Transferring a quantum state over a network of coupled spins
With the advent of advanced quantum information processing, it is of increasing importance to transport quantum information over a physical medium (think of a wire, or a network of wires). We consider the case where the information is encoded in a spin degree of freedom (think of an electron whose "rotation axis" can point either up or down), and the medium is made up of spins that are all pinned in place.
It turns out that the repulsive forces between the spins can be used to delocalize the information over the whole network, and then localize it again at some other place. This was known for mediums that form a perfect line. I generalize this to more general configurations, finding that information can be sent over many networks that look like a bipartite graph.
My article is planned for publication in SciPost Physics (DOI: 10.21468/scipostphys.6.1.011)
Many-body strategies for multi-qubit gates
Quantum computers, just like their classical counterparts, may use a universal gate set consisting of local gates, in order to approximate any possible operation on it's qubits. Typically, one chooses a two-qubit gate such as the CNOT together with a set of single-qubit gates.
However, we asked ourselves the question: If N qubits are coupled by some interaction of our choice, can we construct interesting gates that act on all qubits at the same time?
For this to work, we look at the so-called Krawtchouk chain, which is special because all of it's eigenvalues are integer numbers. Because this system is well understood, we can apply condensed-matter many-body techniques, resulting in two surprising new contributions:
- The eigengate, which maps computational states into eigenstates of the coupling Hamiltonian.
- Resonant driving, which, together with knowledge of the simple spectrum, allows us to select precisely 2 our of 2^N (and no more!) to undergo a transition.
Our article was recently published in PRA (https://journals.aps.org/pra/abstract/10.1103/PhysRevA.97.042321). Find the version without paywall at ArXiv or my GDrive.