Quantum processing with ensembles of rare-earth ions in a stoichiometric crystal

Ahlefeldt, Rose L.; Pearce, M. J.; Hush, Michael; Sellars, Matthew

doi:10.1103/physreva.101.012309

Cited by 34 publications

(22 citation statements)

References 59 publications

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“…EuCl 3 .6H 2 O is a stoichiometric crystal in which the Eu 3+ ion occupies a single site of C 2 symmetry. Several papers over many years have studied the electronic and Zeeman-hyperfine structure [63][64][65][66][67][68][69], and it has more recently been investigated for quantum information applications [70][71][72].…”

Section: Eucl36h2o C2 Centermentioning

confidence: 99%

Complete crystal field calculation of Zeeman-hyperfine splittings in europium

Smith,

Reid,

Sellars

et al. 2021

Preprint

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Computational crystal-field models have provided consistent models of both electronic and Zeeman-hyperfine structure for several rare earth ions. These techniques have not yet been applied to the Zeeman-hyperfine structure of Eu 3+ because modeling the structure of the J = 0 singlet levels in Eu 3+ requires inclusion of the commonly omitted lattice electric quadrupole and nuclear Zeeman interactions. Here, we include these terms in a computational model to fit the crystal field levels and the Zeeman-hyperfine structure of the 7 F0 and 5 D0 states in three Eu 3+ sites: the C4v and C3v sites in CaF2 and the C2 site in EuCl3.6H2O. Close fits are obtained for all three sites which are used to resolve ambiguities in previously published parameters, including quantifying the anomalously large crystal-field-induced state mixing in the C3v site and determining the signs of Zeeman-hyperfine parameters in all three sites. We show that this model allows accurate prediction of properties for Eu 3+ important for quantum information applications of these ions, such as relative transition strengths. The model could be used to improve crystal field calculations for other non-Kramers singlet states. We also present a spin Hamiltonian formalism without the normal assumption of no J mixing, suitable for other rare earth ion energy levels where this effect is important.

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Section: Eucl36h2o C2 Centermentioning

confidence: 99%

Complete crystal field calculation of Zeeman-hyperfine splittings in europium

Smith,

Reid,

Sellars

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…The rareearth platform is versatile and has shown promise in fields related to quantum computing, such as quantum memories [7][8][9][10][11][12][13][14][15][16][17][18], conversion between optical and microwave signals [19][20][21], and single photon sources [22]. Much work has also been devoted to quantum computing [23][24][25][26][27][28][29][30][31][32][33], which is the topic that here is investigated through simulations. Since the topic is rather complex, we start by providing a general overview of the system.…”

Section: Introductionmentioning

confidence: 99%

“…However, due to the difficulty of detecting single ions, most results so far have been limited to use the ensemble approach where the qubit consists of many rare-earthions, and where the resulting inhomogeneities complicate * adam.kinos@fysik.lth.se the gates and limit the fidelities [38,39,[41][42][43][44][45][46]. Furthermore, this ensemble approach has been shown to scale poorly [28], but might still be useful, e.g., when using stoichiometric materials where small quantum processors have been envisioned [31]. Fortunately, recent progress in single-ion detection [47][48][49][50][51][52] paves the way for singleion rare-earth quantum computing.…”

Section: Introductionmentioning

confidence: 99%

Designing gate operations for single ion quantum computing in rare-earth-ion-doped crystals

Kinos,

Rippe,

Kröll

et al. 2021

Preprint

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Quantum computers based on rare-earth-ion-doped crystals show promising properties in terms of scalability and connectivity if single ions can be used as qubits. Through simulations, we investigate gate operations on such qubits and discuss how gate and system parameters affect gate errors, the required frequency bandwidth per qubit, and the risk of instantaneous spectral diffusion (ISD) occurring. Furthermore, we examine how uncertainties in the system parameters affect the gate errors, and how precisely the system needs to be known. We find gate errors for arbitrary singlequbit gates of 2.1 • 10 −4 when ISD is not considered and 3.4 • 10 −4 when we take heed to minimize it. Additionally, we construct two-qubit gates with errors ranging from 5 • 10 −4 → 3 • 10 −3 over a broad range of dipole-dipole interaction strengths.

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“…Rare-earth-ion-doped crystals are versatile materials that have been used in, e.g., quantum memories [1][2][3][4][5][6][7][8][9][10][11][12], conversion between optical and microwave signals [13][14][15], and quantum computing [16][17][18][19][20][21][22][23][24][25][26][27]. This has in large part been thanks to their long life- [28] and coherence times [29][30][31], and their capacity to store large amounts of information.…”

Section: Introductionmentioning

confidence: 99%

Microscopic treatment of instantaneous spectral diffusion and its effect on quantum gate fidelities in rare-earth-ion-doped crystals

Kinos,

Rippe,

Walther

et al. 2021

Preprint

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The effect of instantaneous spectral diffusion (ISD) on gate operations in rare-earth-ion-doped crystals is an important question to answer for the future of rare-earth quantum computing. ISD has previously been extensively studied for ensemble systems, where it is observed as a dephasing that depends on the degree of excitation. However, for applications that use single ions, a microscopic modeling that highlights the stochastic nature of the ISD phenomena is necessary. Here we present such a model and use it to investigate ISD errors on single-qubit gate operations. However, directly simulating how the qubit is affected by all non-qubit ions is intractable since the size of the system grows exponentially with the number of ions. To circumvent this problem, we present a method to estimate the error of the full system by examining smaller subsystems, each evaluating the rotation and shrinkage of the qubit Bloch vector due to only one error source. In the case of ISD, the different error sources are individual ions causing ISD, but the method is general and thus applicable to other systems as long as the errors are largely independent. After studying ISD due to the ions surrounding a qubit, we conclude that transmission windows (prepared by optical pumping) are necessary to suppress the ISD errors. Despite using such windows, there remains a roughly 0.3% risk that a qubit has an ISD error larger than the error from other sources. However, in those cases the qubit can be discarded and its frequency channel can be reused by another qubit. In most cases the ISD errors are significantly smaller than other errors, thus opening up the possibility to perform noisy intermediate-scale quantum (NISQ) algorithms despite ISD being present. Finally, the approach presented here creates a foundation that can be used to study how ISD affects even more complicated gate operations.

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Quantum processing with ensembles of rare-earth ions in a stoichiometric crystal

Cited by 34 publications

References 59 publications

Complete crystal field calculation of Zeeman-hyperfine splittings in europium

Complete crystal field calculation of Zeeman-hyperfine splittings in europium

Designing gate operations for single ion quantum computing in rare-earth-ion-doped crystals

Microscopic treatment of instantaneous spectral diffusion and its effect on quantum gate fidelities in rare-earth-ion-doped crystals

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