Related papers: Limits of the Kucera-Gacs coding method
The traditional method for computation in either the surface code or in the Raussendorf model is the creation of holes or "defects" within the encoded lattice of qubits that are manipulated via topological braiding to enact logic gates.…
We work out a theory of approximate quantum error correction that allows us to derive a general lower bound for the entanglement fidelity of a quantum code. The lower bound is given in terms of Kraus operators of the quantum noise. This…
This paper presents an achievability bound that evaluates the exact probability of error of an ensemble of random codes that are decoded by a minimum distance decoder. Compared to the state-of-the-art which demands exponential computation…
This paper studies the parameters for which Reed-Muller (RM) codes over $GF(2)$ can correct random erasures and random errors with high probability, and in particular when can they achieve capacity for these two classical channels.…
Quantum computers are poised to radically outperform their classical counterparts by manipulating coherent quantum systems. A realistic quantum computer will experience errors due to the environment and imperfect control. When these errors…
We introduce the new concept of computation coding. Similar to how rate-distortion theory is concerned with the lossy compression of data, computation coding deals with the lossy computation of functions. Particularizing to linear…
A real \alpha is called recursively enumerable ("r.e." for short) if there exists a computable, increasing sequence of rationals which converges to \alpha. It is known that the randomness of an r.e. real \alpha can be characterized in…
This work investigates linear precoding over non-singular linear channels with additive white Gaussian noise, with lattice-type inputs. The aim is to maximize the minimum distance of the received lattice points, where the precoder is…
We study universal compression of sequences generated by monotonic distributions. We show that for a monotonic distribution over an alphabet of size $k$, each probability parameter costs essentially $0.5 \log (n/k^3)$ bits, where $n$ is the…
We extract verified algorithms for exact real number computation from constructive proofs. To this end we use a coinductive representation of reals as streams of binary signed digits. The main objective of this paper is the formalisation of…
We investigate the strength of a randomness notion $\mathcal R$ as a set-existence principle in second-order arithmetic: for each $Z$ there is an $X$ that is $\mathcal R$-random relative to $Z$. We show that the equivalence between…
We consider the linear regression model with observation error in the design. In this setting, we allow the number of covariates to be much larger than the sample size. Several new estimation methods have been recently introduced for this…
Testing algorithms across a wide range of problem instances is crucial to ensure the validity of any claim about one algorithm's superiority over another. However, when it comes to inference algorithms for probabilistic logic programs,…
In this paper, we study the problem of lossless universal source coding for stationary memoryless sources on countably infinite alphabets. This task is generally not achievable without restricting the class of sources over which…
Experimental design is an approach for selecting samples among a given set so as to obtain the best estimator for a given criterion. In the context of linear regression, several optimal designs have been derived, each associated with a…
Existing gradient coding schemes introduce identical redundancy across the coordinates of gradients and hence cannot fully utilize the computation results from partial stragglers. This motivates the introduction of diverse redundancies…
The lower bound on the decoding error probability for the optimal code given a signal-to-noise ratio and a code rate are investigated in this letter for the reconfigurable intelligent surface (RIS) communication system over a Rician fading…
Solving linear systems of equations is a fundamental problem with a wide variety of applications across many fields of science, and there is increasing effort to develop quantum linear solver algorithms. [Suba\c{s}i et al., Phys. Rev. Lett.…
We analyze the list-decodability, and related notions, of random linear codes. This has been studied extensively before: there are many different parameter regimes and many different variants. Previous works have used complementary styles…
Selecting the best code solution from multiple generated ones is an essential task in code generation, which can be achieved by using some reliable validators (e.g., developer-written test cases) for assistance. Since reliable test cases…