Related papers: Quantum Magic in Discrete-Time Quantum Walk
Nonstabilizerness or `magic' is a crucial resource for quantum computers which can be distilled from noisy quantum states. However, determining the magic of mixed quantum has been a notoriously difficult task. Here, we provide efficient…
We formulate continuous time quantum walks (CTQW) in a discrete quantum mechanical phase space. We define and calculate the Wigner function (WF) and its marginal distributions for CTQWs on circles of arbitrary length $N$. The WF of the CTQW…
Identifying the boundary between classical and quantum computation is a central challenge in quantum information. In multi-qubit systems, entanglement and magic are the key resources underlying genuinely quantum behaviour. While…
We present a mathematical formalism for the description of unrestricted quantum walks with entangled coins and one walker. The numerical behaviour of such walks is examined when using a Bell state as the initial coin state, two different…
A discrete-time Quantum Walk (QW) is essentially an operator driving the evolution of a single particle on the lattice, through local unitaries. Some QWs admit a continuum limit, leading to familiar PDEs (e.g. the Dirac equation). Recently…
Quantum magic, or non-stabilizerness, is an important quantum resource that characterizes computational power beyond classically simulable Clifford operations and is therefore essential for achieving quantum advantage. While previous…
Discrete quantum walks are dynamical protocols for controlling a single quantum particle. Despite of its simplicity, quantum walks display rich topological phenomena and provide one of the simplest systems to study and understand…
Quantum state discrimination plays a central role in defining the possible and impossible operations through a restricted class of quantum operations. A seminal result by Bennett et al. [Phys. Rev. A 59, 1070 (1999)] demonstrates the…
A new family of discrete-time quantum walks (DTQWs) on the line with an exact discrete $U(N)$ gauge invariance is introduced. It is shown that the continuous limit of these DTQWs, when it exists, coincides with the dynamics of a Dirac…
We show that a quantum state transfer, previously studied as a continuous time process in networks of interacting spins, can be achieved within the model of discrete time quantum walks with position dependent coin. We argue that due to…
Magic is a property of quantum states that enables universal fault-tolerant quantum computing using simple sets of gate operations. Understanding the mechanisms by which magic is created or destroyed is, therefore, a crucial step towards…
We extend the idea of a discrete-time quantum walk on a graph by placing a qubit on each vertex, and allowing the walker to interact with the qubit at its current position. We show that allowing for a controlled-Z interaction at each time…
We present a review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains, based on spatial- and time-multiplexing techniques, respectively. Additionally, we propose a detailed novel scheme…
To achieve universal quantum computation via general fault-tolerant schemes, stabilizer operations must be supplemented with other non-stabilizer quantum resources. Motivated by this necessity, we develop a resource theory for magic quantum…
We explore a discrete-time, coined quantum walk on a quantum network where the coherent superposition of walker-moves originates from the unitary interaction of the walker-coin with the qubit degrees of freedom in the quantum network. The…
Quantum walks are considered in a one-dimensional random medium characterized by static or dynamic disorder. Quantum interference for static disorder can lead to Anderson localization which completely hinders the quantum walk and it is…
Quantum and random walks have been shown to be equivalent in the following sense: a time-dependent random walk can be constructed such that its vertex distribution at all time instants is identical to the vertex distribution of any…
Notions of nonstabilizerness, or "magic", quantify how non-classical quantum states are in a precise sense: states exhibiting low nonstabilizerness preclude quantum advantage. We introduce 'pseudomagic' ensembles of quantum states that,…
Unraveling the secrets of how much nonstabilizerness a quantum dynamic can generate is crucial for harnessing the power of magic states, the essential resources for achieving quantum advantage and realizing fault-tolerant quantum…
A quantum walk on a toral phase space involving translations in position and its conjugate momentum is studied in the simple context of a coined walker in discrete time. The resultant walk, with a family of coins parametrized by an angle is…