42 research outputs found
Efficient learning of the structure and parameters of local Pauli noise channels
The unavoidable presence of noise is a crucial roadblock for the development
of large-scale quantum computers and the ability to characterize quantum noise
reliably and efficiently with high precision is essential to scale quantum
technologies further. Although estimating an arbitrary quantum channel requires
exponential resources, it is expected that physically relevant noise has some
underlying local structure, for instance that errors across different qubits
have a conditional independence structure. Previous works showed how it is
possible to estimate Pauli noise channels with an efficient number of samples
in a way that is robust to state preparation and measurement errors, albeit
departing from a known conditional independence structure.
We present a novel approach for learning Pauli noise channels over n qubits
that addresses this shortcoming. Unlike previous works that focused on learning
coefficients with a known conditional independence structure, our method learns
both the coefficients and the underlying structure. We achieve our results by
leveraging a groundbreaking result by Bresler for efficiently learning Gibbs
measures and obtain an optimal sample complexity of O(log(n)) to learn the
unknown structure of the noise acting on n qubits. This information can then be
leveraged to obtain a description of the channel that is close in diamond
distance from O(poly(n)) samples. Furthermore, our method is efficient both in
the number of samples and postprocessing without giving up on other desirable
features such as SPAM-robustness, and only requires the implementation of
single qubit Cliffords. In light of this, our novel approach enables the
large-scale characterization of Pauli noise in quantum devices under minimal
experimental requirements and assumptions.Comment: 8 Pages, 1 Figur
Learning quantum many-body systems from a few copies
Estimating physical properties of quantum states from measurements is one of
the most fundamental tasks in quantum science. In this work, we identify
conditions on states under which it is possible to infer the expectation value
of all quasi-local observables of a given locality up to a relative error from
a number of samples that grows polylogarithmically with system size and
polynomially on the locality of the target observables. This constitutes an
exponential improvement over known tomography methods in some regimes. We
achieve our results by combining one of the most well-established techniques to
learn quantum states, the maximum entropy method, with techniques from the
emerging fields of quantum optimal transport and classical shadows. We
conjecture that our condition holds for all states exhibiting some form of
decay of correlations and establish it for several subsets thereof. These
include widely studied classes of states such as one-dimensional thermal and
gapped ground states and high-temperature Gibbs states of local commuting
Hamiltonians on arbitrary hypergraphs. Moreover, we show improvements of the
maximum entropy method beyond the sample complexity of independent interest.
These include identifying regimes in which it is possible to perform the
postprocessing efficiently and novel bounds on the condition number of
covariance matrices of many-body states.Comment: 37 pages, 3 figure
A game of quantum advantage: linking verification and simulation
We present a formalism that captures the process of proving quantum
superiority to skeptics as an interactive game between two agents, supervised
by a referee. Bob, is sampling from a classical distribution on a quantum
device that is supposed to demonstrate a quantum advantage. The other player,
the skeptical Alice, is then allowed to propose mock distributions supposed to
reproduce Bob's device's statistics. He then needs to provide witness functions
to prove that Alice's proposed mock distributions cannot properly approximate
his device. Within this framework, we establish three results. First, for
random quantum circuits, Bob being able to efficiently distinguish his
distribution from Alice's implies efficient approximate simulation of the
distribution. Secondly, finding a polynomial time function to distinguish the
output of random circuits from the uniform distribution can also spoof the
heavy output generation problem in polynomial time. This pinpoints that
exponential resources may be unavoidable for even the most basic verification
tasks in the setting of random quantum circuits. Beyond this setting, by
employing strong data processing inequalities, our framework allows us to
analyse the effect of noise on classical simulability and verification of more
general near-term quantum advantage proposals.Comment: 44 pages, to be published in Quantum. New version is substantially
extended and contains new connections between previous results and the linear
cross entrop
Efficient classical simulation and benchmarking of quantum processes in the Weyl basis
One of the crucial steps in building a scalable quantum computer is to
identify the noise sources which lead to errors in the process of quantum
evolution. Different implementations come with multiple hardware-dependent
sources of noise and decoherence making the problem of their detection
manyfoldly more complex. We develop a randomized benchmarking algorithm which
uses Weyl unitaries to efficiently identify and learn a mixture of error models
which occur during the computation. We provide an efficiently computable
estimate of the overhead required to compute expectation values on outputs of
the noisy circuit relying only on locality of the interactions and no further
assumptions on the circuit structure. The overhead decreases with the noise
rate and this enables us to compute analytic noise bounds that imply efficient
classical simulability. We apply our methods to ansatz circuits that appear in
the Variational Quantum Eigensolver and establish an upper bound on classical
simulation complexity as a function of noise, identifying regimes when they
become classically efficiently simulatable
Lower Bounds on Learning Pauli Channels
Understanding the noise affecting a quantum device is of fundamental
importance for scaling quantum technologies. A particularly important class of
noise models is that of Pauli channels, as randomized compiling techniques can
