Intrinsic phonon effects on analog quantum simulators with ultracold trapped ions

Wang, C.-C. Joseph; Freericks, J. K.

doi:10.1103/physreva.86.032329

Cited by 27 publications

(24 citation statements)

References 29 publications

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“…The effective spin Hamiltonian and the time dependent evolution of the wave function from the Hamiltonian H OD have been rigorously studied when the system is cooled to low temperature to start from the phonon vacuum [13,30] immediately before the onset of the quantum simulation. The evolution of the entangled spin-phonon states are captured by the time evolution operator…”

Section: Effective Spin Hamiltonian With Axial Phonon Modesmentioning

confidence: 99%

Phonon-mediated quantum spin simulator employing a planar ionic crystal in a Penning trap

2013

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We derive the normal modes for a rotating Coulomb ion crystal in a Penning trap, quantize the motional degrees of freedom, and illustrate how they can by driven by a spin-dependent optical dipole force to create a quantum spin simulator on a triangular lattice with hundreds of spins. The analysis for the axial modes (oscillations perpendicular to the two-dimensional crystal plane) follow a standard normal-mode analysis, while the remaining planar modes are more complicated to analyze because they have velocity-dependent forces in the rotating frame. After quantizing the normal modes into phonons, we illustrate some of the different spin-spin interactions that can be generated by entangling the motional degrees of freedom with the spin degrees of freedom via a spindependent optical dipole force. In addition to the well-known power-law dependence of the spin-spin interactions when driving the axial modes blue of phonon band, we notice certain parameter regimes in which the level of frustration between the spins can be engineered by driving the axial or planar phonon modes at different energies. These systems may allow for the analog simulation of quantum spin glasses with large numbers of spins.

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Section: Effective Spin Hamiltonian With Axial Phonon Modesmentioning

confidence: 99%

Phonon-mediated quantum spin simulator employing a planar ionic crystal in a Penning trap

2013

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“…This indicates that the bang-bang shortcut might have an advantage in preparing specific low-energy excitations, because the other excitations are low in probability. Another advantage might be with regards to phonon creation, especially if the continuous change in time of the Hamiltonian with the locally adiabatic ramp actually creates more phonons {this is quantitatively determined by the magnitude of dtB z (t) [21]}. But that would have to be part of a different study on this topic.…”

Section: Fig 4 (Color Online)mentioning

confidence: 99%

Bang-bang shortcut to adiabaticity in trapped-ion quantum simulators

et al. 2018

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We model the bang-bang optimization protocol as a shortcut to adiabaticity in the ground-state preparation of an ion-trap-based quantum simulator. Compared to a locally adiabatic evolution, the bang-bang protocol produces a somewhat lower ground-state probability, but its implementation is so much simpler than the locally adiabatic approach, that it remains an excellent choice to use for maximizing ground-state preparation in systems that cannot be solved with conventional computers. We describe how one can optimize the shortcut and provide specific details for how it can be implemented with current ion-trap-based quantum simulators. Introduction. There has been much recent progress in ion-trap-based quantum simulation. Original experiments focused on adiabatic state preparation [1-3] of the transverse-field Ising model by initially orienting all of the spins along the field axis (in a large initial field) and then ramping the field to zero to create the ground state of the Ising model. But when the system size was increased, and frustrated antiferromagnetic systems were examined, it became clear that these experiments would have a large amount of diabatic excitation [4], which led to the study of excited states [4][5][6][7] and to a protocol that optimizes the field ramp with a locally adiabatic criterion [8]. In addition, other experimental situations were examined, such as Lieb-Robinson bounds [9, 10] and higher-spin cases [11]. Currently, there are two foci for adiabatic state preparation: (i) find shortcuts which will allow the original protocol to be achieved or (ii) use the diabatic excitations as a means to study low-energy excitations. Within the first category, recent work has found an exact shortcut for adiabatic state preparation [12,13] (at least for the nearest-neighbor transverse field Ising model), but the multiple-spin interactions needed to accomplish this goal are too complicated to implement in the current generation of quantum simulators. In the second category, we already mentioned experimental [4,5,7] and theoretical [6] methods to produce or measure specific excitations. It also is possible, in some cases, for the diabatic excitations to resemble an equilibrium thermal state, especially for ferromagnetic systems [14].

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“…At short times, when the excitation out of the ground state is small, the approach proposed here will not work because experimental uncertainty and noise will wash out the ability to measure small amplitude signals. In this regime, if one has enough information about the low-lying spectrum and matrix elements coupling states together, then one can use the adiabatic perturbation theory analysis of Wang and Freericks [14] to approximate the ground-state probability. Of course, those formulas only hold when the excitation is small.…”

Section: Transverse-field Ising Modelmentioning

confidence: 99%

Estimating the ground-state probability of a quantum simulation with product-state measurements

Yoshimura

Freericks

2015

Front. Phys.

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One of the goals in quantum simulation is to adiabatically generate the ground state of a complicated Hamiltonian by starting with the ground state of a simple Hamiltonian and slowly evolving the system to the complicated one. If the evolution is adiabatic and the initial and final ground states are connected due to having the same symmetry, then the simulation will be successful. But in most experiments, adiabatic simulation is not possible because it would take too long, and the system has some level of diabatic excitation. In this work, we quantify the extent of the diabatic excitation even if we do not know a priori what the complicated ground state is. Since many quantum simulator platforms, like trapped ions, can measure the probabilities to be in a product state, we describe techniques that can employ these simple measurements to estimate the probability of being in the ground state of the system after the diabatic evolution. These techniques do not require one to know any properties about the Hamiltonian itself, nor to calculate its eigenstate properties. All the information is derived by analyzing the product-state measurements as functions of time.

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Intrinsic phonon effects on analog quantum simulators with ultracold trapped ions

Cited by 27 publications

References 29 publications

Phonon-mediated quantum spin simulator employing a planar ionic crystal in a Penning trap

Phonon-mediated quantum spin simulator employing a planar ionic crystal in a Penning trap

Bang-bang shortcut to adiabaticity in trapped-ion quantum simulators

Estimating the ground-state probability of a quantum simulation with product-state measurements

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