14 research outputs found
Quantum gate learning in engineered qubit networks: Toffoli gate with always-on interactions
We put forward a strategy to encode a quantum operation into the unmodulated
dynamics of a quantum network without the need of external control pulses,
measurements or active feedback. Our optimization scheme, inspired by
supervised machine learning, consists in engineering the pairwise couplings
between the network qubits so that the target quantum operation is encoded in
the natural reduced dynamics of a network section. The efficacy of the proposed
scheme is demonstrated by the finding of uncontrolled four-qubit networks that
implement either the Toffoli gate, the Fredkin gate, or remote logic
operations. The proposed Toffoli gate is stable against imperfections, has a
high-fidelity for fault tolerant quantum computation, and is fast, being based
on the non-equilibrium dynamics.Comment: 8 pages, 3 figure
One-step replica symmetry breaking in the language of tensor networks
We develop an exact mapping between the one-step replica symmetry breaking
cavity method and tensor networks. The two schemes come with complementary
mathematical and numerical toolboxes that could be leveraged to improve the
respective states of the art. As an example, we construct a tensor-network
representation of Survey Propagation, one of the best deterministic k-SAT
solvers. The resulting algorithm outperforms any existent tensor-network solver
by several orders of magnitude. We comment on the generality of these ideas,
and we show how to extend them to the context of quantum tensor networks
Neural-Network Quantum States, String-Bond States, and Chiral Topological States
Neural-Network Quantum States have been recently introduced as an Ansatz for
describing the wave function of quantum many-body systems. We show that there
are strong connections between Neural-Network Quantum States in the form of
Restricted Boltzmann Machines and some classes of Tensor-Network states in
arbitrary dimensions. In particular we demonstrate that short-range Restricted
Boltzmann Machines are Entangled Plaquette States, while fully connected
Restricted Boltzmann Machines are String-Bond States with a nonlocal geometry
and low bond dimension. These results shed light on the underlying architecture
of Restricted Boltzmann Machines and their efficiency at representing many-body
quantum states. String-Bond States also provide a generic way of enhancing the
power of Neural-Network Quantum States and a natural generalization to systems
with larger local Hilbert space. We compare the advantages and drawbacks of
these different classes of states and present a method to combine them
together. This allows us to benefit from both the entanglement structure of
Tensor Networks and the efficiency of Neural-Network Quantum States into a
single Ansatz capable of targeting the wave function of strongly correlated
systems. While it remains a challenge to describe states with chiral
topological order using traditional Tensor Networks, we show that
Neural-Network Quantum States and their String-Bond States extension can
describe a lattice Fractional Quantum Hall state exactly. In addition, we
provide numerical evidence that Neural-Network Quantum States can approximate a
chiral spin liquid with better accuracy than Entangled Plaquette States and
local String-Bond States. Our results demonstrate the efficiency of neural
networks to describe complex quantum wave functions and pave the way towards
the use of String-Bond States as a tool in more traditional machine-learning
applications.Comment: 15 pages, 7 figure
Kinetically Constrained Quantum Dynamics in Superconducting Circuits
We study the dynamical properties of the bosonic quantum East model at low
temperature. We show that a naive generalization of the corresponding spin-1/2
quantum East model does not posses analogous slow dynamical properties. In
particular, conversely to the spin case, the bosonic ground state turns out to
be not localized. We restore localization by introducing a repulsive
interaction term. The bosonic nature of the model allows us to construct rich
families of many-body localized states, including coherent, squeezed and cat
states. We formalize this finding by introducing a set of superbosonic
creation-annihilation operators which satisfy the bosonic commutation relations
and, when acting on the vacuum, create excitations exponentially localized
around a certain site of the lattice. Given the constrained nature of the
model, these states retain memory of their initial conditions for long times.
Even in the presence of dissipation, we show that quantum information remains
localized within decoherence times tunable with the parameters of the system.