effectively bring any quantum channel to this form and are significantly more
structured than general quantum channels. In this paper, we show fundamental
lower bounds on the sample complexity for learning Pauli channels in diamond
norm with unentangled measurements. We consider both adaptive and non-adaptive
strategies. In the non-adaptive setting, we show a lower bound of
to learn an -qubit Pauli channel. In
particular, this shows that the recently introduced learning procedure by
Flammia and Wallman is essentially optimal. In the adaptive setting, we show a
lower bound of for
, and a lower bound of
for any . This last lower bound
even applies for arbitrarily many sequential uses of the channel, as long as
they are only interspersed with other unital operations
Group transference techniques for the estimation of the decoherence times and capacities of quantum Markov semigroups
Capacities of quantum channels and decoherence times both quantify the extent
to which quantum information can withstand degradation by interactions with its
environment. However, calculating capacities directly is known to be
intractable in general. Much recent work has focused on upper bounding certain
capacities in terms of more tractable quantities such as specific norms from
operator theory. In the meantime, there has also been substantial recent
progress on estimating decoherence times with techniques from analysis and
geometry, even though many hard questions remain open. In this article, we
introduce a class of continuous-time quantum channels that we called
transferred channels, which are built through representation theory from a
classical Markov kernel defined on a compact group. We study two subclasses of
such kernels: H\"ormander systems on compact Lie-groups and Markov chains on
finite groups. Examples of transferred channels include the depolarizing
channel, the dephasing channel, and collective decoherence channels acting on
qubits. Some of the estimates presented are new, such as those for channels
that randomly swap subsystems. We then extend tools developed in earlier work
by Gao, Junge and LaRacuente to transfer estimates of the classical Markov
kernel to the transferred channels and study in this way different
non-commutative functional inequalities. The main contribution of this article
is the application of this transference principle to the estimation of various
capacities as well as estimation of entanglement breaking times, defined as the
first time for which the channel becomes entanglement breaking. Moreover, our
estimates hold for non-ergodic channels such as the collective decoherence
channels, an important scenario that has been overlooked so far because of a
lack of techniques.Comment: 35 pages, 2 figures. Close to published versio
On contraction coefficients, partial orders and approximation of capacities for quantum channels
The data processing inequality is the most basic requirement for any
meaningful measure of information. It essentially states that
distinguishability measures between states decrease if we apply a quantum
channel. It is the centerpiece of many results in information theory and
justifies the operational interpretation of most entropic quantities. In this
work, we revisit the notion of contraction coefficients of quantum channels,
which provide sharper and specialized versions of the data processing
inequality. A concept closely related to data processing are partial orders on
quantum channels. We discuss several quantum extensions of the well known less
noisy ordering and then relate them to contraction coefficients. We further
define approximate versions of the partial orders and show how they can give
strengthened and conceptually simple proofs of several results on approximating
capacities. Moreover, we investigate the relation to other partial orders in
the literature and their properties, particularly with regards to
tensorization. We then investigate further properties of contraction
coefficients and their relation to other properties of quantum channels, such
as hypercontractivity. Next, we extend the framework of contraction
coefficients to general f-divergences and prove several structural results.
Finally, we consider two important classes of quantum channels, namely
Weyl-covariant and bosonic Gaussian channels. For those, we determine new
contraction coefficients and relations for various partial orders.Comment: 47 pages, 2 figure
Provably Efficient Learning of Phases of Matter via Dissipative Evolutions
The combination of quantum many-body and machine learning techniques has
recently proved to be a fertile ground for new developments in quantum
computing. Several works have shown that it is possible to classically
efficiently predict the expectation values of local observables on all states
within a phase of matter using a machine learning algorithm after learning from
data obtained from other states in the same phase. However, existing results
are restricted to phases of matter such as ground states of gapped Hamiltonians
and Gibbs states that exhibit exponential decay of correlations. In this work,
we drop this requirement and show how it is possible to learn local expectation
values for all states in a phase, where we adopt the Lindbladian phase
definition by Coser \& P\'erez-Garc\'ia [Coser \& P\'erez-Garc\'ia, Quantum 3,
174 (2019)], which defines states to be in the same phase if we can drive one
to other rapidly with a local Lindbladian. This definition encompasses the
better-known Hamiltonian definition of phase of matter for gapped ground state
phases, and further applies to any family of states connected by short unitary
circuits, as well as non-equilibrium phases of matter, and those stable under
external dissipative interactions. Under this definition, we show that samples suffice to learn local
expectation values within a phase for a system with qubits, to error
with failure probability . This sample complexity is
comparable to previous results on learning gapped and thermal phases, and it
encompasses previous results of this nature in a unified way. Furthermore, we
also show that we can learn families of states which go beyond the Lindbladian
definition of phase, and we derive bounds on the sample complexity which are
dependent on the mixing time between states under a Lindbladian evolution.Comment: 19 pages, 3 figures, 21 page appendi