Related papers: Low Overhead Universal Quantum Computation with Tr…
High-rate quantum LDPC (qLDPC) codes reduce memory overhead by densely packing many logical qubits into a single block of physical qubits. Here we extend this concept to high-rate computation by constructing \emph{batched} fault-tolerant…
Steane's 7-qubit quantum error-correcting code admits a set of fault-tolerant gates that generate the Clifford group, which in itself is not universal for quantum computation. The 15-qubit Reed-Muller code also does not admit a universal…
The preparation of a quantum state using a noisy quantum computer (gate noise strength $\delta$), will necessarily affect an O($\delta$)-fraction of the qubits, no matter which protocol is used. Here, we show that fault-tolerant quantum…
We show how to perform scalable fault-tolerant non-Clifford gates in two dimensions by introducing domain walls between the surface code and a non-Abelian topological code whose codespace is stabilized by Clifford operators. We formulate a…
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…
We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes, and topological color codes for error correction. Color codes have a set of transversal…
We show how to realize a general quantum circuit involving gates between arbitrary pairs of qubits by means of geometrically local quantum operations and efficient classical computation. We prove that circuit-level local stochastic noise…
Von Neumann's classic "multiplexing" method is unique in achieving high-threshold fault-tolerant classical computation (FTCC), but has several significant barriers to implementation: i) the extremely complex circuits required by randomized…
Transversality is a simple and effective method for implementing quantum computation fault-tolerantly. However, no quantum error-correcting code (QECC) can transversally implement a quantum universal gate set (Eastin and Knill, Phys. Rev.…
We construct a fault-tolerant quantum error-correcting protocol based on a qubit encoded in a large spin qudit using a spin-cat code, analogous to the continuous variable cat encoding. With this, we can correct the dominant error sources,…
The threshold theorem is a fundamental result in the theory of fault-tolerant quantum computation stating that arbitrarily long quantum computations can be performed with a polylogarithmic overhead provided the noise level is below a…
Color code is a promising topological code for fault-tolerant quantum computing. Insufficient research on the color code has delayed its practical application. In this work, we address several key issues to facilitate practical…
Quantum computation based on geometric phase is generally believed to be more robust against certain errors or noises than the conventional dynamical strategy. However, the gate error caused by the decoherence effect is inevitable, and thus…
Quantum squaring operation is a useful building block in implementing quantum algorithms such as linear regression, regularized least squares algorithm, order-finding algorithm, quantum search algorithm, Newton Raphson division, Euclidean…
Quantum Error Correction (QEC) is essential for future quantum computers due to its ability to exponentially suppress physical errors. The surface code is a leading error-correcting code candidate because of its local topological structure,…
Standard approaches to quantum error correction for fault-tolerant quantum computing are based on encoding a single logical qubit into many physical ones, resulting in asymptotically zero encoding rates and therefore huge resource…
Recent discoveries in asymptotically good quantum codes have intensified research on their application in quantum computation and fault-tolerant operations. This study focuses on the addressability problem within CSS codes: what circuits…
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…
Transversal encoded gatesets are highly desirable for fault tolerant quantum computing. However, a quantum error correcting code which exactly corrects for local erasure noise and supports a universal set of transversal gates is ruled out…
Recent experimental advances have made it possible to implement logical multi-qubit transversal gates on surface codes in a multitude of platforms. A transversal controlled-NOT (tCNOT) gate on two surface codes introduces correlated errors…