Protocol of a quantum walk in circuit QED

Mandal

IEEE Trans. Quantum Eng.

et al. 2021

Quantum walks play an important role for developing quantum algorithms and quantum simulations. Here, we introduce a first of its kind one-dimensional lazy quantum walk in the ternary quantum domain and show its equivalence for circuit realization in ternary quantum logic. Using an appropriate logical mapping of the position space on which a walker evolves onto the multi-qutrit states, we present efficient quantum circuits for the implementation of lazy quantum walks in one-dimensional position space in ternary quantum system. We also address scalability in terms of n-qutrit ternary system with example circuits for a three qutrit state space.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

One-Dimensional Lazy Quantum Walk in Ternary System

Mandal

IEEE Trans. Quantum Eng.

et al. 2021

“…The evolution itself consists of the recurrent application of a coin and shift operator which in general leads to entanglement between the walker and coin. Quantum walks have already been realized in a variety of physical systems such as cold atoms [10,11], trapped ions [12,13], superconducting qubits [14,15], neutral atoms [16,17], nuclear magnetic resonance systems [18,19] and photonic architectures [20][21][22]. Hybrid entanglement generation has been observed as well [23,24].…”

Section: Introductionmentioning

confidence: 99%

Universal and optimal coin sequences for high entanglement generation in 1D discrete time quantum walks

Gratsea,

Metz,

Busch

2020

Preprint

Entanglement is a key resource in many quantum information applications and achieving high values independently of the initial conditions is an important task. Here we address the problem of generating highly entangled states in a discrete time quantum walk irrespective of the initial state using two different approaches. First, we present and analyze a deterministic sequence of coin operators which produces high values of entanglement in a universal manner for a class of localized initial states. In a second approach, we directly optimize the sequence of coin operators using a reinforcement learning algorithm. While the amount of entanglement produced by the deterministic sequence is fully independent of the initial states considered, the optimized sequences achieve in general higher average values of entanglement that do however depend on the initial state parameters. Our proposed sequence and optimization algorithm are especially useful in cases where the initial state is not fully known or entanglement has to be generated in a universal manner for a range of initial states.

“…But implementation of discrete-time quantum walk (DTQW) with superconducting qubits is difficult since on-chip superconducting qubits cannot hop between lattice sites. To overcome this problem, an efficient protocol has been proposed for the implementation of DTQW in circuit quantum electrodynamics (QED), in which only N + 1 qutrits and N assistant cavities are needed for an N -step DTQW [28]. As qutrits can be used to encode more information, more researchers are fascinated towards working with ternary quantum system in recent years.…”

Section: Introductionmentioning

confidence: 99%

One-Dimensional Lazy Quantum walk in Ternary System

Saha,

Mandal,

Saha

et al. 2020

Preprint

Quantum walks play an important role for developing quantum algorithms and quantum simulations.Here we present one dimensional three-state quantum walk(lazy quantum walk) and show its equivalence for circuit realization in ternary quantum logic for the first of its kind. Using an appropriate logical mapping of the position space on which a walker evolves onto the multi-qutrit states, we present efficient quantum circuits considering the nearest neighbour position space for the implementation of lazy quantum walks in one-dimensional position space in ternary quantum system. We also address scalability in terms of n-qutrit ternary system with example circuits for a three qutrit state space.