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arXiv:1511.04602 · Physical Review A

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

S. Balasubramanian, Shuyang Han, Bryce Yoshimura, James K. Freericks

Published Feb 12, 2018• 15 citations
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Abstract

We model the bang-bang optimization protocol as a shortcut to adiabaticity in the ground-state preparation of a trapped-ion quantum simulator. Compared to a locally adiabatic evolution, the bang-bang protocol typically produces a lower ground-state probability, but its implementation is so much simpler than the locally adiabatic approach, that it can become a competitive 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 trapped-ion quantum simulators. However, when frustration is strong enough, no method appears to work well for adiabatic state preparation within the experimental time frames, and one must confront the issue of dealing with diabatic excitations within the simulation.

DOI
10.1103/physreva.97.022313

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We model the bang-bang optimization protocol as a shortcut to adiabaticity in the ground-state preparation of a trapped-ion quantum simulator. Compared to a locally adiabatic evolution, the bang-bang protocol typically produces a lower ground-state probability, but its implementation is so much simpler than the locally adiabatic approach, that it can become a competitive 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 trapped-ion quantum simulators. However, when frustration is strong enough, no method appears to work well for adiabatic state preparation within the experimental time frames, and one must confront the issue of dealing with diabatic excitations within the simulation.
We introduce a bang-bang shortcut to adiabaticity for the Dicke model, which we implement via a two-dimensional array of trapped ions in a Penning trap with a spin-dependent force detuned close to the center-of-mass drumhead mode. Our focus is on employing this shortcut to create highly entangled states that can be used in high-precision metrology. We highlight that the performance of the bang-bang approach is comparable to standard preparation methods, but can be applied over a much shorter time frame. We compare these theoretical ideas with experimental data which serve as a first step towards realizing this theoretical procedure for generating multi-partite entanglement.
Abstract The fast and faithful preparation of the ground state of quantum systems is a challenging but crucial task for several applications in the realm of quantum-based technologies. Decoherence limits the maximum time-window allowed to an experiment to faithfully achieve such desired states. This is of particular significance in systems featuring a quantum phase transition, where the vanishing energy gap challenges an adiabatic ground state preparation. We show that a bang–bang protocol, consisting of a time evolution under two different values of an externally tunable parameter, allows for a high-fidelity ground state preparation in evolution times no longer than those required by the application of standard optimal control techniques, such as the chopped-random basis quantum optimization. In addition, owing to their reduced number of variables, such bang–bang protocols are very well suited to optimization tasks, reducing the high computational cost of other optimal control protocols. We benchmark the performance of such approach through two paradigmatic models, namely the Landau–Zener and the Lipkin–Meshkov–Glick model. Remarkably, we find that the critical ground state of the latter model, i.e. its ground state at the critical point, can be prepared with a high fidelity in a total evolution time that scales slower than the inverse of the vanishing energy gap.
One broad goal of quantum simulation is to start a simple quantum system in its ground state and slowly evolve the Hamiltonian to a complex one, maintaining the ground state throughout the evolution (called adiabatic state preparation). This provides a natural setting to create a highly entangled and correlated quantum state if the final Hamiltonian supports such a ground state. In ion-trap-based quantum simulations, coherence times are too short to allow for such ground-state evolution for large chains, because the rapid evolution of the system creates excitations to higher energy states. Because the probability for this excitation depends exponentially on the excitation energy and because the thermal distribution also depends exponentially on the excitation energy, we investigate whether this so-called diabatic excitation can create the analog of a thermal distribution; as this could serve as an alternative for creating thermal states of complex quantum systems without requiring contact with a heat bath. In this work, we explore this relationship and determine situations, where diabatic excitation can approximately create thermal states.
The application of adiabatic protocols in quantum technologies is severely limited by environmental sources of noise and decoherence. Shortcuts to adiabaticity by counterdiabatic driving constitute a powerful alternative that speed up time-evolution while mimicking adiabatic dynamics. Here we report the experimental implementation of counterdiabatic driving in a continuous variable system, a shortcut to the adiabatic transport of a trapped ion in phase space. The resulting dynamics is equivalent to a 'fast-motion video' of the adiabatic trajectory. The robustness of this protocol is shown to surpass that of competing schemes based on classical local controls and Fourier optimization methods. Our results demonstrate that shortcuts to adiabaticity provide a robust speedup of quantum protocols of wide applicability in quantum technologies.
A bang-bang (BB) algorithm prepares the ground state of a two-dimensional (2D) quantum many-body Hamiltonian H=H1+H2H={H}_{1}+{H}_{2}H=H1​+H2​ by evolving an initial product state alternating between H1{H}_{1}H1​ and H2{H}_{2}H2​. We use the neighborhood tensor update to simulate the BB evolution with an infinite pair-entangled projected state (iPEPS). The alternating sequence is optimized with the final energy as a cost function. The energy is calculated with a tangent space power method for the sake of its stability. The method is benchmarked in the 2D transverse field quantum Ising model near its quantum critical point against a ground state obtained with variational optimization of the iPEPS. The optimal BB sequence differs nonperturbatively from a sequence simulating quantum annealing or adiabatic preparation (AP) of the ground state. The optimal BB energy converges with the number of bangs much faster than the optimal AP energy.