Related papers: Remarks on Bounds for Quantum Codes
Approximate controllability for a quantum system on a graph using as control parameters boundary conditions will be proven. This establishes a first theoretical proof of the feasibility of the quantum control at the boundary paradigm. A…
One central theme in quantum error-correction is to construct quantum codes that have a large minimum distance. In this paper, we first present a construction of classical codes based on certain class of polynomials. Through these classical…
We report two analytical bounds for quantum error-correcting codes that do not have preexisting classical counterparts. Firstly the quantum Hamming and Singleton bounds are combined into a single tighter bound, and then the combined bound…
We show that semiclassical formulas such as the Gutzwiller trace formula can be implemented on a quantum computer more efficiently than on a classical device. We give explicit quantum algorithms which yield quantum observables from…
We study two-dimensional classically integrable field theory with independent boundary condition on each end, and obtain three possible generating functions for integrals of motion when this model is an ultralocal one. Classically…
There is an advantage in simultaneously transmitting both classical and quantum information over a quantum channel compared to sending independent transmissions. The successful implementation of simultaneous transmissions of quantum and…
The importance of quantum error correction in paving the way to build a practical quantum computer is no longer in doubt. This dissertation makes a threefold contribution to the mathematical theory of quantum error-correcting codes.…
Neural networks are being used to improve the probing of the state spaces of many particle systems as approximations to wavefunctions and in order to avoid the recurring sign problem of quantum monte-carlo. One may ask whether the usual…
An important part of the information theory folklore had been about the output statistics of codes that achieve the capacity and how the empirical distributions compare to the output distributions induced by the optimal input in the channel…
Contrary to the classical case, the relation between quantum programming languages and quantum Turing Machines (QTM) has not being fully investigated. In particular, there are features of QTMs that have not been exploited, a notable example…
In the present contribution we discuss the role of experimental limitations in the classical limit problem. We studied some simple models and found that Quantum Mechanics does not re-produce classical mechanical predictions, unless we…
Quantum states are very delicate, so it is likely some sort of quantum error correction will be necessary to build reliable quantum computers. The theory of quantum error-correcting codes has some close ties to and some striking differences…
Quantum information theory is the study of the achievable limits of information processing within quantum mechanics. Many different types of information can be accommodated within quantum mechanics, including classical information, coherent…
The classical PCP theorem is arguably the most important achievement of classical complexity theory in the past quarter century. In recent years, researchers in quantum computational complexity have tried to identify approaches and develop…
Modern quantum engineering techniques enabled successful foundational tests of quantum mechanics. Yet, the universal validity of quantum postulates is an open question. Here we propose a new theoretical framework of Q-data tests, which…
In classical coding, a single quantum state is encoded into classical information. Decoding this classical information in order to regain the original quantum state is known to be impossible. However, one can attempt to construct a state…
The use of quantum computing for machine learning is among the most exciting prospective applications of quantum technologies. However, machine learning tasks where data is provided can be considerably different than commonly studied…
We study the difference between quantum and classical behavior in a pair of nonidentical cavities with second-harmonic generation. In the classical limit, each cavity has a limit-cycle solution, in which the photon number oscillates…
We introduce the concept of generalized concatenated quantum codes. This generalized concatenation method provides a systematical way for constructing good quantum codes, both stabilizer codes and nonadditive codes. Using this method, we…
Scientists have demonstrated that quantum computing has presented novel approaches to address computational challenges, each varying in complexity. Adapting problem-solving strategies is crucial to harness the full potential of quantum…