Related papers: Hyperdense Coding Modulo 6 with Filter-Machines
Efficient encoding of classical data into quantum state -- currently referred to as quantum encoding -- holds crucial significance in quantum computation. For finite-size databases and qubit registers, a common strategy of the quantum…
The autoencoder is one of machine learning algorithms used for feature extraction by dimension reduction of input data, denoising of images, and prior learning of neural networks. At the same time, autoencoders using quantum computers are…
Quantum signal processing and quantum singular value transformation are powerful tools to implement polynomial transformations of block-encoded matrices on quantum computers, and has achieved asymptotically optimal complexity in many…
We study coded distributed matrix multiplication from an approximate recovery viewpoint. We consider a system of $P$ computation nodes where each node stores $1/m$ of each multiplicand via linear encoding. Our main result shows that the…
Running quantum algorithms often involves implementing complex quantum circuits with such a large number of multi-qubit gates that the challenge of tackling practical applications appears daunting. To date, no experiments have successfully…
We give new quantum algorithms for evaluating composed functions whose inputs may be shared between bottom-level gates. Let $f$ be an $m$-bit Boolean function and consider an $n$-bit function $F$ obtained by applying $f$ to conjunctions of…
Let {\alpha} be the maximal value such that the product of an n x n^{\alpha} matrix by an n^{\alpha} x n matrix can be computed with n^{2+o(1)} arithmetic operations. In this paper we show that \alpha>0.30298, which improves the previous…
This paper introduces quantum circuit methodologies for pointwise multiplication and convolution of complex functions, conceptualized as "processing through encoding". Leveraging known techniques, we describe an approach where multiple…
This paper introduces the $w$-product, a novel wavelet-based tensor multiplication scheme leveraging second-generation wavelet transforms to achieve linear transformation complexity while preserving essential algebraic properties. The…
Universally decodable matrices can be used for coding purposes when transmitting over slow fading channels. These matrices are parameterized by positive integers $L$ and $n$ and a prime power $q$. Based on Pascal's triangle we give an…
Topological quantum computation may provide a robust approach for encoding and manipulating information utilizing the topological properties of anyonic quasi-particle excitations. We develop an efficient means to map between dense and…
Unitary decomposition is a widely used method to map quantum algorithms to an arbitrary set of quantum gates. Efficient implementation of this decomposition allows for translation of bigger unitary gates into elementary quantum operations,…
High-dimensional quantum units of information, or qudits, can carry more than one quantum bit of information in a single degree of freedom, and can therefore be used to boost the performance of quantum communication and quantum computation…
Quantum computing is emerging as a new computing resource that could be superior to conventional computing for certain classes of optimization problems. However, in principle, most existing approaches to quantum optimization are intended to…
We consider the problem of multiplying sparse matrices (over a semiring) where the number of non-zero entries is larger than main memory. In the classical paper of Hong and Kung (STOC '81) it was shown that to compute a product of dense $U…
We present one-shot compression protocols that optimally encode ensembles of $N$ identically prepared mixed states into $O(\log N)$ qubits. In contrast to the case of pure-state ensembles, we find that the number of encoding qubits drops…
Many quantum information tasks rely on entanglement, which is used as a resource, for example, to enable efficient and secure communication. Typically, noise, accompanied by loss of entanglement, reduces the efficiency of quantum protocols.…
A channel with continuous phase modulation and 1-bit ADC with oversampling is considered. Due to oversampling, higher-order modulations yield a higher achievable rate and this work presents a method to approach this with sophisticated…
A quantum compiler is a software program for decomposing ("compiling") an arbitrary unitary matrix into a sequence of elementary operations (SEO). The author of this paper is also the author of a quantum compiler called Qubiter. Qubiter…
We derive one-shot upper bounds for quantum noisy channel codes. We do so by regarding a channel code as a bipartite operation with an encoder belonging to the sender and a decoder belonging to the receiver, and imposing constraints on the…