Related papers: Strongly Universal Hamiltonian Simulators
In this work we extend the notion of universal quantum Hamiltonians to the setting of translationally-invariant systems. We present a construction that allows a two-dimensional spin lattice with nearest-neighbour interactions, open…
Recent work has characterised rigorously what it means for one quantum system to simulate another, and demonstrated the existence of universal Hamiltonians -- simple spin lattice Hamiltonians that can replicate the entire physics of any…
A family of quantum Hamiltonians is said to be universal if any other finite-dimensional Hamiltonian can be approximately encoded within the low-energy space of a Hamiltonian from that family. If the encoding is efficient, universal…
Quantum simulation is a promising near term application for mesoscale quantum information processors, with the potential to solve computationally intractable problems at the scale of just a few dozen interacting quantum systems. Recent…
Recent work has demonstrated the existence of universal Hamiltonians - simple spin lattice models that can simulate any other quantum many body system to any desired level of accuracy. Until now proofs of universality have relied on…
We investigate the power of quantum systems for the simulation of Hamiltonian time evolutions on a cubic lattice under the constraint of translational invariance. Given a set of translationally invariant local Hamiltonians and short range…
Quantum many-body systems exhibit an extremely diverse range of phases and physical phenomena. Here, we prove that the entire physics of any other quantum many-body system is replicated in certain simple, "universal" spin-lattice models. We…
Spin models are widely studied in the natural sciences, from investigating magnetic materials in condensed matter physics to studying neural networks. Previous work has demonstrated that there exist simple classical spin models that are…
Any quantum system with a non-trivial Hamiltonian is able to simulate any other Hamiltonian evolution provided that a sufficiently large group of unitary control operations is available. We show that there exist finite groups with this…
Current quantum devices execute specific tasks that are hard for classical computers and have the potential to solve problems such as quantum simulation of material science and chemistry, even without error correction. For practical…
We construct a simple translationally invariant, nearest-neighbor Hamiltonian on a chain of 10-dimensional qudits that makes it possible to realize universal quantum computing without any external control during the computational process.…
We consider 1D lattices described by Hubbard or Bose-Hubbard models, in the presence of periodic high-frequency perturbations, such as uniform ac force or modulation of hopping coefficients. Effective Hamiltonians for interacting particles…
We propose dynamical control schemes for Hamiltonian simulation in many-body quantum systems that avoid instantaneous control operations and rely solely on realistic bounded-strength control Hamiltonians. Each simulation protocol consists…
We prove that estimating the ground state energy of a translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is QMAEXP-complete, even for systems of low local dimension (roughly 40). This is an improvement over the best…
Although a universal quantum computer is still far from reach, the tremendous advances in controllable quantum devices, in particular with solid-state systems, make it possible to physically implement "quantum simulators". Quantum…
The presence of symmetries, be they discrete or continuous, in a physical system typically leads to a reduction in the problem to be solved. Here we report that neither translational invariance nor rotational invariance reduce the…
We construct a Hamiltonian whose dynamics simulate the dynamics of every other Hamiltonian up to exponentially long times in the system size. The Hamiltonian is time-independent, local, one-dimensional, and translation invariant. As a…
Simple families of quantum Hamiltonians can simulate general many-body systems at arbitrary precision through the use of perturbative gadgets, however this generally requires interaction strengths spanning many orders of magnitude which…
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…
Quantum control in large dimensional Hilbert spaces is essential for realizing the power of quantum information processing. For closed quantum systems the relevant input/output maps are unitary transformations, and the fundamental challenge…