The power of qutrits for non-adaptive measurement-based quantum computing

Mackeprang, Jelena; Bhatti, Daniel; Hoban, Matty J.; Barz, Stefanie

doi:10.1088/1367-2630/acdf77

Cited by 3 publications

(1 citation statement)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the future, we wish to generalize the above results to multi-settings and hope to obtain more robust Bell inequalities for n-partite d-dimensional systems. Moreover, Bell inequalities on multipartite, multi-settings, and high-dimensional systems have wide applications, such as the construction of Hardy-type paradox [41][42][43][44][45][46], quantum communication [47], quantum computing [48], and quantum network [49][50][51][52][53]. We hope that the iteration formula of generic Bell inequalities can promote the development of related fields.…”

Section: Discussionmentioning

confidence: 98%

The iteration formula of (n, 2, d) full-correlated multi-component Bell function and its applications

Meng,

Zhang,

Fan

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

No matter for a scientific or technological reason, constructing Bell inequalities for multipartite and high-dimensional systems is a significant task. The Mermin-Ardehali-Belinski˘ı-Klyshko (MABK) inequality is expressed in the form of iteration formula and correlation functions, and is the generalization of the Clauser-Horne-Shimony-Holt (CHSH) inequality to multi-partite cases. In the sense of detecting the nonlocality of the noisy maximally entangled states with the most white noises for the corresponding quantum system, the Collins-Gisin-Linden-Massar-Popescu (CGLMP) inequality, expressed in the joint probabilities form, is the high-dimensional analogue of the Clauser-Horne (CH) inequalities on joint probabilities. In the sense of detecting the nonlocality of the noisy Greenberger-Horne-Zeilinger(GHZ) states with the most white noises for the n-qudit system, it is a challenging task to construct the multi-partite analogue of the CGLMP inequality with iteration formula and correlation functions. In this paper, we generalize the multi-component correlationfunctions [Phys. Rev. A 71, 032107 (2005)] for bipartite d-dimensional systems to n-partite ddimensional ones, introduce the general full-correlated multi-component Bell function In;d, and construct the corresponding Bell inequality. By this way, we can reproduce both the CGLMP inequality and the Bell inequality in [Phys. Rev. A 71, 032107 (2005)] for the case n = 2, and the MABK inequality for the case d = 2. Inspired by the iteration formula form of the MABK inequality, we prove that for prime d the general Bell function In;d can be reformulated by iterating two Bell functions In−1;d. As applications, for prime d, confined to the unbiased symmetric (d × 2)-port beam splitters and the noisy n-qudit GHZ states, we recover the most robust Bell inequalities for small n and d, such as for the (3; 2; 3); (4; 2; 3); (5; 2; 3); and (3; 2; 5) Bell scenarios, with the iteration formula and the most robust Bell inequalities for the (2; 2; d) scenario. This implies that the iteration formula is an efficient way of constructing the multi-partite analogues of the CGLMP inequality with correlation functions. In addition, we also give some new Bell inequalities with the same robustness but inequivalent to the known ones.

show abstract

Section: Discussionmentioning

confidence: 98%

The iteration formula of (n, 2, d) full-correlated multi-component Bell function and its applications

Meng,

Zhang,

Fan

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

Non-adaptive measurement-based quantum computation on IBM Q

Mackeprang,

Bhatti,

Barz

2023

Sci Rep

Self Cite

View full text Add to dashboard Cite

We test the quantumness of IBM’s quantum computer IBM Quantum System One in Ehningen, Germany. We generate generalised n-qubit GHZ states and measure Bell inequalities to investigate the n-party entanglement of the GHZ states. The implemented Bell inequalities are derived from non-adaptive measurement-based quantum computation (NMQC), a type of quantum computing that links the successful computation of a non-linear function to the violation of a multipartite Bell-inequality. The goal is to compute a multivariate Boolean function that clearly differentiates non-local correlations from local hidden variables (LHVs). Since it has been shown that LHVs can only compute linear functions, whereas quantum correlations are capable of outputting every possible Boolean function it thus serves as an indicator of multipartite entanglement. Here, we compute various non-linear functions with NMQC on IBM’s quantum computer IBM Quantum System One and thereby demonstrate that the presented method can be used to characterize quantum devices. We find a violation for a maximum of seven qubits and compare our results to an existing implementation of NMQC using photons.

show abstract

Quantum advantage in temporally flat measurement-based quantum computation

Oliveira,

Barbosa,

Galvão

2024

Quantum

View full text Add to dashboard Cite

Several classes of quantum circuits have been shown to provide a quantum computational advantage under certain assumptions. The study of ever more restricted classes of quantum circuits capable of quantum advantage is motivated by possible simplifications in experimental demonstrations. In this paper we study the efficiency of measurement-based quantum computation with a completely flat temporal ordering of measurements. We propose new constructions for the deterministic computation of arbitrary Boolean functions, drawing on correlations present in multi-qubit Greenberger, Horne, and Zeilinger (GHZ) states. We characterize the necessary measurement complexity using the Clifford hierarchy, and also generally decrease the number of qubits needed with respect to previous constructions. In particular, we identify a family of Boolean functions for which deterministic evaluation using non-adaptive MBQC is possible, featuring quantum advantage in width and number of gates with respect to classical circuits.

show abstract

The power of qutrits for non-adaptive measurement-based quantum computing

Cited by 3 publications

References 47 publications

The iteration formula of (n, 2, d) full-correlated multi-component Bell function and its applications

The iteration formula of (n, 2, d) full-correlated multi-component Bell function and its applications

Non-adaptive measurement-based quantum computation on IBM Q

Quantum advantage in temporally flat measurement-based quantum computation

Contact Info

Product

Resources

About