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arXiv:2212.12164 · Physical Review A

Multipartite high-dimensional quantum state engineering via discrete-time quantum walk

Junhong Nie, Meng Li, Xiaoming Sun

Published Mar 29, 2024• 4 citations
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Abstract

Quantum state engineering, namely, the generation and control of arbitrary quantum states, is drawing more and more attention due to its wide applications in quantum information and computation. However, there is no general method in theory, and the existing schemes also depend heavily on the selected experimental platform. In this article, we give two schemes for the generating task of arbitrary quantum state in $c$-partite $d$-dimensional system, both of which are based on a discrete-time quantum walk with a ${2}^{c}$-dimensional time- and position-dependent coin. The first procedure is a $d$-step quantum walk where all the $d$ coins are nonidentity, while the second procedure is an $O(d)$-step quantum walk where only $O(logd)$ coins are nonidentity. A concrete example of preparing generalized Bell states is given to demonstrate the first scheme we proposed. Furthermore, the first scheme can be applied to give an alternative approach to the quantum state preparation problem which is one of the fundamental tasks of quantum information processing. We design circuits for quantum state preparation with the help of our quantum state engineering scheme that match the best current result in both size and depth of the circuit asymptotically.

DOI
10.1103/physreva.109.032229

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Efficient generation of arbitrary superposed quantum states in high-dimensional systems is crucial for various quantum technologies but remains fundamentally challenging because of the intricate and extensive parameter control. In this work, we propose a generalized discrete one-dimensional quantum walk model with time- and position-dependent coin operations, and varied shift lengths. This approach enables deterministic and direct preparation of any qudit state | ϕ 〉 = ∑ k = 0 d − 1 a k | k 〉 using binary or ternary tree structures, without solving quadratic equations. Our method requires only O ( log d ) steps and O ( d ) coin operations, significantly reducing the resource requirements compared to the previous approach of O ( d ) steps and O ( d 2 ) coin operations. Additionally, we propose an experimental scheme based on successive interferometers, demonstrating that our method is compatible with current state-of-the-art experimental technologies. This efficient method for preparing quantum superposition states lays a foundation for advancing quantum technologies, with broad applications in quantum information processing.
Quantum state preparation in high-dimensional systems is an essential requirement for many quantum-technology applications. The engineering of an arbitrary quantum state is, however, typically strongly dependent on the experimental platform chosen for implementation, and a general framework is still missing. Here we show that coined quantum walks on a line, which represent a framework general enough to encompass a variety of different platforms, can be used for quantum state engineering of arbitrary superpositions of the walker's sites. We achieve this goal by identifying a set of conditions that fully characterize the reachable states in the space comprising walker and coin and providing a method to efficiently compute the corresponding set of coin parameters. We assess the feasibility of our proposal by identifying a linear optics experiment based on photonic orbital angular momentum technology.
High-dimensional quantum systems can offer extended possibilities and multiple advantages while developing advanced quantum technologies. In this paper, we propose a class of quantum-walk architecture networks that admit the efficient routing of high-dimensional quantum states. Perfect state transfer of an arbitrary unknown qudit state can be achieved between two arbitrary nodes via a one-dimensional lackadaisical discrete-time quantum walk. In addition, this method can be generalized to the high-dimensional lattices, where it allows distillable entanglement to be shared between arbitrary input and output ports. Implementation of our scheme is more feasible through exploiting the coin degrees of freedom and the settings of the coin flipping operators are simple. These results provide a direct application in a high-dimensional computational architecture to process much more information.
The capability to generate and manipulate quantum states in high-dimensional Hilbert spaces is a crucial step for the development of quantum technologies, from quantum communication to quantum computation. One-dimensional quantum walk dynamics represents a valid tool in the task of engineering arbitrary quantum states. Here we affirm such potential in a linear-optics platform that realizes discrete-time quantum walks in the orbital angular momentum degree of freedom of photons. Different classes of relevant qudit states in a six-dimensional space are prepared and measured, confirming the feasibility of the protocol. Our results represent a further investigation of quantum walk dynamics in photonics platforms, paving the way for the use of such a quantum state-engineering toolbox for a large range of applications.
We analyze the strengths and limitations of steered discrete-time quantum walks with position-independent coins in generating quantum states of bipartite quantum systems comprising of a qubit coupled to a qudit system. We demonstrate that not all quantum states in the composite space are accessible through such quantum walks, even under the most generalized definition of a quantum step, leading to a bifurcation of the composite Hilbert space into ``walk-accessible states'' and the ``walk-inaccessible states.'' We give an algorithm for generating any walk-accessible state from a simple-to-realize product state in a minimal number of walk steps, all of unit step size. We further give a prescription towards constructing minimal quantum walks between any pair of such walk-accessible states. Linear optics has been a popular physical system for implementing coin-based quantum walks, where the composite space is built up of spin and orbital angular momenta of light beams. We establish that in such an implementation, any generalized quantum step can be implemented up to a global phase using a single qqq-plate and a pair of homogeneous wave plates. We then give a quantum walk based scheme for realizing arbitrary vector beams consisting of a finite number of OAM components, using only qqq plates and wave plates.