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We use the quantum version of Chebyshev polynomials to explicitly construct the recursive formulas for the Kronecker quantum cluster algebra with principal coefficients. As a byproduct, we obtain two bar-invariant positive…
Recently, it was shown that the qudits used in circuits of a convolutional form (e.g., Matrix Product State sand Multi-scale Entanglement Renormalization Ansatz) can be reset unitarily…
To unleash the potential of quantum computers, noise effects on qubits' performance must be carefully managed. The decoders responsible for diagnosing noise-induced computational errors must use resources efficiently to enable scaling to…
The paper proposes an implicit (i.e., machine-independent) complexity approach to studying computation by polynomial-size, constant-depth circuits with gates counting modulo a constant through the lens of discrete ordinary differential…
Efficiently implementing Clifford circuits is crucial for quantum error correction and quantum algorithms. Linear reversible circuits, equivalent to circuits composed of CNOT gates, have important applications in classical computing. In…
A large class of problems in the current era of quantum devices involve interfacing between the quantum and classical system. These include calibration procedures, characterization routines, and variational algorithms. The control in these…
Given an arbitrary $2^w \times 2^w$ unitary matrix $U$, a powerful matrix decomposition can be applied, leading to four different syntheses of a $w$-qubit quantum circuit performing the unitary transformation. The demonstration is based on…
Matrix-product codes over finite fields are an important class of long linear codes by combining several commensurate shorter linear codes with a defining matrix over finite fields. The construction of matrix-product codes with certain…
The Causal Dynamical Triangulation (CDT) approach to quantum gravity is a lattice approximation to the gravitational path integral. Developed by Ambj\o{}rn, Jurkiewicz and Loll, it has yielded some important results, notably the emergence…
Quantum synchronizable codes are quantum error-correcting codes designed to correct the effects of both quantum noise and block synchronization errors. While it is known that quantum synchronizable codes can be constructed from cyclic codes…
In this paper, we introduce a construction of quantum convolutional codes (QCCs) based on difference triangle sets (DTSs). To construct QCCs, one must determine polynomial stabilizers $X(D)$ and $Z(D)$ that commute (symplectic…
Homogenous Boolean function is an essential part of any cryptographic system. The ability to construct an optimized reversible circuits for homogeneous Boolean functions might arise the possibility of building cryptographic system on novel…
To generate arbitrary one- and two-qubit gates, the universal decompositions are usually used in quantum computing, and the universality of these decompositions has been demonstrated. However, in realistic experiments, gate errors may…
Continuous unitary transformations are a powerful tool to extract valuable information out of quantum many-body Hamiltonians, in which the so-called flow equation transforms the Hamiltonian to a diagonal or block-diagonal form in second…
In this paper, we introduce novel fast matrix inversion algorithms that leverage triangular decomposition and recurrent formalism, incorporating Strassen's fast matrix multiplication. Our research places particular emphasis on triangular…
Quantum error correction is vital for implementing universal quantum computing. A key component is the encoding circuit that maps a product state of physical qubits into the encoded multipartite entangled logical state. Known methods are…
Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits…
We present dimensional circuit synthesis, a new method for generating digital logic circuits that improve the efficiency of training and inference of machine learning models from sensor data. The hardware accelerators that the method…
Environmental noise that couples longitudinally to a quantum system dephases that system and can limit its coherence lifetime. Performance using quantum superposition in clocks, information processors, communication networks, and sensors…
We consider recursive decoding for Reed-Muller (RM) codes and their subcodes. Two new recursive techniques are described. We analyze asymptotic properties of these algorithms and show that they substantially outperform other decoding…