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