Translationally-Invariant Universal Quantum Hamiltonians in 1D
- URL: http://arxiv.org/abs/2003.13753v2
- Date: Mon, 25 Oct 2021 15:14:29 GMT
- Title: Translationally-Invariant Universal Quantum Hamiltonians in 1D
- Authors: Tamara Kohler and Stephen Piddock and Johannes Bausch and Toby Cubitt
- Abstract summary: We show that there are universal models even in translationally invariant spin chains in 1D.
We construct the first known toy model of 2D--1D holographic duality between local Hamiltonians.
- Score: 6.0409040218619685
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: 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 other quantum many body system. Previous universality results have required
proofs involving complicated `chains' of perturbative `gadgets'. In this paper,
we derive a significantly simpler and more powerful method of proving
universality of Hamiltonians, directly leveraging the ability to encode quantum
computation into ground states. This provides new insight into the origins of
universal models, and suggests a deep connection between universality and
complexity. We apply this new approach to show that there are universal models
even in translationally invariant spin chains in 1D. This gives as a corollary
a new Hamiltonian complexity result, that the local Hamiltonian problem for
translationally-invariant spin chains in one dimension with an
exponentially-small promise gap is PSPACE-complete. Finally, we use these new
universal models to construct the first known toy model of 2D--1D holographic
duality between local Hamiltonians.
Related papers
- Quantifying non-Hermiticity using single- and many-particle quantum properties [14.37149160708975]
The non-Hermitian paradigm of quantum systems displays salient features drastically different from Hermitian counterparts.
We propose a formalism that quantifies the (dis-)similarity of these right and left ensembles, for single- as well as many-particle quantum properties.
Our findings can be instrumental in unveiling new exotic quantum phases of non-Hermitian quantum many-body systems.
arXiv Detail & Related papers (2024-06-19T13:04:47Z) - Robust Hamiltonian Engineering for Interacting Qudit Systems [50.591267188664666]
We develop a formalism for the robust dynamical decoupling and Hamiltonian engineering of strongly interacting qudit systems.
We experimentally demonstrate these techniques in a strongly-interacting, disordered ensemble of spin-1 nitrogen-vacancy centers.
arXiv Detail & Related papers (2023-05-16T19:12:41Z) - Universal features of entanglement entropy in the honeycomb Hubbard
model [44.99833362998488]
This paper introduces a new method to compute the R'enyi entanglement entropy in auxiliary-field quantum Monte Carlo simulations.
We demonstrate the efficiency of this method by extracting, for the first time, universal subleading logarithmic terms in a two dimensional model of interacting fermions.
arXiv Detail & Related papers (2022-11-08T15:52:16Z) - A construction of Combinatorial NLTS [22.539300644593936]
NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of high complexity.
Here, we prove a weaker version called the NLTS, where a quantum circuit lower bound is shown against states that violate a (small) constant fraction of local terms.
arXiv Detail & Related papers (2022-06-06T16:55:34Z) - Multipartite entangled states in dipolar quantum simulators [0.0]
We show that the native Hamiltonian dynamics of state-of-the-art quantum simulation platforms can act as a robust source of multipartite entanglement.
Our results suggest that the native Hamiltonian dynamics of state-of-the-art quantum simulation platforms, such as Rydberg-atom arrays, can act as a robust source of multipartite entanglement.
arXiv Detail & Related papers (2022-05-08T16:23:48Z) - Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware.
We present an algorithm that compresses the Trotter steps into a single block of quantum gates.
This results in a fixed depth time evolution for certain classes of Hamiltonians.
arXiv Detail & Related papers (2021-08-06T19:38:01Z) - Strongly Universal Hamiltonian Simulators [0.38073142980733]
A universal family of Hamiltonians can be used to simulate any local Hamiltonian.
We provide an efficient construction by which these universal families are in fact "strongly" universal.
arXiv Detail & Related papers (2021-02-05T04:18:38Z) - General conditions for universality of Quantum Hamiltonians [6.0409040218619685]
We classify the simulation ability of quantum Hamiltonians by their complexity classes.
Although the result concerns the theory of analogue Hamiltonian simulation - a promising application of near-term quantum technology - the proof relies on abstract complexity theoretic concepts and the theory of quantum universality.
arXiv Detail & Related papers (2021-01-28T23:20:43Z) - Digital-Analog Quantum Simulations Using The Cross-Resonance Effect [0.0]
Digital-analog quantum computation aims to reduce the currently infeasible resource requirements needed for near-term quantum information processing.
We consider superconducting architectures and extend the cross-resonance effect, up to first order in theory, from a two-qubit interaction to an analog Hamiltonian acting on 1D chains and 2D square lattices.
arXiv Detail & Related papers (2020-11-20T17:07:28Z) - Hamiltonian operator approximation for energy measurement and ground
state preparation [23.87373187143897]
We show how to approximate the Hamiltonian operator as a sum of propagators using a differential representation.
The proposed approach, named Hamiltonian operator approximation (HOA), is designed to benefit analog quantum simulators.
arXiv Detail & Related papers (2020-09-07T18:11:00Z) - Universal Translationally-Invariant Hamiltonians [8.020742121274418]
We extend the notion of universal quantum Hamiltonians to the setting of translationally-invariant systems.
We show that qubit Hamiltonians consisting of Heisenberg or XY interactions of varying interaction strengths are universal.
arXiv Detail & Related papers (2020-01-22T15:10:29Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.