Related papers: Quantum-inspired Huffman Coding
Tree codes, introduced by Schulman, are combinatorial structures essential to coding for interactive communication. An infinite family of tree codes with both rate and distance bounded by positive constants is called asymptotically good.…
Kernel methods are powerful for machine learning, as they can represent data in feature spaces that similarities between samples may be faithfully captured. Recently, it is realized that machine learning enhanced by quantum computing is…
Quantum-inspired algorithms can deliver substantial speedups over classical state-of-the-art methods by executing quantum algorithms with tensor networks on conventional hardware. Unlike circuit models restricted to unitary gates, tensor…
Quantum algorithms offer significant speed-ups over their classical counterparts in various applications. In this paper, we develop quantum algorithms for the Kalman filter widely used in classical control engineering using the block…
Subword tokenization is the de facto standard for tokenization in neural language models and machine translation systems. Three advantages are frequently cited in favor of subwords: shorter encoding of frequent tokens, compositionality of…
High-rate concatenated quantum codes offer a promising pathway toward fault-tolerant quantum computation, yet designing efficient decoders that fully exploit their error-correction capability remains a significant challenge. In this work,…
It is known that the following five counting problems lead to the same integer sequence~$f_t(n)$: the number of nonequivalent compact Huffman codes of length~$n$ over an alphabet of $t$ letters, the number of `nonequivalent' canonical…
We describe a method for lossless quantum compression if the output of the information source is not known. We compute the best possible compression rate, minimizing the expected base length of the output quantum bit string (the base length…
We report an experimental demonstration of Schumacher's quantum noiseless coding theorem. Our experiment employs a sequence of single photons each of which represents three qubits. We initially prepare each photon in one of a set of 8…
We present an improved version of a quantum amplitude encoding scheme that encodes the $N$ entries of a unit classical vector $\vec{v}=(v_1,..,v_N)$ into the amplitudes of a quantum state. Our approach has a quadratic speed-up with respect…
Quantum cryptography is a rapidly-developing area which leverages quantum information to accomplish classically-impossible tasks. In many of these protocols, quantum states are used as long-term cryptographic keys. Typically, this is to…
For realizing a quantum memory we suggest to first encode quantum information via a quantum error correcting code and then concatenate combined decoding and re-encoding operations. This requires that the encoding and the decoding operation…
The causal structure of a stochastic process can be more efficiently transmitted via a quantum channel than a classical one, an advantage that increases with codeword length. While previously difficult to compute, we express the quantum…
We describe an algorithm computing an optimal prefix free code from $N$ unsorted positive integer weights in time linear in the number of machine words holding those weights. This algorithm takes advantage of common non-algebraic…
Coded source compression, also known as source compression with helpers, has been a major variant of distributed source compression, but has hitherto received little attention in the quantum regime. This work treats and solves the…
Data compression combined with effective encryption is a common requirement of data storage and transmission. Low cost of these operations is often a high priority in order to increase transmission speed and reduce power usage. This…
A text written using symbols from a given alphabet can be compressed using the Huffman code, which minimizes the length of the encoded text. It is necessary, however, to employ a text-specific codebook, i.e. the symbol-codeword dictionary,…
The quantum error correction theory is as a rule formulated in a rather convoluted way, in comparison to classical algebraic theory. This work revisits the error correction in a noisy quantum channel so as to make it intelligible to…
Quantum dense coding is a protocol for transmitting two classical bits of information from a sender (Alice) to a remote receiver (Bob) by sending only one quantum bit (qubit). In this article, we propose an experimentally feasible scheme to…
We introduce a protocol called ENCORE which simultaneously compresses and encrypts data in a one-pass process that can be implemented efficiently and possesses a number of desirable features as a streaming encoder/decoder. Motivated by the…