Related papers: Quantum simulation in the Heisenberg picture via v…
Quantum mechanics has introduced a new theoretical framework for the study of molecules, enabling the prediction of properties and dynamics through the solution of the Schr\"odinger equation applied to these systems. However, solving this…
Linear response theory and Green's functions provide a universal framework for understanding dynamical correlations in strongly correlated open quantum systems. While the theoretical foundation for non-Hermitian linear response has been…
Simulating quantum circuits on classical hardware is a powerful and necessary tool for developing and testing quantum algorithms and hardware as well as evaluating claims of quantum supremacy in the Noisy Intermediate-Scale Quantum (NISQ)…
Quantum computing has emerged as a promising avenue for achieving significant speedup, particularly in large-scale PDE simulations, compared to classical computing. One of the main quantum approaches involves utilizing Hamiltonian…
Recently, Jin et al. proposed a quantum simulation technique for ANY linear partial differential equations (PDEs), called Schr\"{o}dingerisation [1,2,3]. In this paper, the Schr\"{o}dingerisation technique for quantum simulation is expanded…
In this paper we study quantum simulation algorithms on the elastic wave equations using the Schr\"odingerisation method. The Schr\"odingerisation method transforms any linear PDEs into a system of Schr\"odinger-type PDEs -with unitary…
Classical simulations of quantum circuits play a vital role in the development of quantum computers and for taking the temperature of the field. Here, we classically simulate various physically-motivated circuits using 2D tensor network…
This paper presents techniques for theoretically and practically efficient and scalable Schr\"odinger-style quantum circuit simulation. Our approach partitions a quantum circuit into a hierarchy of subcircuits and simulates the subcircuits…
If a large Quantum Computer (QC) existed today, what type of physical problems could we efficiently simulate on it that we could not simulate on a classical Turing machine? In this paper we argue that a QC could solve some relevant physical…
The parameters of a quantum system grow exponentially with the number of involved quantum particles. Hence, the associated memory requirement goes well beyond the limit of best classic computers for quantum systems composed of a few dozen…
We have shown that quantum systems on finite-dimensional Hilbert spaces are equivalent under local transformations. Using these transformations give rise to a gauge group that connects the hamiltonian operators associated with each quantum…
Recent breakthroughs have opened the possibility to intermediate-scale quantum computing with tens to hundreds of qubits, and shown the potential for solving classical challenging problems, such as in chemistry and condensed matter physics.…
In this note, we develop a framework to describe open quantum systems in the Heisenberg picture, i.e., via time evolving operator algebras. We point out the incompleteness of the previous proposals in this regard. We argue that a complete…
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 present a quantum computational framework that systematically converts classical linear iterative algorithms with fixed iteration operators into their quantum counterparts using the Schr\"odingerization technique [Shi Jin, Nana Liu and…
Simulating quantum dynamics is one of the most important applications of quantum computers. Traditional approaches for quantum simulation involve preparing the full evolved state of the system and then measuring some physical quantity.…
Quantum algorithms reformulate computational problems as quantum evolutions in a large Hilbert space. Most quantum algorithms assume that the time-evolution is perfectly unitary and that the full Hilbert space is available. However, in…
We give a detailed exposition of the "vectorized" notation for dealing with quantum operations. This notation is used to highlight the relationships between representations of completely-positive dynamics. Vectorization considerably…
With the rapid progress in quantum hardware and software, the need for verification of quantum systems becomes increasingly crucial. While model checking is a dominant and very successful technique for verifying classical systems, its…
We show that the theory of operator quantum error correction can be naturally generalized by allowing constraints not only on states but also on observables. The resulting theory describes the correction of algebras of observables (and may…