Efficient realization of quantum algorithms with qudits

Nikolaeva, Alexandra; Kiktenko, E. O.; Fedorov, Aleksey K.

doi:10.48550/arxiv.2111.04384

Cited by 9 publications

(11 citation statements)

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“…As it has been shown in Ref. [89], the qudit-based realization provides an advantage both in the circuit width and depth. We would like also note that the use of qudits besides quantum computing, offers certain perspectives in quantum teleportation [64] and quantum communications [110,111], as well as opens up opportunities for uncovering fundamental concepts of quantum mechanics [57,61,112].…”

Section: Discussionmentioning

confidence: 78%

“…An interesting feature of certain physical quantum platforms is their multilevel structure, which can be efficiently used for scaling quantum processors with the use of qudits -d-level quantum systems . There are several approaches: (i) encoding several qubits in a single qudit and (ii) the use of additional qudit levels to substitute ancilla qubits in multiqubit gate decompositions [82] (for example, for the Toffoli gate [53,55,68,69,[83][84][85][86][87][88]), which can be efficiently combined [89]. Both approaches allow increasing of QV since a d-state qudit can be treated as log 2 d qubits; also certain two-qubit operations can be replaced by single-qudit ones.…”

Section: Introductionmentioning

confidence: 99%

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Realizing quantum gates with optically-addressable $^{171}$Yb$^{+}$ ion qudits

Aksenov¹,

V.²,

Semerikov³

et al. 2022

Preprint

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The use of multilevel information carriers, also known as qudits, is a promising path for exploring scalability of quantum computing devices. In this work, we present a proof-of-principle realization of a quantum processor that uses optically-addressed 171 Yb + ion qudits in a linear trap. The rich level structure of 171 Yb + ions makes it possible to use the Zeeman sublevels of the quadrupole clock transition at 435.5 nm for efficient and robust qudit encoding. We demonstrate the realization of the universal set of gates consisting of single-qudit rotations and two-qudit entangling operation with a two-ququart system, which is formally equivalent to a universal gate-based four-qubit processor. Our results paves a way towards further studies of more efficient implementations of quantum algorithms with trapped-ion-based processors.

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Section: Discussionmentioning

confidence: 78%

Section: Introductionmentioning

confidence: 99%

Realizing quantum gates with optically-addressable $^{171}$Yb$^{+}$ ion qudits

Aksenov¹,

V.²,

Semerikov³

et al. 2022

Preprint

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show abstract

“…We note that multiqubit gate decomposition can be further improved using qudits, which are multilevel quantum systems. As it has been shown, the upper levels of qudits can be used instead of ancilla qubits in the decomposition [40][41][42][43][44].…”

Section: Toffoli and Controlled Rotation Gatesmentioning

confidence: 99%

Multiclass classification using quantum convolutional neural networks with hybrid quantum-classical learning

Bokhan¹,

Mastiukova²,

Boev³

et al. 2022

Preprint

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Multiclass classification is of great interest for various machine learning applications, for example, it is a common task in computer vision, where one needs to categorize an image into three or more classes. Here we propose a quantum machine learning approach based on quantum convolutional neural networks for solving this problem. The corresponding learning procedure is implemented via TensorFlowQuantum as a hybrid quantum-classical (variational) model, where quantum output results are fed to softmax cost function with subsequent minimization of it via optimization of parameters of quantum circuit. Our conceptional improvements include a new model for quantum perceptron and optimized structure of the quantum circuit. We use the proposed approach to demonstrate the 4-class classification for the case of the MNIST dataset using eight qubits for data encoding and four acnilla qubits. Our results demonstrate comparable accuracy of our solution with classical convolutional neural networks with comparable numbers of trainable parameters. We expect that our finding provide a new step towards the use of quantum machine learning for solving practically relevant problems in the NISQ era and beyond.

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“…This approach has been widely studied both theoretically and experimentally . Despite its simplicity and efficiency, there is a number of limitations associated with finding optimal qudit-to-qubit mappings [41]. The second approach is to employ higher qudit levels can be used for substituting ancilla qubits, which is of specific interest in the problem of decomposing multi-qubit gates [40], such as the Toffoli gate [19,26,27,29,[42][43][44][45][46].…”

mentioning

confidence: 99%

“…We have developed the scheme for the generalized N -qubit Toffoli gate, which is efficient in terms of the required number of 2N − 3 two-qutrit gates, types of qudits (qutrits only), and coupling between information carriers. The developed approach can combined with other techniques allowing one to reduce the complexity of the implementation of quantum algorithms by using qudits [41]. We have used native gates of the superconducting quantum processors for our scheme, which makes it directly applicable for such category of NISQ devices.…”

mentioning

confidence: 99%

Decomposing the generalized Toffoli gate with qutrits

Nikolaeva,

Kiktenko,

Fedorov

2021

Preprint

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Efficient realization of quantum algorithms with qudits

Cited by 9 publications

References 0 publications

Realizing quantum gates with optically-addressable $^{171}$Yb$^{+}$ ion qudits

Realizing quantum gates with optically-addressable $^{171}$Yb$^{+}$ ion qudits

Multiclass classification using quantum convolutional neural networks with hybrid quantum-classical learning

Decomposing the generalized Toffoli gate with qutrits

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