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

Yoshimura, Bryce; Freericks, J. K.

doi:10.3389/fphy.2015.00085

Front. Phys.

2015

DOI: 10.3389/fphy.2015.00085

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

Bryce Yoshimura

J. K. Freericks

Abstract: 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 diab… Show more

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Cited by 3 publications

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“…An experimental implementation requires determining the probability to be in the final ground state to carry out the optimization. This might be difficult to achieve if the system is so complex that one does not know a priori what the ground state is, but even then, techniques exist that allow for an estimation of the ground-state probability [20].…”

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

et al. 2018

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Shortcuts to adiabaticity: Concepts, methods, and applications

et al. 2019

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Shortcuts to adiabaticity (STA) are fast routes to the final results of slow, adiabatic changes of the controlling parameters of a system. The shortcuts are designed by a set of analytical and numerical methods suitable for different systems and conditions. A motivation to apply STA methods to quantum systems is to manipulate them on timescales shorter than decoherence times. Thus shortcuts to adiabaticity have become instrumental in preparing and driving internal and motional states in atomic, molecular, and solid-state physics. Applications range from information transfer and processing based on gates or analog paradigms, to interferometry and metrology. The multiplicity of STA paths for the controlling parameters may be used to enhance robustness versus noise and perturbations, or to optimize relevant variables. Since adiabaticity is a widespread phenomenon, STA methods also extended beyond the quantum world, to optical devices, classical mechanical systems, and statistical physics. Shortcuts to adiabaticity combine well with other concepts and techniques, in particular with optimal control theory, and pose fundamental scientific and engineering questions such as finding speed limits, quantifying the third law, or determining process energy costs and efficiencies. We review concepts, methods and applications of shortcuts to adiabaticity and outline promising prospects, as well as open questions and challenges ahead.

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Improving quantum annealing by engineering the coupling to the environment

S. Najafabadi,

Schumayer,

Lee

et al. 2023

EPJ Quantum Technol.

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A large class of optimisation problems can be mapped to the Ising model where all details are encoded in the coupling of spins. The task of the original mathematical optimisation is then equivalent to finding the ground state of the corresponding spin system which can be achieved via quantum annealing relying on the adiabatic theorem. Some of the inherent disadvantages of this procedure can be alleviated or resolved using a stochastic approach, and by coupling to the external environment. We show that careful engineering of the system-bath coupling at an individual spin level can further improve annealing.

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

Cited by 3 publications

References 15 publications

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

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

Shortcuts to adiabaticity: Concepts, methods, and applications

Improving quantum annealing by engineering the coupling to the environment

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