We propose an implementation of the bosonic quantum East model based on
state-of-the-art superconducting circuits, which could be used in the near
future to explore dynamical properties of kinetically constrained models in
modern platforms.Comment: 26 pages, 18 figures; improved Sec. IV, V and V
Speed-ups to isothermality: Enhanced quantum thermal machines through control of the system-bath coupling
Isothermal transformations are minimally dissipative but slow processes, as
the system needs to remain close to thermal equilibrium along the protocol.
Here, we show that smoothly modifying the system-bath interaction can
significantly speed up such transformations. In particular, we construct
protocols where the overall dissipation decays with the total
time of the protocol as , where each value can be obtained by a suitable
modification of the interaction, whereas corresponds to a standard
isothermal process where the system-bath interaction remains constant.
Considering heat engines based on such speed-ups, we show that the
corresponding efficiency at maximum power interpolates between the
Curzon-Ahlborn efficiency for and the Carnot efficiency for . Analogous enhancements are obtained for the coefficient of
performance of refrigerators. We confirm our analytical results with two
numerical examples where , namely the time-dependent
Caldeira-Leggett and resonant-level models, with strong system-environment
correlations taken fully into account. We highlight the possibility of
implementing our proposed speed-ups with ultracold atomic impurities and
mesoscopic electronic devices.Comment: 21 pages, 14 figures. Final author versio
A Rydberg platform for non-ergodic chiral quantum dynamics
We propose a mechanism for engineering chiral interactions in Rydberg atoms
via a directional antiblockade condition, where an atom can change its state
only if an atom to its right (or left) is excited. The scalability of our
scheme enables us to explore the many-body dynamics of kinetically constrained
models with unidirectional character. We observe non-ergodic behavior via
either scars, confinement, or localization, upon simply tuning the strength of
two driving fields acting on the atoms. We discuss how our mechanism persists
in the presence of classical noise and how the degree of chirality in the
interactions can be tuned, providing paths for investigating a wide range of
models.Comment: 5+3 pages, 3+1 figure
Mind the gap: Achieving a super-Grover quantum speedup by jumping to the end
We present a quantum algorithm that has rigorous runtime guarantees for
several families of binary optimization problems, including Quadratic
Unconstrained Binary Optimization (QUBO), Ising spin glasses (-spin model),
and -local constraint satisfaction problems (-CSP). We show that either
(a) the algorithm finds the optimal solution in time for an
-independent constant , a advantage over Grover's algorithm; or
(b) there are sufficiently many low-cost solutions such that classical random
guessing produces a approximation to the optimal cost value in
sub-exponential time for arbitrarily small choice of . Additionally, we
show that for a large fraction of random instances from the -spin model and
for any fully satisfiable or slightly frustrated -CSP formula, statement (a)
is the case. The algorithm and its analysis is largely inspired by Hastings'
short-path algorithm [ (2018) 78].Comment: 49 pages, 3 figure
Quantum East model: localization, non-thermal eigenstates and slow dynamics
We study in detail the properties of the quantum East model, an interacting
quantum spin chain inspired by simple kinetically-constrained models of
classical glasses. Through a combination of analytics, exact diagonalization
and tensor-network methods we show the existence of a transition, from a fast
to a slow thermalization regime, which manifests itself throughout the
spectrum. On the slow side, by exploiting the localization of the ground state
and the form of the Hamiltonian, we explicitly construct a large (exponential
in size) number of non-thermal states which become exact finite-energy-density
eigenstates in the large-size limit, as expected for a true phase transition. A
``super-spin'' generalization allows us to find a further large class of
area-law states proved to display very slow relaxation. These states retain
memory of their initial conditions for extremely long times. Our numerical
analysis reveals that the localization properties are not limited to the ground
state and that} many eigenstates have large overlap with product states and can
be approximated well by matrix product states at arbitrary energy densities.
The mechanism that induces localization to the ground state, and hence the
non-thermal behavior of the system, can be extended to a wide range of models
including a number of simple spin chains. We discuss implications of our
results for slow thermalization and non-ergodicity more generally in
disorder-free systems with constraints and we give numerical evidence that
these results may be extended to two dimensional systems.Comment: 21 pages, 16 figure