Universal quantum computation and quantum error correction with ultracold atomic mixtures

Kasper, Valentin; González-Cuadra, Daniel; Hegde, Apoorva; Xia, Andy; Dauphin, Alexandre; Huber, Felix; Tiemann, E.; Lewenstein, Maciej; Jendrzejewski, Fred; Hauke, Philipp

doi:10.1088/2058-9565/ac2d39

Cited by 23 publications

(9 citation statements)

References 93 publications

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“…Defect-free optical tweezer arrays will provide high control over single atoms 38 , 39 and their repeated observation, as recently demonstrated for strontium atoms 60 . Such repeated measurements are necessary for the realization of quantum error correction schemes, where the logical qubits are implemented in the optical tweezers and the Bose–Einstein condensate mediates entanglement between them 61 .…”

Section: Discussionmentioning

confidence: 99%

Stochastic dynamics of a few sodium atoms in presence of a cold potassium cloud

Bhatt

Kilinc

Höcker

et al. 2022

Sci Rep

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Single particle resolution is a requirement for numerous experimental protocols that emulate the dynamics of small systems in a bath. Here, we accurately resolve through atom counting the stochastic dynamics of a few sodium atoms in presence of a cold potassium cloud. This capability enables us to rule out the effect of inter-species interaction on sodium atom number dynamics, at very low atomic densities present in these experiments. We study the noise sources for sodium and potassium in a common framework. Thereby, we assign the detection limits to 4.3 atoms for potassium and 0.2 atoms (corresponding to 96% fidelity) for sodium. This opens possibilities for future experiments with a few atoms immersed in a quantum degenerate gas.

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Section: Discussionmentioning

confidence: 99%

Stochastic dynamics of a few sodium atoms in presence of a cold potassium cloud

Bhatt

Kilinc

Höcker

et al. 2022

Sci Rep

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“…We first discuss the Hilbert space for qudits and operators acting on this Hilbert space, namely angular momentum operators and generalized Pauli operators. These two classes of operators can be implemented experimentally, for example, in atomic mixtures [33] or trapped-ion setups [29]. Next, we give a summary of the general structure of the QAOA [14].…”

Section: Qaoa For Qudit Systemsmentioning

confidence: 99%

“…(24). Specifically, quadratic cost functions can be experimentally realized in two distinct atomic platforms: cold atomic mixtures [33] and cold quantum gases in a cavity [34]. In both systems, the qudit is realized as a long collective spin by cooling atoms with internal degrees of freedom into the ground state of optical lattice sites.…”

Section: E Realization Of the Qudit-qaoa With Cold Atomsmentioning

confidence: 99%

“…In this article, we discuss the QAOA for qudit systems, and its possible realization in cold atomic systems with long range interactions, e.g., in cold atomic mixtures [33] or quantum gases inside an optical cavity [34]. Specifically, we elaborate the representations of cost functions and constraints of integer optimization problems with qudits.…”

Section: Introductionmentioning

confidence: 99%

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Quantum approximate optimization algorithm for qudit systems with long-range interactions

Deller¹,

Schmitt²,

Lewenstein³

et al. 2022

Preprint

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A frequent starting point of quantum computation platforms are two-state quantum systems, i.e., qubits. However, in the context of integer optimization problems, relevant to scheduling optimization and operations research, it is often more resource-efficient to employ quantum systems with more than two basis states, so-called qudits. Here, we discuss the quantum approximate optimization algorithm (QAOA) for qudits, layout its implementation in platforms with long-range interactions between qudits such as trapped ions, cold atomic mixtures, Rydberg atoms and atoms in cavities. We illustrate how the QAOA can be used to formulate a variety of integer optimization problems such as graph coloring problems or electric vehicle (EV) charging optimization. In addition, we comment on the implementation of constraints and describe three methods to include these into a quantum circuit of a QAOA by penalty contributions to the cost Hamiltonian, conditional gates using ancilla qubits, and a dynamical decoupling strategy. Finally, as a showcase of qudit-based QAOA, we present numerical results for a charging optimization problem mapped onto a maxk-graph coloring problem. Our work illustrates the flexibility of qudit systems to solve integer optimization problems.

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“…In the context of j = 1 spinor Bose-Einstein condensates (BEC), by restricting the spin states to effective two-dimensional subspaces, entanglement has also been probed via those SSI [5,15,20,21,28]. In parallel, the last decade has witnessed the development of several experiments investigating much-larger-j spinor gases [1, 3, 7, 8, 11, 12, 15, 16, 20-24, 28, 33, 36, 37], mixtures [2,17], or effective qudits ensembles [29]. In these systems, the populations of all Zeeman sublevels s = −j, −j + 1, .…”

Section: Introductionmentioning

confidence: 99%

Probing quantum entanglement from magnetic-sublevels populations: beyond spin squeezing inequalities

Müller-Rigat,

Lewenstein,

Frérot

2022

Preprint

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Spin squeezing inequalities (SSI) represent a major tool to probe quantum entanglement among a collection of few-level atoms, and are based on collective spin measurements and their fluctuations. Yet, for atomic ensembles of spin-j atoms and ultracold spinor gases, many experiments can image the populations in all Zeeman sublevels s = −j, −j + 1, . . . , j, potentially revealing finer features of quantum entanglement not captured by SSI. Here we present a systematic approach which exploits Zeeman-sublevel population measurements in order to construct novel entanglement criteria, and illustrate our approach on ground states of spin-1 and spin-2 Bose-Einstein condensates. Beyond these specific examples, our approach allows one to infer, in a systematic manner, the optimal permutationally-invariant entanglement witness for any given set of collective measurements in an ensemble of dlevel quantum systems.

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Universal quantum computation and quantum error correction with ultracold atomic mixtures

Cited by 23 publications

References 93 publications

Stochastic dynamics of a few sodium atoms in presence of a cold potassium cloud

Stochastic dynamics of a few sodium atoms in presence of a cold potassium cloud

Quantum approximate optimization algorithm for qudit systems with long-range interactions

Probing quantum entanglement from magnetic-sublevels populations: beyond spin squeezing inequalities

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