As quantum machines have scaled up in their number of qubits, significant research has turned towards increasing their fidelity with quantum error correction codes. Although promising results have been shown with the surface code, which only requires near-neighbor connections between qubits, the high qubit overhead of such local codes promises to be problematic. Consequently, recent work has explored non-local quantum LDPC (qLDPC) codes, which have good asymptotic encoding rates. Despite theoretical progress, hardware implementations of these codes have been a longstanding challenge. At the experimental level, demonstrations of movement based communication on atom arrays suggest this is a powerful new primitive to achieve non-local connectivity. Leveraging this, we present a protocol for implementing non-local qLDPC codes in hardware. Our protocol, qSIEVE, is a co-design of such codes with movement in atom arrays. qSIEVE defines a restricted family of qLDPC codes that can be implemented efficiently with systolic movement. We then quantify the utility of qSIEVE in the context of a complete fault tolerant architecture. We compare the cost of implementing benchmark programs in a standard, surface code only architecture and a mixed architecture where data is stored in qLDPC memory with qSIEVE and loaded to surface codes for computation.

Quantum computing is in an era of limited resources. Current hardware lacks high fidelity gates, long coherence times, and the number of computational units required to perform meaningful computation. Contemporary quantum devices typically use a binary system, where each qubit exists in a superposition of the 0 and 1 states. However, it is often possible to access the 2 or even 3 states in the same physical unit by manipulating the system in different ways. In this work, we consider automatically encoding two qubits into one four-state ququart via a compression scheme. We use quantum optimal control to design efficient proof-of-concept gates that fully replicate standard qubit computation on these encoded qubits.

Superconducting quantum devices are a leading technology for quantum computation, but they face several challenges. Gate errors, coherence errors and a lack of connectivity all contribute to low fidelity results. In particular, connectivity restrictions enforce a gate set that requires three-qubit gates to be decomposed into one- or two-qubit gates. This substantially increases the number of two-qubit gates that need to be executed. However, many quantum devices have access to higher energy levels. We can expand the qubit abstraction of |0〉 and |1〉 to a ququart which has access to the |2〉 and |3〉 state, but with shorter coherence times. This allows for two qubits to be encoded in one ququart, enabling increased virtual connectivity between physical units from two adjacent qubits to four fully connected qubits. This connectivity scheme allows us to more efficiently execute three-qubit gates natively between two physical devices.