Related papers: Low-Overhead Entangling Gates from Generalised Deh…
A basic question in the theory of fault-tolerant quantum computation is to understand the fundamental resource costs for performing a universal logical set of gates on encoded qubits to arbitrary accuracy. Here we consider qubits encoded…
Hypergraph product codes are a class of quantum low density parity check (LDPC) codes discovered by Tillich and Z\'emor. These codes have a constant encoding rate and were recently shown to have a constant fault-tolerant error threshold.…
A defining feature of topologically ordered states of matter is the existence of locally indistinguishable states on spaces with non-trivial topology. These degenerate states form a representation of the mapping class group (MCG) of the…
One of the most promising routes towards fault-tolerant quantum computation utilizes topological quantum error correcting codes, such as the $\mathbb{Z}_2$ surface code. Logical qubits can be encoded in a variety of ways in the surface…
We systematically construct and classify fault-tolerant logical gates implemented by constant-depth circuits for quantum codes using cohomology operations and symmetry. These logical gates are obtained from unitary operators given by…
Quantum error-correcting codes are essential to the implementation of fault-tolerant quantum computation. Homological products of classical codes offer a versatile framework for constructing quantum error-correcting codes with desirable…
A great deal of work has been done developing quantum codes with varying overhead and connectivity constraints. However, given the such an abundance of codes, there is a surprising shortage of fault-tolerant logical gates supported therein.…
Transversal gates are the ideal gates in a fault-tolerant scenario; relatively easy to implement, and minimally error propagating. Their availability will maximise fault tolerant thresholds, enabling universal quantum computation in a wider…
Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation, we introduce phantom…
We present an entirely 2D transversal realization of phase gates at any level of the Clifford hierarchy, and beyond, using non-Abelian surface codes. Our construction encodes a logical qubit in the quantum double $D(G)$ of a non-Abelian…
It is an oft-cited fact that no quantum code can support a set of fault-tolerant logical gates that is both universal and transversal. This no-go theorem is generally responsible for the interest in alternative universality constructions…
The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new…
A fundamental problem in fault-tolerant quantum computation is the tradeoff between universality and dimensionality, exemplified by the the Bravyi-K\"onig bound for $n$-dimensional topological stabilizer codes. In this work, we extend…
We propose hardware-efficient schemes for implementing logical H and S gates transversally on rotated surface codes with reconfigurable neutral atom arrays. For logical H gates, we develop a simple strategy to rotate code patches…
Starting with an explicit framework for designing logical Clifford circuits for CSS codes, we construct logical gates for Hypergraph Product Codes. We first derive symplectic matrices for CNOT, CZ, Phase, and Hadamard operators, which…
This work provides the first explicit and non-random family of $[[N,K,D]]$ LDPC quantum codes which encode $K \in \Theta(N^\frac{4}{5})$ logical qubits with distance $D \in \Omega(N^\frac{3}{5})$. The family is constructed by amalgamating…
Transversal gates are the simplest form of fault-tolerant gates and are relatively easy to implement in practice. Yet designing codes that support useful transversal operations -- especially non-Clifford or addressable gates -- remains…
We take initial steps towards a general framework for constructing logical gates in general quantum CSS codes. Viewing CSS codes as cochain complexes, we observe that cohomology invariants naturally give rise to diagonal logical gates. We…
Quantum error correction is believed to be essential for scalable quantum computation, but its implementation is challenging due to its considerable space-time overhead. Motivated by recent experiments demonstrating efficient manipulation…
Qubits encoded in a decoherence-free subsystem and realized in exchange-coupled silicon quantum dots are promising candidates for fault-tolerant quantum computing. Benefits of this approach include excellent coherence, low control…