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An important topic in quantum information is the theory of error correction codes. Practical situations often involve quantum systems with states in an infinite dimensional Hilbert space, for example coherent states. Motivated by these…

Specific quantum algorithms exist to-in theory-break elliptic curve cryptographic protocols. Implementing these algorithms requires designing quantum circuits that perform elliptic curve arithmetic. To accurately judge a cryptographic…

The matrix functions can be defined by Cauchy's integral formula and can be approximated by the linear combination of inverses of shifted matrices using a quadrature formula. In this paper, we show a concrete construction of a framework to…

We review a recent theoretical proposal for a universal quantum computing platform based on tunable nonlinear electromechanical nano-oscillators, in which qubits are encoded in the anharmonic vibrational modes of mechanical resonators…

Current proposals for quantum compilers require the synthesis and optimization of linear reversible circuits and among them CNOT circuits. Since these circuits represent a significant part of the cost of running an entire quantum circuit,…

Over a decade ago, it was demonstrated that quantum computing has the potential to revolutionize numerical linear algebra by enabling algorithms with complexity superior to what is classically achievable, e.g., the seminal HHL algorithm for…

Error operator bases for systems of any dimension are defined and natural generalizations of the bit/sign flip error basis for qubits are given. These bases allow generalizing the construction of quantum codes based on eigenspaces of…

Codeword stabilized quantum codes provide a unified approach to constructing quantum error-correcting codes, including both additive and non-additive quantum codes. Standard codeword stabilized quantum codes encode quantum information into…

We formulate a semi-classical circuit model to clarify the role of quantum entanglement in the recently discovered encoding phase transitions in quantum circuits with measurements. As a starting point we define a random circuit model with…

We present a description of encoding/decoding for a concatenated quantum code that enables both protection against quantum computational errors and the occurrence of one quantum erasure. For this, it is presented how encoding and decoding…

We study error correction type protocols in which a quantum channel encodes logical information into an enlarged Hilbert space. Specifically, we consider channels realized by one dimensional random noisy quantum circuits with spatially…

Recently, Yamaguchi and Kempf [Phys. Rev. Lett. 136:010801, arXiv:2501.02757] proved that encrypted qubits can be cloned. In this work, we generalize the encrypted cloning protocol and prove that it also applies to higher-order quantum…

We construct a classical algorithm that designs quantum circuits for algorithmic quantum simulation of arbitrary qudit channels on fault-tolerant quantum computers within a pre-specified error tolerance with respect to diamond-norm…

We show how to explicitly construct an $O(nd)$ size and constant quantum depth circuit which encodes any given $n$-qubit stabilizer code with $d$ generators. Our construction is derived using the graphic description for stabilizer codes and…

We determine the optimal rates of universal quantum codes for entanglement transmission and generation under channel uncertainty. In the simplest scenario the sender and receiver are provided merely with the information that the channel…

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 computing opens exciting opportunities for kernel-based machine learning methods, which have broad applications in data analysis. Recent works show that quantum computers can efficiently construct a model of a classifier by…

In order to compress quantum messages without loss of information it is necessary to allow the length of the encoded messages to vary. We develop a general framework for variable-length quantum messages in close analogy to the classical…

Quantum computation can be performed by encoding logical qubits into the states of two or more physical qubits, and controlling a single effective exchange interaction and possibly a global magnetic field. This "encoded universality"…

Over the last decade, Quantum Computing hardware has rapidly developed and become a very intriguing, promising, and active research field among scientists worldwide. To achieve the desired quantum functionalities, quantum algorithms require…