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Quantum walks contribute significantly to developing quantum algorithms and quantum simulations. Here, we introduce a first of its kind one-dimensional quantum walk in the $d$-dimensional quantum domain, where $d>2$, and show its…
Encoding a qubit in the continuous degrees of freedom of an oscillator is a promising path to error-corrected quantum computation. One advantageous way to achieve this is through Gottesman-Kitaev-Preskill (GKP) grid states, whose symmetries…
The study of quantum walk processes has been widely divided into two standard variants, the discrete-time quantum walk (DTQW) and the continuous-time quantum walk (CTQW). The connection between the two variants has been established by…
Open Quantum Walks (OQW) are a type of quantum walk governed by the system's interaction with its environment. We explore the time evolution and the limit behavior of the OQW framework for Quantum Computation and show how we can represent…
Coherent evolution governs the behaviour of all quantum systems, but in nature it is often subjected to influence of a classical environment. For analysing quantum transport phenomena quantum walks emerge as suitable model systems. In…
We present the first robust implementation of a coined quantum walk over five steps using only passive optical elements. By employing a fiber network loop we keep the amount of required resources constant as the walker's position Hilbert…
We perform generalized measurements of a qubit by realizing the qubit as a coin in a photonic quantum walk and subjecting the walker to projective measurements. Our experimental technique can be used to realize photonically any rank-1…
We formalize the problem of dissipative quantum encoding, and explore the advantages of using Markovian evolution to prepare a quantum code in the desired logical space, with emphasis on discrete-time dynamics and the possibility of exact…
Quantum walk is a useful model to simulate complex quantum systems and to build quantum algorithms; in particular, to develop spatial search algorithms on graphs, which aim to find a marked vertex as quickly as possible. Quantum walks are…
A significant obstacle for practical quantum computation is the loss of physical qubits in quantum computers, a decoherence mechanism most notably in optical systems. Here we experimentally demonstrate, both in the quantum circuit model and…
We demonstrate a quadratic phase gate for one-way quantum computation in the continuous-variable regime. This canonical gate, together with phase-space displacements and Fourier rotations, completes the set of universal gates for realizing…
Quantum state transfer and teleportation, with qubits encoded in internal states of the atoms in cavities, among spatially separated nodes of a quantum network in decoherence-free subspace are proposed, based on a cavity-assisted…
Quantum computers provide a fundamentally new computing paradigm that promises to revolutionize our ability to solve broad classes of problems. Surprisingly, the basic mathematical structures of gate-based quantum computing, such as unitary…
Exploiting multi-dimensional quantum walks as feasible platforms for quantum computation and quantum simulation is attracting constantly growing attention from a broad experimental physics community. Here, we propose a two-dimensional…
The Gottesman-Kitaev-Preskill (GKP) code was proposed in 2001 by Daniel Gottesman, Alexei Kitaev, and John Preskill as a way to encode a qubit in an oscillator. The GKP codewords are coherent superpositions of periodically displaced…
In order to achieve fault-tolerant quantum computing, we make use of quantum error correction schemes designed to protect the logical information of the system from decoherence. A promising way to preserve such information is to use the…
Continuous-variable (CV) systems have shown remarkable potential for quantum computation, particularly excelling in scalability and error correction through bosonic encoding. Within this framework, the foundational notion of computational…
Binary quantum information can be fault tolerantly encoded in states defined in infinite dimensional Hilbert spaces. Such states define a computational basis, and permit a perfect equivalence between continuous and discrete universal…
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…
We study, by means of the stabilizer formalism, a quantum error correcting code which is alternative to the standard block codes since it embeds a qubit into a qudit. The code exploits the non-commutative geometry of discrete phase space to…