Creating analogs of thermal distributions from diabatic excitations in ion-trap-based quantum simulation

Lim, Myung-Soo; Yoshimura, Bryce; Freericks, J. K.

doi:10.1088/1367-2630/18/4/043026

Cited by 3 publications

(4 citation statements)

References 18 publications

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“…Another interesting question is the following: In cases where the pure state |ψ 0 represents a thermal distribution well, in the sense that the coefficients |C n | 2 are nearly proportional to the Boltzmann factor [22], then does the pure state retarded spin-spin Green's function represent the thermally averaged retarded Green's function well? One might expect this to be true, because the diagonal elements in the summation will closely resemble the trace employed in the calculation of the thermal Green's functions, and the off diagonal elements should become small as the system size becomes large due to cancellations from the complex phases.…”

Section: Discussionmentioning

confidence: 99%

Measuring nonequilibrium retarded spin-spin Green's functions in an ion-trap-based quantum simulator

Yoshimura

Freericks

2016

Phys. Rev. A

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Recent work proposed a variant on Ramsey interferometry for coupled spin-1/2 systems that directly measures the retarded spin-spin Green's function. We expand on that work by investigating nonequilibrium retarded spin-spin Green's functions within the transverse-field Ising model. We derive the lowest four spectral moments to understand the short-time behavior and we employ a Lehmann-like representation to determine the spectral behavior. We simulate a Ramsey protocol for a nonequilibrium quantum spin system that consists of a coherent superposition of the ground state and diabatically excited higher-energy states via a temporally ramped transverse magnetic field. We then apply the Ramsey spectroscopy protocol to the final Hamiltonian, which has a constant transverse field. The short-time behavior directly relates to Lieb-Robinson bounds for the transport of many-body correlations, while the long-time behavior relates to the excitation spectra of the Hamiltonian. Compressive sensing is employed in the data analysis to efficiently extract that spectra.arXiv:1512.05316v1 [quant-ph]

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Section: Discussionmentioning

confidence: 99%

Measuring nonequilibrium retarded spin-spin Green's functions in an ion-trap-based quantum simulator

Yoshimura

Freericks

2016

Phys. Rev. A

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“…But in general, our results also show that when a system has significant frustration, no technique can maintain a high probability in the ground state, and so it is more useful to consider working with the diabatic distribution of excited states that ensues. In some cases, these distributions can closely mimic thermal distributions [14], but this does not often occur for frustrated spin systems. We examined the distributions of excited states for some of the different systems studied here, and found that the locally adiabatic distribution was not too thermal, but did have a preponderance of the excitations towards the lower energy part of the spectrum.…”

Section: Fig 4 (Color Online)mentioning

confidence: 99%

“…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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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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“…5, we show the numerical evaluation of the G . Note that this wavefunction is not a thermal state, but it is a linear combination of the eigenstates with the amplitudes of each state chosen to have the same probability as in a thermal state [19]. Dots indicate measurements of the transverse-field Ising model Green's function at the particular times which correspond to the simulation of the XY model Green's function.…”

Section: E Green's Functionmentioning

confidence: 99%

Relationship between the transverse-field Ising model and the XY model via the rotating-wave approximation

Kiely

Freericks

2018

Phys. Rev. A

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In a large transverse field, there is an energy cost associated with flipping spins along the axis of the field. This penalty can be employed to relate the transverse-field Ising model in a large field to the XY model in no field (when measurements are performed at the right stroboscopic times). We describe the details for how this relationship works and, in particular, we also show under what circumstances it fails. We examine wavefunction overlap between the two models and observables, such as spin-spin Green's functions. In general, the mapping is quite robust at short times, but will ultimately fail if the run time becomes too long. There is also a trade-off between the length of time one can run a simulation out to and the time jitter of the stroboscopic measurements that must be balanced when planning to employ this mapping.

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Creating analogs of thermal distributions from diabatic excitations in ion-trap-based quantum simulation

Cited by 3 publications

References 18 publications

Measuring nonequilibrium retarded spin-spin Green's functions in an ion-trap-based quantum simulator

Measuring nonequilibrium retarded spin-spin Green's functions in an ion-trap-based quantum simulator

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

Relationship between the transverse-field Ising model and the XY model via the rotating-wave approximation

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