2,656 research outputs found
Optimal State Transfer and Entanglement Generation in Power-law Interacting Systems
We present an optimal protocol for encoding an unknown qubit state into a
multiqubit Greenberger-Horne-Zeilinger-like state and, consequently,
transferring quantum information in large systems exhibiting power-law
() interactions. For all power-law exponents between
and , where is the dimension of the system, the protocol yields a
polynomial speedup for and a superpolynomial speedup for
, compared to the state of the art. For all , the
protocol saturates the Lieb-Robinson bounds (up to subpolynomial corrections),
thereby establishing the optimality of the protocol and the tightness of the
bounds in this regime. The protocol has a wide range of applications, including
in quantum sensing, quantum computing, and preparation of topologically ordered
states. In addition, the protocol provides a lower bound on the gate count in
digital simulations of power-law interacting systems.Comment: Updated Table I, Additional discussion on a lower bound for the gate
count in digital quantum simulatio
Locality and digital quantum simulation of power-law interactions
The propagation of information in non-relativistic quantum systems obeys a
speed limit known as a Lieb-Robinson bound. We derive a new Lieb-Robinson bound
for systems with interactions that decay with distance as a power law,
. The bound implies an effective light cone tighter than all
previous bounds. Our approach is based on a technique for approximating the
time evolution of a system, which was first introduced as part of a quantum
simulation algorithm by Haah et al., FOCS'18. To bound the error of the
approximation, we use a known Lieb-Robinson bound that is weaker than the bound
we establish. This result brings the analysis full circle, suggesting a deep
connection between Lieb-Robinson bounds and digital quantum simulation. In
addition to the new Lieb-Robinson bound, our analysis also gives an error bound
for the Haah et al. quantum simulation algorithm when used to simulate
power-law decaying interactions. In particular, we show that the gate count of
the algorithm scales with the system size better than existing algorithms when
(where is the number of dimensions).Comment: 18 pages, 10 figure
Hierarchy of Linear Light Cones with Long-Range Interactions
In quantum many-body systems with local interactions, quantum information and entanglement cannot spread outside of a linear light cone, which expands at an emergent velocity analogous to the speed of light. Local operations at sufficiently separated spacetime points approximately commute—given a many-body state |ψ⟩, O_x(t)O_y|ψ⟩≈O_yO_x(t)|ψ⟩ with arbitrarily small errors—so long as |x−y|≳vt, where v is finite. Yet, most nonrelativistic physical systems realized in nature have long-range interactions: Two degrees of freedom separated by a distance r interact with potential energy V(r)∝1/r^α. In systems with long-range interactions, we rigorously establish a hierarchy of linear light cones: At the same α, some quantum information processing tasks are constrained by a linear light cone, while others are not. In one spatial dimension, this linear light cone exists for every many-body state |ψ⟩ when α>3 (Lieb-Robinson light cone); for a typical state |ψ⟩ chosen uniformly at random from the Hilbert space when α>5/2 (Frobenius light cone); and for every state of a noninteracting system when α>2 (free light cone). These bounds apply to time-dependent systems and are optimal up to subalgebraic improvements. Our theorems regarding the Lieb-Robinson and free light cones—and their tightness—also generalize to arbitrary dimensions. We discuss the implications of our bounds on the growth of connected correlators and of topological order, the clustering of correlations in gapped systems, and the digital simulation of systems with long-range interactions. In addition, we show that universal quantum state transfer, as well as many-body quantum chaos, is bounded by the Frobenius light cone and, therefore, is poorly constrained by all Lieb-Robinson bounds
Hierarchy of linear light cones with long-range interactions
In quantum many-body systems with local interactions, quantum information and
entanglement cannot spread outside of a linear light cone, which expands at an
emergent velocity analogous to the speed of light. Local operations at
sufficiently separated spacetime points approximately commute -given a
many-body state, with arbitrarily small errors -- so
long as , where is finite. Yet most non-relativistic
physical systems realized in nature have long-range interactions: two degrees
of freedom separated by a distance interact with potential energy . In systems with long-range interactions, we rigorously
establish a hierarchy of linear light cones: at the same , some quantum
information processing tasks are constrained by a linear light cone while
others are not. In one spatial dimension, this linear light cone exists for
every many-body state when (Lieb-Robinson light cone); for a typical
state chosen uniformly at random from the Hilbert space when
(Frobenius light cone); for every state of a
non-interacting system when (free light cone). These bounds apply to
time-dependent systems and are optimal up to subalgebraic improvements. Our
theorems regarding the Lieb-Robinson and free light cones -- and their
tightness -- also generalize to arbitrary dimensions. We discuss the
implications of our bounds on the growth of connected correlators and of
topological order, the clustering of correlations in gapped systems, and the
digital simulation of systems with long-range interactions. In addition, we
show that universal quantum state transfer, as well as many-body quantum chaos,
are bounded by the Frobenius light cone, and therefore are poorly constrained
by all Lieb-Robinson bounds.Comment: 36 pages; 6 figures; v2: revised and expanded introduction, a few
extra results; v3: minor revision
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