Codes, Circuits, and Networks for Modular Quantum Computation

Quantum error correction (QEC) is one of the key technologies needed for large-scale quantum computation, and while several known quantum algorithms demonstrate that quantum computers may be far superior to ordinary computers, QEC has not been fully demonstrated thus far. The proposed research program is broadly focused on QEC and concerns coherence protection, the key enabling technology for quantum computation and quantum cryptography.

Achieving scalability in quantum computation is a complex task, whose solution may require a modular approach with quantum devices of different nature used for storage, logic, and communication between the units. Quantum codes with the potential to utilize the benefits of such a heterogeneous hardware will be constructed and analyzed at the circuit level to optimize their fault-tolerant performance.

In more technical terms, the proposed research targets theory of quantum error-correcting codes operating in a fault-tolerant regime. It includes concurrent optimization of syndrome measurement circuits and networks representing architecture of single- and multi-node quantum computers, and analysis of phase transitions in related statistical-mechanical models.

New in this funding cycle is the focus on heterogeneous hardware, in particular, theory of mixed-base codes combining qubits, qudits, harmonic oscillators, and optical communication channels for entanglement exchange via teleportation. New codes and code families will be constructed; error propagation and associated correlations in Clifford measurement circuits will be analyzed and used to construct near-optimal decoding schemes; and the successful decoding probability will be analyzed in terms of associated statistical-mechanical models.

Construction of such models mapped to the actual architecture of a quantum computer, encoded as a network, will allow the optimization of the node size and the connectivity between the nodes required for scalability.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.