Related papers: General entropic constraints on CSS codes within m…
Motivated by their necessity for most fault-tolerant quantum computation schemes, we formulate a resource theory for magic states. We first show that robustness of magic is a well-behaved magic monotone that operationally quantifies the…
The quantum relative entropy is known to play a key role in determining the asymptotic convertibility of quantum states in general resource-theoretic settings, often constituting the unique monotone that is relevant in the asymptotic…
Many proposals for fault-tolerant quantum computation require injection of 'magic states' to achieve a universal set of operations. Some qubit states are above a threshold fidelity, allowing them to be converted into magic states via 'magic…
We present numerical simulation results for the 7-to-1 and 15-to-1 state distillation circuits, constructed using transversal CNOTs acting on multiple surface code patches. The distillation circuits are decoded iteratively using the method…
Reliable quantum computation requires fault-tolerant protocols to prevent errors from propagating during syndrome extraction in quantum error correction. We present a novel fault-tolerant syndrome extraction technique for CSS codes, which…
High-fidelity logical \emph{T}-gate realization constitutes a core prerequisite for large-scale fault-tolerant quantum computing. However, conventional magic state distillation requires massive physical qubit overhead across successive…
Universal quantum computation requires the implementation of a logical non-Clifford gate. In this paper, we characterize all stabilizer codes whose code subspaces are preserved under physical $T$ and $T^{-1}$ gates. For example, this could…
Any physical quantum device for quantum information processing is subject to errors in implementation. In order to be reliable and efficient, quantum computers will need error correcting or error avoiding methods. Fault-tolerance achieved…
Universal fault-tolerant quantum computation requires overcoming the Eastin--Knill theorem on quantum error correction (QEC) codes that protect information from noise. This is often accomplished through strategies like magic state…
Magic state distillation is a resource intensive subroutine that consumes noisy input states to produce high-fidelity resource states that are used to perform logical operations in practical quantum-computing architectures. The resource…
The statistical mechanics of particles that populate indistinguishable energy sub-states is explored. In particular, the mathematical treatment of the microstates differs from conventional statistical mechanics where for a given degeneracy,…
Distributed quantum computing allows the modular construction of large-scale quantum computers and enables new protocols for blind quantum computation. However, such applications in the large-scale, fault-tolerant regime place stringent…
Recent results on the non-universality of fault-tolerant gate sets underline the critical role of resource states, such as magic states, to power scalable, universal quantum computation. Here we develop a resource theory, analogous to the…
Quantum error-correcting codes are a vital technology for demonstrating reliable quantum computation. They require data qubits for encoding quantum information and ancillary qubits for taking error syndromes necessary for error correction.…
Quantum secret sharing is a method for sharing a secret quantum state among a number of individuals such that certain authorized subsets of participants can recover the secret shared state by collaboration and other subsets cannot. In this…
Magic-state resource theory is a fundamental framework with far-reaching applications in quantum error correction and the classical simulation of quantum systems. Recent advances have significantly deepened our understanding of magic as a…
Fault-tolerant logical operations for qubits encoded by CSS codes are discussed, with emphasis on methods that apply to codes of high rate, encoding k qubits per block with k>1. It is shown that the logical qubits within a given block can…
As there is no quantum error correction code with universal set of transversal gates, several approaches have been proposed which, in combination of transversal gates, make universal fault-tolerant quantum computation possible. Magic state…
Given stabilizer operations and the ability to repeatedly prepare a single-qubit mixed state rho, can we do universal quantum computation? As motivation for this question, "magic state" distillation procedures can reduce the general…
A set of stabilizer operations augmented by some special initial states known as 'magic states', gives the possibility of universal fault-tolerant quantum computation. However, magic state preparation inevitably involves nonideal operations…