相关论文: The Iterative Unitary Matrix Multiply Method and I…
In this paper, we propose an iterative algorithm using polar decomposition to approximate a channel characterized by a single unitary matrix based on input-output quantum state pairs. In limited data, we state and prove that the optimal…
Density matrices evolved according the von Neumann equation are commonly used to simulate the dynamics of driven quantum systems. However, computational methods using density matrices are often too slow to explore the large parameter spaces…
The quantum kicked prime number rotator (QKPR) is defined as the rotator whose energy levels are prime numbers. The long time behavior is decided by the kick period $\tau$ and kick strength $k$. When $\frac{\tau}{2\pi}$ is irrational, QKPR…
We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In particular, we show how the method can be used for the simulation of…
This is the first of a series of two papers. We discuss some basic problems of the quantum kicked rotator (QKR) and review some important results in the literature. We point out the flaws in the inverse Cayley transform method to prove…
The power method (or iteration) is a well-known classical technique that can be used to find the dominant eigenpair of a matrix. Here, we present a variational quantum circuit method for the power iteration, which can be used to find the…
We propose to use the complex quantum dynamics of a massive particle in a non-quadratic potential to reconstruct an initial unknown motional quantum state. We theoretically show that the reconstruction can be efficiently done by measuring…
Quantum state preparation is a fundamental component of quantum algorithms, particularly in quantum machine learning and data processing, where classical data must be encoded efficiently into quantum states. Existing amplitude encoding…
We study numerically the effects of measurements on dynamical localization in the kicked rotator model simulated on a quantum computer. Contrary to the previous studies, which showed that measurements induce a diffusive probability…
In this work we present a method of decomposition of arbitrary unitary matrix $U\in\mathbf U(2^k)$ into a product of single-qubit negator and controlled-$\sqrt{\mbox{NOT}}$ gates. Since the product results with negator matrix, which can be…
We present a new technique to obtain polynomial decay estimates for the matrix coefficients of unitary operators. Our approach, based on commutator methods, applies to nets of unitary operators, unitary representations of topological…
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,…
We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The…
Gradient descent method, as one of the major methods in numerical optimization, is the key ingredient in many machine learning algorithms. As one of the most fundamental way to solve the optimization problems, it promises the function value…
An iterative algorithm is adopted to construct approximate representations of matrices describing the scattering properties of arbitrary objects. The method is based on the implicit evaluation of scattering responses from iteratively…
An algorithm is proposed to convert arbitrary unitary matrix to a sequence of $X$ gates and fully controlled $R_y, R_z$ and $R_1$ gates. This algorithm is used to generate Q# implementation for arbitrary unitary matrix. Some optimizations…
The simulation of complex quantum systems on a quantum computer is studied, taking the kicked Harper model as an example. This well-studied system has a rich variety of dynamical behavior depending on parameters, displays interesting…
It is suggested to map the qubits into solid state NMR spin system collective states instead of the states of the individual spin. Such an approach introduces the stable computational basis without any additional actions and allows to…
We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on…
Modeling quantum many-body systems is enormously challenging due to the exponential scaling of Hilbert dimension with system size. Finding efficient compressions of the wavefunction is key to building scalable models. Here, we introduce…