One-Dimensional Lazy Quantum Walk in Ternary System

Saha, Anil; Mandal, Sudhindu Bikash; Saha, Debasri; Chakrabarti, Amlan

doi:10.1109/tqe.2021.3074707

Cited by 11 publications

(5 citation statements)

References 40 publications

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“…Qudit technology is concerned with d-ary quantum systems, where d > 2 [28,29]. We graduate to qudits for providing a larger state space and simultaneous multiple control operations, which in the long run reduce the circuit complexity and uplift the efficiency of quantum algorithms [30][31][32]. For example, N qubits can be depicted as N log2d qudits, which straightway reduces a log 2 d-factor from the run-time of a quantum algorithm [33].…”

Section: Moving D-dimensional Quantum States Via Higher Dimensional Q...mentioning

confidence: 99%

Moving Quantum States without SWAP via Intermediate Higher Dimensional Qudits

Saha¹,

Saha²,

Chakrabarti³

2021

Preprint

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Quantum algorithms can be realized in the form of a quantum circuit. To map quantum circuit for specific quantum algorithm to quantum hardware, qubit mapping is an imperative technique based on the qubit topology. Due to the neighbourhood constraint of qubit topology, the implementation of quantum algorithm rightly, is essential for moving information around in a quantum computer. Swapping of qubits using SWAP gate moves the quantum state between two qubits and solves the neighbourhood constraint of qubit topology. Though, one needs to decompose the SWAP gate into three CNOT gates to implement SWAP gate efficiently, but unwillingly quantum cost with respect to gate count and depth increases. In this paper, a new formalism of moving quantum states without using SWAP operation is introduced for the first time to the best of our knowledge. Moving quantum states through qubits have been attained with the adoption of temporary intermediate qudit states. This introduction of intermediate qudit states has exhibited a three times reduction in quantum cost with respect to gate count and approximately two times reduction in respect to circuit depth compared to the state-of-the-art approach of SWAP gate insertion. Further, the proposed approach is generalized to any dimensional quantum system.

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Section: Moving D-dimensional Quantum States Via Higher Dimensional Q...mentioning

confidence: 99%

Moving Quantum States without SWAP via Intermediate Higher Dimensional Qudits

Saha¹,

Saha²,

Chakrabarti³

2021

Preprint

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“…Moreover, with the introduction of the mathematical notion of a qudit in [6], the boundaries of quantum computing are extended beyond the binary state space. Qudits are states in a d-dimensional Hilbert space where d > 2, thus allowing a much larger state space to store and process information as well as simultaneous control operations [7][8][9][10][11][12][13]. It has been shown that usage of qudits leads to circuit complexity reduction as well as enhanced efficiency of some quantum algorithms.…”

Section: Introductionmentioning

confidence: 99%

QuDiet: A classical simulation platform for qubit‐qudit hybrid quantum systems

Chatterjee

Das

Bala

et al. 2023

IET Quantum Communication

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In recent years, numerous research advancements have extended the limit of classical simulation of quantum algorithms. Although, most of the state‐of‐the‐art classical simulators are only limited to binary quantum systems, which restrict the classical simulation of higher‐dimensional quantum computing systems. Through recent developments in higher‐dimensional quantum computing systems, it is realised that implementing qudits improves the overall performance of a quantum algorithm by increasing memory space and reducing the asymptotic complexity of a quantum circuit. Hence, in this article, QuDiet, a state‐of‐the‐art user‐friendly python‐based higher‐dimensional quantum computing simulator is introduced. QuDiet offers multi‐valued logic operations by utilising generalised quantum gates with an abstraction so that any naive user can simulate qudit systems with ease as compared to the existing ones. Various benchmark quantum circuits is simulated in QuDiet and show the considerable speedup in simulation time as compared to the other simulators without loss in precision. Finally, QuDiet provides a full qubit‐qudit hybrid quantum simulator package with quantum circuit templates of well‐known quantum algorithms for fast prototyping and simulation. Comprehensive simulation up to 20 qutrits circuit on depth 80 on QuDiet was successfully achieved. The complete code and packages of QuDiet is available at https://github.com/LegacYFTw/QuDiet.

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“…The research on quantum walks (QWs) began in the early 2000s [1,2], and QWs play important roles in various fields, and a variety of QW models have been analyzed theoretically and numerically. This paper focuses on the mathematical analysis of discrete-time three-state QWs on the integer lattice, studied intensively by [3][4][5][6][7][8][9]. Three-state QWs have an interesting property called localization, where the probability of finding the particle around the initial position remains positive in the long-time limit.…”

Section: Introductionmentioning

confidence: 99%

Localization of space-inhomogeneous three-state quantum walks

Kiumi¹

2022

J. Phys. A: Math. Theor.

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Mathematical analysis on the existence of eigenvalues is essential because it is deeply related to localization, which is an exceptionally crucial property of quantum walks. We construct the method for the eigenvalue problem via the transfer matrix for space-inhomogeneous three-state quantum walks in one dimension with a self-loop, which is an extension of the technique in a previous study (Quantum Inf. Process 20(5), 2021). This method reveals the necessary and sufficient condition for the eigenvalue problem of a two-phase three-state quantum walk with one defect whose time evolution varies in the negative part, positive part, and at the origin.

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One-Dimensional Lazy Quantum Walk in Ternary System

Cited by 11 publications

References 40 publications

Moving Quantum States without SWAP via Intermediate Higher Dimensional Qudits

Moving Quantum States without SWAP via Intermediate Higher Dimensional Qudits

QuDiet: A classical simulation platform for qubit‐qudit hybrid quantum systems

Localization of space-inhomogeneous three-state quantum walks

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