Related papers: Polynomial-time algorithm for simulation of weakly…
We consider dynamically constrained Monte-Carlo dynamics and show that this leads to the generation of long ranged effective interactions. This allows us to construct a local algorithm for the simulation of charged systems without ever…
Harrow, Hassidim, and Lloyd showed that for a suitably specified $N \times N$ matrix $A$ and $N$-dimensional vector $\vec{b}$, there is a quantum algorithm that outputs a quantum state proportional to the solution of the linear system of…
Variational quantum algorithms (VQAs) have emerged in recent years as a promise to obtain quantum advantage. These task-oriented algorithms work in a hybrid loop combining a quantum processor and classical optimization. Using a specific…
Quantum algorithms for diverse problems, including search and optimization problems, require the implementation of a reflection operator over a target state. Commonly, such reflections are approximately implemented using phase estimation.…
Characterization of qubit couplings in many-body quantum systems is essential for benchmarking quantum computation and simulation. We propose a tomographic measurement scheme to determine all the coupling terms in a general many-body…
A milestone in the field of quantum computing will be solving problems in quantum chemistry and materials faster than state-of-the-art classical methods. The current understanding is that achieving quantum advantage in this area will…
Quantum chemistry has been viewed as one of the potential early applications of quantum computing. Two techniques have been proposed for electronic structure calculations: (i) the variational quantum eigensolver and (ii) the…
Given a generic time-dependent many-body quantum state, we determine the associated parent Hamiltonian. This procedure may require, in general, interactions of any sort. Enforcing the requirement of a fixed set of engineerable Hamiltonians,…
The need for Hamiltonians with many-body interactions arises in various applications of quantum computing. However, interactions beyond two-body are difficult to realize experimentally. Perturbative gadgets were introduced to obtain…
It is crucial to reduce the resources required to run quantum algorithms and simulate physical systems on quantum computers due to coherence time limitations. With regards to Hamiltonian simulation, a significant effort has focused on…
The general problem of finding the ground state energy of lattice Hamiltonians is known to be very hard, even for a quantum computer. We show here that this is the case even for translationally invariant systems. We also show that a quantum…
We investigate the entanglement in the ground state of systems comprising two and three qubits with random interactions. Since the Hamiltonians also contain deterministic one-body terms, by varying the interaction strength, one can…
Many quantum algorithms for ground-state preparation and energy estimation require the implementation of high-degree polynomials of a Hamiltonian to achieve better convergence rates. Their circuit implementation typically relies on quantum…
Consider two quantum systems A and B interacting according to a product Hamiltonian H = H_A x H_B. We show that any two such Hamiltonians can be used to simulate each other reversibly (i.e., without efficiency losses) with the help of local…
Precisely knowing an interaction Hamiltonian is crucial to realize quantum information tasks, especially to experimentally demonstrate a quantum computer and a quantum memory. We propose a scheme to experimentally evaluate the spin-spin…
We study how parallelism can speed up quantum simulation. A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians with good sparse structures, called uniform-structured Hamiltonians, including…
Parity-time ($PT$) symmetric Hamiltonians are generally non-Hermitian and give rise to exotic behaviour in quantum systems at exceptional points, where eigenvectors coalesce. The recent realisation of $PT$-symmetric Hamiltonians in quantum…
Generally, the local interactions in a many-body quantum spin system on a lattice do not commute with each other. Consequently, the Hamiltonian of a local region will generally not commute with that of the entire system, and so the two…
We study necessary conditions for the efficient simulation of both bipartite and multipartite Hamiltonians, which are independent of the eigenvalues and based on the algebraic-geometric invariants introduced in [1-2]. Our results indicate…
The Hamiltonian operator plays a central role in quantum theory being a generator of unitary quantum dynamics. Its expectation value describes the energy of a quantum system. Typically being a non-unitary operator, the action of the…