54 research outputs found
Bell sampling from quantum circuits
A central challenge in the verification of quantum computers is benchmarking
their performance as a whole and demonstrating their computational
capabilities. In this work, we find a model of quantum computation, Bell
sampling, that can be used for both of those tasks and thus provides an ideal
stepping stone towards fault-tolerance. In Bell sampling, we measure two copies
of a state prepared by a quantum circuit in the transversal Bell basis. We show
that the Bell samples are classically intractable to produce and at the same
time constitute what we call a circuit shadow: from the Bell samples we can
efficiently extract information about the quantum circuit preparing the state,
as well as diagnose circuit errors. In addition to known properties that can be
efficiently extracted from Bell samples, we give two new and efficient
protocols, a test for the depth of the circuit and an algorithm to estimate a
lower bound to the number of T gates in the circuit. With some additional
measurements, our algorithm learns a full description of states prepared by
circuits with low T -count.Comment: 5+14 pages, 2 figures. Comments welcom
Entanglement structure of current-driven diffusive fermion systems
When an extended system is coupled at its opposite boundaries to two
reservoirs at different temperatures or chemical potentials, it cannot achieve
a global thermal equilibrium and is instead driven to a set of current-carrying
nonequilibrium states. Despite the broad relevance of such a scenario to
metallic systems, there have been limited investigations of the entanglement
structure of the resulting long-time states, in part, due to the fundamental
difficulty in solving realistic models for disordered, interacting electrons.
We investigate this problem by carefully analyzing two "toy" models for
coherent quantum transport of diffusive fermions: the celebrated
three-dimensional, noninteracting Anderson model and a class of random quantum
circuits acting on a chain of qubits, which exactly maps to a diffusive,
interacting fermion problem. Crucially, the random circuit model can also be
tuned to have no interactions between the fermions, similar to the Anderson
model. We show that the long-time states of driven noninteracting fermions
exhibit volume-law mutual information and entanglement, both for our random
circuit model and for the nonequilibrium steady-state of the Anderson model.
With interactions, the random circuit model is quantum chaotic and approaches
local equilibrium, with only short-range entanglement. These results provide a
generic picture for the emergence of local equilibrium in current-driven
quantum-chaotic systems, and also provide examples of stable, highly-entangled
many-body states out of equilibrium. We discuss experimental techniques to
probe these effects in low-temperature mesoscopic wires or ultracold atomic
gases.Comment: v5: 32 pages, 11 figures, note adde
Correlated photon dynamics in dissipative Rydberg media
Rydberg blockade physics in optically dense atomic media under the conditions
of electromagnetically induced transparency (EIT) leads to strong dissipative
interactions between single photons. We introduce a new approach to analyzing
this challenging many-body problem in the limit of large optical depth per
blockade radius. In our approach, we separate the single-polariton EIT physics
from Rydberg-Rydberg interactions in a serialized manner while using a
hard-sphere model for the latter, thus capturing the dualistic particle-wave
nature of light as it manifests itself in dissipative Rydberg-EIT media. Using
this approach, we analyze the saturation behavior of the transmission through
one-dimensional Rydberg-EIT media in the regime of non-perturbative dissipative
interactions relevant to current experiments. Our model is able to capture the
many-body dynamics of bright, coherent pulses through these strongly
interacting media. We compare our model with available experimental data in
this regime and find good agreement. We also analyze a scheme for generating
regular trains of single photons from continuous-wave input and derive its
scaling behavior in the presence of imperfect single-photon EIT.Comment: Final version. 6 pages, 4 figures (+ Supplemental Material; 7 pages,
3 figures
Scalable probes of measurement-induced criticality
We uncover a local order parameter for measurement-induced phase transitions:
the average entropy of a single reference qubit initially entangled with the
system. Using this order parameter, we identify scalable probes of
measurement-induced criticality (MIC) that are immediately applicable to
advanced quantum computing platforms. We test our proposal on a 1+1 dimensional
stabilizer circuit model that can be classically simulated in polynomial time.
We introduce the concept of a "decoding light cone" to establish the local and
efficiently measurable nature of this probe. We also estimate bulk and surface
critical exponents for the transition. Developing scalable probes of MIC in
more general models may be a useful application of noisy-intermediate scale
quantum (NISQ) devices, as well as point to more efficient realizations of
fault-tolerant quantum computation.Comment: 6 pages, 3 figures, v2 added Figure 2 and supplemen
Localization as an entanglement phase transition in boundary-driven Anderson models
The Anderson localization transition is one of the most well studied examples
of a zero temperature quantum phase transition. On the other hand, many open
questions remain about the phenomenology of disordered systems driven far out
of equilibrium. Here we study the localization transition in the prototypical
three-dimensional, noninteracting Anderson model when the system is driven at
its boundaries to induce a current carrying non-equilibrium steady state.
Recently we showed that the diffusive phase of this model exhibits extensive
mutual information of its non-equilibrium steady-state density matrix. We show
that that this extensive scaling persists in the entanglement and at the
localization critical point, before crossing over to a short-range (area-law)
scaling in the localized phase. We introduce an entanglement witness for
fermionic states that we name the mutual coherence, which, for fermionic
Gaussian states, is also a lower bound on the mutual information. Through a
combination of analytical arguments and numerics, we determine the finite-size
scaling of the mutual coherence across the transition. These results further
develop the notion of entanglement phase transitions in open systems, with
direct implications for driven many-body localized systems, as well as
experimental studies of driven-disordered systems.Comment: 5 pages, 2 figures, and supplemen
High-Order Multipole Radiation from Quantum Hall States in Dirac Materials
We investigate the optical response of strongly disordered quantum Hall
states in two-dimensional Dirac materials and find qualitatively different
effects in the radiation properties of the bulk versus the edge. We show that
the far-field radiation from the edge is characterized by large multipole
moments (> 50) due to the efficient transfer of angular momentum from the
electrons into the scattered light. The maximum multipole transition moment is
a direct measure of the coherence length of the edge states. Accessing these
multipole transitions would provide new tools for optical spectroscopy and
control of quantum Hall edge states. On the other hand, the far-field radiation
from the bulk appears as random dipole emission with spectral properties that
vary with the local disorder potential. We determine the conditions under which
this bulk radiation can be used to image the disorder landscape. Such optical
measurements can probe sub-micron length scales over large areas and provide
complementary information to scanning probe techniques. Spatially resolving
this bulk radiation would serve as a novel probe of the percolation transition
near half-filling.Comment: v2: 8 pages, 4 figure
Thresholds in the Robustness of Error Mitigation in Noisy Quantum Dynamics
Extracting useful information from noisy near-term quantum simulations
requires error mitigation strategies. A broad class of these strategies rely on
precise characterization of the noise source. We study the robustness of such
strategies when the noise is imperfectly characterized. We adapt an Imry-Ma
argument to predict the existence of a threshold in the robustness of error
mitigation for random spatially local circuits in spatial dimensions : noise characterization disorder below the threshold rate allows for error
mitigation up to times that scale with the number of qubits. For
one-dimensional circuits, by contrast, mitigation fails at an
time for any imperfection in the characterization of disorder. As a result,
error mitigation is only a practical method for sufficiently well-characterized
noise. We discuss further implications for tests of quantum computational
advantage, fault-tolerant probes of measurement-induced phase transitions, and
quantum algorithms in near-term devices.Comment: 11 pages, 4 figure
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