Related papers: Hamiltonian singular value transformation and inve…
Digital-analog is a quantum computational paradigm that employs the natural interaction Hamiltonian of a system as the entangling resource, combined with single qubit gates, to implement universal quantum operations. As in the case of its…
Quantum computing has brought a paradigm change in computer science, where non-classical technologies have promised to outperform their classical counterpart. Such an advantage was only demonstrated for tasks without practical applications,…
The Hamiltonian model of quantum error correction code in the literature is often constructed with the help of its stabilizer formalism. But there have been many known examples of nonadditive codes which are beyond the standard quantum…
We introduce the concept of embedding quantum simulators, a paradigm allowing the efficient quantum computation of a class of bipartite and multipartite entanglement monotones. It consists in the suitable encoding of a simulated quantum…
We show in detail how the Jordan-Wigner transformation can be used to simulate any fermionic many-body Hamiltonian on a quantum computer. We develop an algorithm based on appropriate qubit gates that takes a general fermionic Hamiltonian,…
A permutation-invariant code on m qubits is a subspace of the symmetric subspace of the m qubits. We derive permutation-invariant codes that can encode an increasing amount of quantum information while suppressing leading order spontaneous…
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…
Modeling non-Hermitian Hamiltonians is increasingly important in classical and quantum domains, especially when studying open systems, $PT$ symmetry, and resonances. However, the quantum simulation of these models has been limited by the…
Group convolutions and cross-correlations, which are equivariant to the actions of group elements, are commonly used in mathematics to analyze or take advantage of symmetries inherent in a given problem setting. Here, we provide efficient…
Singular value thresholding (SVT) operation is a fundamental core module in many mathematical models in computer vision and machine learning, particularly for many nuclear norm minimizing-based problems. We presented a quantum SVT (QSVT)…
One of the main bottlenecks in solving combinatorial optimization problems with quantum annealers is the qubit connectivity in the hardware. A possible solution for larger connectivty is minor embedding. This techniques makes the…
A simple construction is presented which allows computing the transition amplitude of a quantum circuit to be encoded as computing the permanent of a matrix which is of size proportional to the number of quantum gates in the circuit. This…
Quantum algorithms have been developed for efficiently solving linear algebra tasks. However, they generally require deep circuits and hence universal fault-tolerant quantum computers. In this work, we propose variational algorithms for…
Quantum computers have the potential to transform the ways in which we tackle some important problems. The efforts by companies like Google, IBM and Microsoft to construct quantum computers have been making headlines for years. Equally…
Convolution operations are foundational to classical image processing and modern deep learning architectures, yet their extension into the quantum domain has remained algorithmically and physically costly due to inefficient data encoding…
One of the most promising applications of quantum computers is solving partial differential equations (PDEs). By using the Schrodingerisation technique - which converts non-conservative PDEs into Schrodinger equations - the problem can be…
We report the quantum computing of reacting flows by simulating the Hamiltonian dynamics. The scalar transport equation for reacting flows is transformed into a Hamiltonian system, mapping the dissipative and non-Hermitian problem in…
We show how to implement a Rindler transformation of coordinates with an embedded quantum simulator. A suitable mapping allows to realise the unphysical operation in the simulated dynamics by implementing a quantum gate on an enlarged…
Quantum computing is a unique computational approach that promises tremendous performance that cannot be achieved by classical computers, although several problems must be resolved to realize a practical quantum computing system for easy…
We in this paper study the hermiticity of Hamiltonian and energy spectrum for the SU(1; 1) systems. The Hermitian Hamiltonian can possess imaginary eigenvalues in contrast with the common belief that hermiticity is a suffcient condition for…