Related papers: Quantum simulators, continuous-time automata, and …
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.…
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…
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 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 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…
Invariance under translation is exploited to efficiently simulate one-dimensional quantum lattice systems in the limit of an infinite lattice. Both the computation of the ground state and the simulation of time evolution are considered.
Quantum computation can be achieved by preparing an appropriate initial product state of qudits and then letting it evolve under a fixed Hamiltonian. The readout is made by measurement on individual qudits at some later time. This approach…
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…
Traditional quantum physics solves ground states for a given Hamiltonian, while quantum information science asks for the existence and construction of certain Hamiltonians for given ground states. In practical situations, one would be…
Over the last century, a large number of physical and mathematical developments paired with rapidly advancing technology have allowed the field of quantum chemistry to advance dramatically. However, the lack of computationally efficient…
Generating large, non-trivial quantum chemistry test problems with known ground-state solutions remains a core challenge for benchmarking electronic structure methods. Inspired by planted-solution techniques from combinatorial optimization,…
Hamiltonian quantum gates controlled by classical electromagnetic fields form the basis of any realistic model of quantum computers. In this letter, we derive a lower bound on the field energy required to implement such gates and relate…
We derive general lower energy bounds for the ground state energy of any translationally invariant quantum lattice Hamiltonian. The bounds are given by the ground state energy of renormalized Hamiltonians on finite clusters.
Preparing the ground state of a given Hamiltonian and estimating its ground energy are important but computationally hard tasks. However, given some additional information, these problems can be solved efficiently on a quantum computer. We…
Discrete translational symmetry plays a fundamental role in condensed matter physics and lattice gauge theories, enabling the analysis of systems that would otherwise be intractable. Despite this, many open problems remain. Quantum…
We establish a connection between ground states of local quantum Hamiltonians and thermal states of classical spin systems. For any discrete classical statistical mechanical model in any spatial dimension, we find an associated quantum…
We formulate a novel ground state quantum computation approach that requires no unitary evolution of qubits in time: the qubits are fixed in stationary states of the Hamiltonian. This formulation supplies a completely time-independent…
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 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…
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…