Unitary Design of Quantum Spin Networks for Robust Routing, Entanglement Generation, and Phase Sensing

Abstract

Spin chains can be used to describe a wide range of platforms for quantum computation and quantum information. They enable the understanding, demonstration, and modeling of numerous useful phenomena, such as high fidelity transfer of quantum states, creation and distribution of entanglement, and creation of resources for measurement-based quantum processing. In this paper, a more complex spin system, a 2D spin network (SN) engineered by applying suitable unitaries to two uncoupled spin chains, is studied. Considering only the single-excitation subspace of the SN, it is demonstrated that the system can be operated as a router, directing information through the SN. It is also shown that it can serve to generate maximally entangled states between two sites. Furthermore, it is illustrated that this SN system can be used as a sensor device able to determine an unknown phase applied to a system spin. A detailed modeling investigation of the effects of static disorder in the system shows that this system is robust against different types of disorder.

Scalable Quantum Spin Networks from Unitary Construction

“…Utilizing unitary transformations to couple SN components, [ 21 ] we have designed and modeled a range of scalable SN systems, capable of various quantum information processing tasks. We have realized and investigated in detail systems capable of routing and unknown phase sensing.…”

“…, where f (𝜌 red ) i = EOF i represents the EOF calculated from the reduced density operator 𝜌 red of the two relevant sites for a single randomly generated example of disorder. [21,32]…”

“…When considering the presence of random errors in the system, the average of many realizations of EOF is calculated as $$\overline{EOF}=\frac{1}{K}\sum _{i=1}^{K}f(\rho ^{red})_i$$, where $$f(\rho ^{red})_i=EOF_i$$ represents the EOF calculated from the reduced density operator $$\rho ^{red}$$ of the two relevant sites for a single randomly generated example of disorder. [ 21,32 ]…”

“…The effect of this type of error on the system is therefore investigated by adding a perturbation to the coupling interaction of the Hamiltonian $$\mathcal {H}_{XY}$$ in Equation (1) $$$$\begin{equation} J_{i,j}^{perturbed} = J_{i,j} + J_{i,j}^{^{\prime}} \; \end{equation}$$$$where $$J_{i,j}^{^{\prime}} = E d_{i,j}J_{max}$$. The perturbation units are set by $$J_{max}$$, the dimensionless parameter E sets the scale of the error, and $$d_{i,j}$$ represent random numbers, here from a Gaussian distribution with a standard deviation of $$w=\frac{1}{2\sqrt {3}}$$ and a zero mean, [ 21 ]…”

“…Here, we illustrate the possibility of generalizing the results to even more complex and larger SNs. The building blocks of the SN discussed here are uncoupled 3‐site PST chains, coupled together with a unitary transformation, [ 21 ] as shown in Figure for the case of $$M=5$$.…”