Related papers: Necessary conditions for the efficient simulation …
We deduce the eigenvalues and the eigenvectors of a parameter-dependent Hamiltonian $H_\theta$ which is closely related to the Swanson Hamiltonian, and we construct bi-coherent states for it. After that, we show how and in which sense the…
A universal family of Hamiltonians can be used to simulate any local Hamiltonian by encoding its full spectrum as the low-energy subspace of a Hamiltonian from the family. Many spin-lattice model Hamiltonians -- such as Heisenberg or XY…
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic…
We present an efficient method for estimating the eigenvalues of a Hamiltonian $H$ from the expectation values of the evolution operator for various times. For a given quantum state $\rho$, our method outputs a list of eigenvalue estimates…
We propose efficient algorithms for classically simulating Gaussian unitaries and measurements applied to non-Gaussian initial states. The constructions are based on decomposing the non-Gaussian states into linear combinations of Gaussian…
The interplay of Anderson localisation and decoherence results in intricate dynamics but is notoriously difficult to simulate on classical computers. We develop the framework for a quantum simulation of such an open quantum system making…
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…
We examine the problem of simulating lattice gauge theories on a universal quantum computer. The basic strategy of our approach is to transcribe lattice gauge theories in the Hamiltonian formulation into a Hamiltonian involving only Pauli…
We study the problem of learning the Hamiltonian of a quantum many-body system given samples from its Gibbs (thermal) state. The classical analog of this problem, known as learning graphical models or Boltzmann machines, is a well-studied…
Recent advancements in quantum hardware and classical computing simulations have significantly enhanced the accessibility of quantum system data, leading to an increased demand for precise descriptions and predictions of these systems.…
We present a quantum algorithm for simulating the dynamics of a first-quantized Hamiltonian in real space based on the truncated Taylor series algorithm. We avoid the possibility of singularities by applying various cutoffs to the system…
We construct an efficient autonomous quantum-circuit design algorithm for creating efficient quantum circuits to simulate Hamiltonian many-body quantum dynamics for arbitrary input states. The resultant quantum circuits have optimal space…
A quantum simulator is a device engineered to reproduce the properties of an ideal quantum model. It allows the study of quantum systems that cannot be efficiently simulated on classical computers. While a universal quantum computer is also…
The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. Here, we introduce the concept of an "eigenstate witness" and through it…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
Quantum simulators offer the potential to utilize the quantum nature of a physical system to study another physical system. In contrast to conventional simulation, which experiences an exponential increase in computational complexity,…
Quantum simulation has emerged as a key application of quantum computing, with significant progress made in algorithms for simulating both closed and open quantum systems. The simulation of open quantum systems, particularly those governed…
The use of near-term quantum devices that lack quantum error correction, for addressing quantum chemistry and physics problems, requires hybrid quantum-classical algorithms and techniques. Here we present a process for obtaining the…
We provide new constructions of unitary $t$-designs for general $t$ on one qudit and $N$ qubits, and propose a design Hamiltonian, a random Hamiltonian of which dynamics always forms a unitary design after a threshold time, as a basic…
We study the physical resources required to implement general quantum operations, and provide new bounds on the minimum possible size which an environment must be in order to perform certain quantum operations. We prove that contrary to a…