Decomposing the generalized Toffoli gate with qutrits

Nikolaeva, A. S.; Kiktenko, Evgeniy O.; Fedorov, Aleksey K.

doi:10.1103/physreva.105.032621

Cited by 29 publications

(17 citation statements)

References 54 publications

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“…Quantum computing [1] has the remarkable potential to dramatically surpass its classical counterpart on solving certain complex tasks in terms of the processing speed or resource overhead. Universal quantum gates are crucial building blocks in quantum computing, [2][3][4][5][6] quantum algorithms, [7][8][9] quantum simulations, [10] and quantum communication. [11] Photon is generally viewed as one of the promising candidates for flying and solid-state quantum computing owing to its outstanding low decoherence, high-speed transmission, natural information carrier, flexible single-qubit manipulations, and available atom-like qubit interconnector.…”

Section: Introductionmentioning

confidence: 99%

Linear Optical Universal Quantum Gates with Higher Success Probabilities

Liu

Wei

2023

Adv Quantum Tech

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Universal quantum gates lie at the heart of designing quantum computer. Here two compact quantum circuits for implementing post‐selected controlled‐phase‐flip (CPF) gate and Toffoli gate with linear optics are constructed assisted by one and two single photons, respectively. The current existing maximum success probability of 1/4 for linear optical CPF gate is achieved by resorting to an ancillary single photon rather than an entangled photon pair or two single photons. Remarkably, the presented Toffoli gate is accomplished with current maximum success probability of 1/30 and unity fidelity in principle, without using additional entangled photon pairs and the standard decomposition‐based approach. Linear optical implementations of the presented two universal gates are feasible and economical under current technology, and provide a potential application in large‐scale optical quantum computing.

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Section: Introductionmentioning

confidence: 99%

Linear Optical Universal Quantum Gates with Higher Success Probabilities

Liu

Wei

2023

Adv Quantum Tech

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“…In particular, three-dimensional quantum systems, qutrits, have been studied [11][12][13][14][15][16][17][18]. Various recent experiments have explored qutrits for quantum computing and quantum information utilising superconducting [12,[19][20][21][22] or photonic systems [23][24][25][26][27][28], and ion-trap quantum processors [29].…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2023

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Non-locality is not only one of the most prominent quantum features but can also serve as a resource for various information-theoretical tasks. Analysing it from an information-theoretical perspective has linked it to applications such as non-adaptive measurement-based quantum computing (NMQC). In this type of quantum computing the goal is to output a multivariate function. The success of such a computation can be related to the violation of a generalised Bell inequality. So far, the investigation of binary NMQC with qubits has shown that quantum correlations can compute all Boolean functions using at most $2^n-1$ qubits, whereas local hidden variables (LHVs) are restricted to linear functions. Here, we extend these results to NMQC with qutrits and prove that quantum correlations enable the computation of all three-valued logic functions using the generalised qutrit Greenberger-Horne-Zeilinger (GHZ) state as a resource and at most $3^n-1$ qutrits. This yields a corresponding generalised GHZ type paradox for any three-valued logic function that LHVs cannot compute. We give an example for an $n$-variate function that can be computed with only $n+1$ qutrits, which leads to convenient generalised qutrit Bell inequalities whose quantum bound is maximal. Finally, we prove that not all functions can be computed efficiently with qutrit NMQC by presenting a counterexample.

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“…Most work on qutrits and emulation has focussed on classical functions: those that come from a map of classical trits. For instance, using qutrits we can build logarithmic-depth Toffolis [27,41] and binary AND gates on superconducting qutrits [16]. This leaves open the question of whether there is any advantages to emulation by studying 'truly' quantum gates such as diagonal unitaries.…”

Section: Introductionmentioning

confidence: 99%

Phase gadget compilation for diagonal qutrit gates

Wetering¹,

Yeh²

2022

Preprint

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Phase gadgets have proved to be an indispensable tool for reasoning about ZX-diagrams, being used in optimisation and simulation of quantum circuits and the theory of measurement-based quantum computation. In this paper we study phase gadgets for qutrits. We present the flexsymmetric variant of the original qutrit ZX-calculus, which allows for rewriting that is closer in spirit to the original (qubit) ZX-calculus. In this calculus phase gadgets look as you would expect, but there are non-trivial differences in their properties. We devise new qutrit-specific tricks to extend the graphical Fourier theory of qubits, resulting in a translation between the 'additive' phase gadgets and a 'multiplicative' counterpart we dub phase multipliers. This enables us to build different types of qutrit multiplecontrolled phase gates.As an application of these results we find a construction for emulating arbitrary qubit diagonal unitaries, and specifically find an emulation for the qubit CCZ gate that only requires three singlequtrit non-Clifford gates to implement -provably lower than the four T gates needed using just qubit gates.

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Decomposing the generalized Toffoli gate with qutrits

Cited by 29 publications

References 54 publications

Linear Optical Universal Quantum Gates with Higher Success Probabilities

Linear Optical Universal Quantum Gates with Higher Success Probabilities

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

Phase gadget compilation for diagonal qutrit gates

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