Mihir Pant

Abstract We introduce fusion based quantum computing (FBQC) - a model of universal quantum computation in which entangling measurements, called fusions, are performed on the qubits of small constant sized entangled resource states. We introduce a stabilizer formalism for analyzing fault tolerance and computation in these schemes. This framework naturally captures the error structure that arises in certain physical systems, such as linear optics. FBQC can offer significant architectural simplifications, enabling hardware made up of many identical modules, and reducing classical processing requirements. We present two pedagogical examples of fault-tolerant schemes constructed in this framework and numerically evaluate their threshold under a general error model with measurement erasure and error, and a linear-optical error model with fusion failure and photon loss. In these schemes, fusion failures, as well as errors, are directly dealt with by the quantum error correction protocol. We find that tailoring the fault-tolerance framework to the physical system allows the scheme to have a higher threshold than schemes reported in literature. We present a ballistic scheme which can tolerate a 10.3% probability of suffering photon loss in each fusion.

We develop a protocol that allows a pair of users to sift a secret key starting from shared variable-length Greenberger-Horne-Zeilinger (GHZ) states. It is an extension of the BBM’92 protocol which relies on measurements in the matching basis for entanglement witness. We then design an entanglement generation scheme over a quantum network that equips the quantum key generation protocol to achieve key rates that are independent of the distance between the two users. The key new insight in our protocol is to allow a repeater node to use n-qubit GHZ projective measurements that can fuse n successful entangled links, i.e., two-qubit entangled Bell pairs shared across network edges, incident at that node, into an n-qubit GHZ state shared by the far nodes of those edges. If we allow even 3-fusions at the nodes, we find by developing a connection to a modified version of the site-bond percolation problem that despite lossy (hence probabilistic) link-level entanglement generation, and probabilistic success of the fusion measurements at nodes, one can generate entanglement between end two parties at a rate that stays constant as the distance between them increases. This is not possible to attain with any (non-error-corrected) quantum networking protocol using Bell measurements alone.