Related papers: Quantum implementation of non-unitary operations w…
We present the quantum computation of nuclear observables where the operators of interest are first decomposed in terms of the linear combination of unitaries. Then we utilise the Hadamard test and the linear combination of unitaries (LCU)…
Due to the linearity of quantum operations, it is not straightforward to implement nonlinear transformations on a quantum computer, making some practical tasks like a neural network hard to be achieved. In this work, we define a task called…
Recently, machine learning had a remarkable impact, from scientific to everyday-life applications. However, complex tasks often imply unfeasible energy and computational power consumption. Quantum computation might lower such requirements,…
For multiqubit density operators in a suitable tensorial basis, we show that a number of nonunitary operations used in the detection and synthesis of entanglement are classifiable as reflection symmetries, i.e., orientation changing…
Quantum simulation has primarily focused on unitary dynamics, while many physical and engineering systems can be modeled by linear ordinary differential equations whose generators include non-Hermitian terms. Recent studies have shown that…
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
Quantum computing is powerful because unitary operators describing the time-evolution of a quantum system have exponential size in terms of the number of qubits present in the system. We develop a new "Singular value transformation"…
Quantum computers have the potential to efficiently solve a system of nonlinear ordinary differential equations (ODEs), which play a crucial role in various industries and scientific fields. However, it remains unclear which system of…
Quantum machine learning has faced growing scrutiny over its practical advantages compared to classical approaches, particularly following dequantization results and large scale benchmarking studies that have challenged earlier optimistic…
We propose a new framework to design controllers for high-dimensional nonlinear systems. The control is designed through the iterative linear quadratic regulator (ILQR), an algorithm that computes control by iteratively applying the linear…
With the rapid progress in quantum hardware, there has been an increased interest in new quantum algorithms to describe complex many-body systems searching for the still-elusive goal of 'useful quantum advantage'. Surprisingly, quantum…
Based on the matrix realignment and partial transpose, we develop an approach to entangling power and operator entanglement of quantum unitary operators. We demonstrate efficiency of the approach by studying several unitary operators on…
Optimization of unitary transformations in Variational Quantum Algorithms benefits highly from efficient evaluation of cost function gradients with respect to amplitudes of unitary generators. We propose several extensions of the…
We present a quantum algorithm for systems of (possibly inhomogeneous) linear ordinary differential equations with constant coefficients. The algorithm produces a quantum state that is proportional to the solution at a desired final time.…
Nagy's unitary dilation theorem in operator theory asserts the possibility of dilating a contraction into a unitary operator. When used in quantum computing, its practical implementation primarily relies on block-encoding techniques, based…
Simulating non-Hermitian dynamics on quantum computers is often hindered by the decay of success probability and the instability of non-diagonalizable matrices. Here, we present contour-based matrix decomposition (CBMD), a rigorous and…
A simple pseudo-Hamiltonian formulation is proposed for the linear inhomogeneous systems of ODEs. In contrast to the usual Hamiltonian mechanics, our approach is based on the use of non-stationary Poisson brackets, i.e. corresponding…
We show that nonlinear problems including nonlinear partial differential equations can be efficiently solved by variational quantum computing. We achieve this by utilizing multiple copies of variational quantum states to treat…
Unitary operations are physically implementable. We further the understanding of such operations by studying the possible forms of nonlocal unitary operators, which are bipartite or multipartite unitary operators that are not tensor product…
In this paper, we consider the amplified-and-forward relaying in an OFDM system with unitary linear processing at the relay. We proposed a general analytical framework to find the unitary linear processing matrix that maximizes the system…