We show how to implement quantum computation on a system with an intrinsic Hamiltonian by controlling a limited subset of spins. Our primary result is an efficient control sequence on a nearest-neighbor XY spin chain through control of a single site and its interaction with its neighbor. Control of an array of sites yields sufficient parallelism for the implementation of fault-tolerant circuits. The framework exposes contradictions between the control theoretic concept of controllability with the ability of a system to perform quantum computation.
Quantum information processing protocols are efficiently implemented on spin-$\frac{1}{2}$ networks. A quantum communication protocol generally involves a certain number of parties having local access to a subset of a larger system, whose intrinsic dynamics are exploited in order to perform a specific task. In this chapter, we address such a scenario with the quantum dynamical map formalism, where the dynamics of the larger system is expressed as a quantum map acting on the parties' access to their respective subsets of spins. We reformulate widely investigated protocols, such as one-qubit qua…
A dissipative method that allows to access family of phantom Bethe-states (PBS) of boundary driven XXZ spin chains, is introduced. The method consists in coupling the ends of the open spin chain to suitable dissipative magnetic baths to force the edge spins to satisfy specific boundary conditions necessary for the PBS existence. Cumulative monotonous depopulation of the non-chiral components of the density matrix with growing dissipation amplitude is analogous to the depopulation of high-energy states in response to thermal cooling. Compared to generic states, PBS have strong chirality, nontri…
Quantum Computing (QC) has gained immense popularity as a potential solution to deal with the ever-increasing size of data and associated challenges leveraging the concept of quantum random access memory (QRAM). QC promises quadratic or exponential increases in computational time with quantum parallelism and thus offer a huge leap forward in the computation of Machine Learning algorithms. This paper analyzes speed up performance of QC when applied to machine learning algorithms, known as Quantum Machine Learning (QML). We applied QML methods such as Quantum Support Vector Machine (QSVM), and Q…
We study the temperature dependence of energy diffusion in two chaotic gapped quantum spin chains, a tilted-field Ising model and an XZ model, using an open system approach. We introduce an energy imbalance by coupling the chain to thermal baths at its boundary and study the non-equilibrium steady states of the resulting Lindblad dynamics using a matrix product operator ansatz for the density matrix. We define an effective local temperature profile by comparing local reduced density matrices in the steady state to those of a uniform thermal state. We then measure the energy current for a varie…
We study the spreading of quantum correlations and information in a one-dimensional quantum spin chain with critical disorder as encoded in an infinite randomness fixed point. Specifically, we focus on the dynamics after a quantum quench of the Rényi entropies, of the mutual information and of the entanglement negativity in the prototypical XXZ spin chain with random bonds and anisotropy parameters. We provide analytic predictions in the scaling regime based on real-space renormalization group methods. We support these findings through numerical simulations in the non-interacting limit, where …
Quantum gates built out of braid group elements form the building blocks of topological quantum computation. They have been extensively studied in $SU(2)_k$ quantum group theories, a rich source of examples of non-Abelian anyons such as the Ising ($k=2$), Fibonacci ($k=3$) and Jones-Kauffman ($k=4$) anyons. We show that the fusion spaces of these anyonic systems can be precisely mapped to the product state zero modes of certain Nicolai-like supersymmetric spin chains. As a result, we can realize the braid group on the product state zero modes of these supersymmetric systems. These operators ki…
