Related papers: Quantum simulations under translational symmetry
We describe a simple quantum algorithm to simulate time-dependent Hamiltonian, extending the methodology of quantum signal processing. The framework achieves optimal scaling up to some factor with respect to other parameters, and nearly…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
We address the problem of simulating pair-interaction Hamiltonians in n node quantum networks where the subsystems have arbitrary, possibly different, dimensions. We show that any pair-interaction can be used to simulate any other by…
We describe methods to construct digital quantum simulation algorithms for quantum spin systems on a regular lattice with local interactions. In addition to tools such as the Trotter-Suzuki expansion and graph coloring, we also discuss the…
We provide time-evolution operators, gauge transformations and a perturbative treatment for non-Hermitian Hamiltonian systems, which are explicitly time-dependent. We determine various new equivalence pairs for Hermitian and non-Hermitian…
Supersymmetric models are grounded in the intriguing concept of a hypothetical symmetry that relates bosonic and fermionic particles. This symmetry has profound implications, offering valuable extensions to the Standard Model of particle…
We construct commuting transfer matrices for models describing the interaction between a single quantum spin and a single bosonic mode using the quantum inverse scattering framework. The transfer matrices are obtained from certain…
Imaginary time evolution is a powerful technique for computing the ground state of quantum Hamiltonians, where the convergence to ground state in asymptotic imaginary time is guaranteed. However, implementing this method on quantum…
What interactions are sufficient to simulate arbitrary quantum dynamics in a composite quantum system? Dodd et al. (quant-ph/0106064) provided a partial solution to this problem in the form of an efficient algorithm to simulate any desired…
We present a numerical method to simulate the time evolution, according to a Hamiltonian made of local interactions, of quantum spin chains and systems alike. The efficiency of the scheme depends on the amount of the entanglement involved…
We show how to construct Hamiltonian lattice theories with one exact supersymmetry on arbitrary triangulations of curved space in any number of dimensions. Both bosons and fermions satisfy discrete K\"{a}hler-Dirac equations. The…
The appearance of Hamiltonian constraint in the canonical formalism for general relativity reflects the lack of a fixed external time. The dynamics of general relativistic systems can be expressed with respect to an arbitrarily chosen…
Symmetries in a Hamiltonian play an important role in quantum physics because they correspond directly with conserved quantities of the related system. In this paper, we propose quantum algorithms capable of testing whether a Hamiltonian…
Engineering a Hamiltonian system with tunable interactions provides opportunities to optimize performance for quantum sensing and explore emerging phenomena of many-body systems. An optical lattice clock based on partially delocalized…
We prove that generic quantum local Hamiltonians are gapless. In fact, we prove that there is a continuous density of states above the ground state. The Hamiltonian can be on a lattice in any spatial dimension or on a graph with a bounded…
The past few years have witnessed the concrete and fast spreading of quantum technologies for practical computation and simulation. In particular, quantum computing platforms based on either trapped ions or superconducting qubits have…
We prove that translationally invariant Hamiltonians of a chain of $n$ qubits with nearest-neighbour interactions have two seemingly contradictory features. Firstly in the limit $n\rightarrow\infty$ we show that any translationally…
We analyze the complexity of classically simulating continuous-time dynamics of locally interacting quantum spin systems with a constant rate of entanglement breaking noise. We prove that a polynomial time classical algorithm can be used to…
We describe a novel class of quantum mechanical particle oscillations in both relativistic and non-relativistic systems based on $PT$ symmetry and $T^2=-1$ (relevant for fermions), where $P$ is parity and $T$ is time reversal. The…
Motivated by experimental limitations commonly met in the design of solid state quantum computers, we study the problems of non-local Hamiltonian simulation and non-local gate synthesis when only homogeneous local unitaries are performed in…