Related papers: Block Permutation Routing on Ramanujan Hypergraphs…
We consider the routing of neutral atoms on a reconfigurable lattice in terms of hypergraph transformations. We prove the routing number of a Ramanujan $(d,r)$-regular hypergraph on $N$ vertices satisfies $\mathrm{rt}(H) = \Theta(\log N)$,…
Neutral atom arrays have emerged as a promising platform for both analog and digital quantum processing. Recently, devices capable of reconfiguring arrays during quantum processes have enabled new applications for these systems. Atom…
Quantum computer architectures impose restrictions on qubit interactions. We propose efficient circuit transformations that modify a given quantum circuit to fit an architecture, allowing for any initial and final mapping of circuit qubits…
We present methods for implementing arbitrary permutations of qubits under interaction constraints. Our protocols make use of previous methods for rapidly reversing the order of qubits along a path. Given nearest-neighbor interactions on a…
Quantum low-density parity-check codes are promising candidates towards scalable fault-tolerant quantum computation. Among these, bivariate bicycle (BB) codes offer superior encoding rates and large code distance compared to surface codes.…
Topological quantum error correction is a milestone in the scaling roadmap of quantum computers, which targets circuits with trillions of gates that would allow running quantum algorithms for real-world problems. The square-lattice surface…
We propose and analyze a hierarchical quantum error correction (QEC) scheme that concatenates hypergraph product (HGP) codes with rotated surface codes, which is compatible with quantum computers with only nearest-neighbor interactions. The…
In this paper we study a combinatorial reconfiguration problem that involves finding an optimal sequence of swaps to move an initial configuration of tokens that are placed on the vertices of a graph to a final desired one. This problem…
Routing is the task of permuting qubits in such a way that quantum operations can be parallelized maximally, given constraints on the hardware geometry. When simulating fermions in the Jordan-Wigner encoding with qubits, a one-dimensional…
Practical applications of quantum computing depend on fault-tolerant devices that employ error correction. A promising quantum error-correcting code for large-scale quantum computing is the surface code. For this code, Fault-Tolerant…
In this work we propose a high-quality decomposition approach for qubit routing by swap insertion. This optimization problem arises in the context of compiling quantum algorithms onto specific quantum hardware. Our approach decomposes the…
We consider the problem of computing routing schemes in the $\mathsf{HYBRID}$ model of distributed computing where nodes have access to two fundamentally different communication modes. In this problem nodes have to compute small labels and…
Quantum error correction is widely believed to be essential for large-scale quantum computation, but the required qubit overhead remains a central challenge. Quantum low-density parity-check codes can substantially reduce this overhead…
Quantum code surgery is a promising technique to perform fault-tolerant computation on quantum low-density parity-check codes. Recent developments have significantly reduced the space overhead of surgery. However, generic surgery operations…
Transactional data may be represented as a bipartite graph $G:=(L \cup R, E)$, where $L$ denotes agents, $R$ denotes objects visible to many agents, and an edge in $E$ denotes an interaction between an agent and an object. Unsupervised…
The Swap gate is a ubiquitous tool for moving information on quantum hardware, yet it can be considered a classical operation because it does not entangle product states. Genuinely quantum operations could outperform Swap for the task of…
We give a fault tolerant construction for error correction and computation using two punctured quantum Reed-Muller (PQRM) codes. In particular, we consider the $[[127,1,15]]$ self-dual doubly-even code that has transversal Clifford gates…
We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high…
In this paper, we design a family of $[n,k,d]$ block circulant codes that consist of many $[n_0 \ll n,k_0 \ll k,d_0]$ local codes and that satisfy three properties: (1) the code supports distributed erasure decoding, (2) $d$ can be scaled…
There has been a rise in decoding quantum error correction codes with neural network based decoders, due to the good decoding performance achieved and adaptability to any noise model. However, the main challenge is scalability to larger…