76 research outputs found
Optimal resource cost for error mitigation
We provide a general methodology for evaluating the optimal resource cost for
an error mitigation employing methods developed in resource theories. We
consider the probabilistic error cancellation as an error mitigation technique
and show that the optimal sampling cost realizable using the full
expressibility of near-term devices is related to a resource quantifier
equipped with a framework in which noisy implementable operations are
considered as the free resource, allowing us to obtain its universal bounds. As
applications, we show that the cost for mitigating the depolarizing noise
presented in [Temme, Bravyi, and Gambetta, Phys. Rev. Lett. 119, 180509 (2017)]
is optimal, and extend the analysis to several other classes of noise model, as
well as provide generic bounds applicable to general noise channels given in a
certain form. Our results not only provide insights into the potential and
limitations on feasible error mitigation on near-term devices but also display
an application of resource theories as a useful theoretical toolkit.Comment: 5+7 page
Diagonal quantum discord
Quantum discord measures quantum correlation by comparing the quantum mutual
information with the maximal amount of mutual information accessible to a
quantum measurement. This paper analyzes the properties of diagonal discord, a
simplified version of discord that compares quantum mutual information with the
mutual information revealed by a measurement that correspond to the eigenstates
of the local density matrices. In contrast to the optimized discord, diagonal
discord is easily computable; it also finds connections to thermodynamics and
resource theory. Here we further show that, for the generic case of
non-degenerate local density matrices, diagonal discord exhibits desirable
properties as a preferable discord measure. We employ the theory of resource
destroying maps [Liu/Hu/Lloyd, PRL 118, 060502 (2017)] to prove that diagonal
discord is monotonically nonincreasing under the operation of local discord
nongenerating qudit channels, , and provide numerical evidence that such
monotonicity holds for qubit channels as well. We also show that it is
continuous, and derive a Fannes-like continuity bound. Our results hold for a
variety of simple discord measures generalized from diagonal discord.Comment: 15 pages, 3 figures; published versio
Universal fault-tolerant gates on concatenated stabilizer codes
It is an oft-cited fact that no quantum code can support a set of
fault-tolerant logical gates that is both universal and transversal. This no-go
theorem is generally responsible for the interest in alternative universality
constructions including magic state distillation. Widely overlooked, however,
is the possibility of non-transversal, yet still fault-tolerant, gates that
work directly on small quantum codes. Here we demonstrate precisely the
existence of such gates. In particular, we show how the limits of
non-transversality can be overcome by performing rounds of intermediate
error-correction to create logical gates on stabilizer codes that use no
ancillas other than those required for syndrome measurement. Moreover, the
logical gates we construct, the most prominent examples being Toffoli and
controlled-controlled-Z, often complete universal gate sets on their codes. We
detail such universal constructions for the smallest quantum codes, the 5-qubit
and 7-qubit codes, and then proceed to generalize the approach. One remarkable
result of this generalization is that any nondegenerate stabilizer code with a
complete set of fault-tolerant single-qubit Clifford gates has a universal set
of fault-tolerant gates. Another is the interaction of logical qubits across
different stabilizer codes, which, for instance, implies a broadly applicable
method of code switching.Comment: 18 pages + 5 pages appendix, 12 figure
Convex resource theory of non-Gaussianity
Continuous-variable systems realized in quantum optics play a major role in quantum information processing, and it is also one of the promising candidates for a scalable quantum computer. We introduce a resource theory for continuous-variable systems relevant to universal quantum computation. In our theory, easily implementable operations—Gaussian operations combined with feed-forward—are chosen to be the free operations, making the convex hull of the Gaussian states the natural free states. Since our free operations and free states cannot perform universal quantum computation, genuine non-Gaussian states—states not in the convex hull of Gaussian states—are the necessary resource states for universal quantum computation together with free operations. We introduce a monotone to quantify the genuine non-Gaussianity of resource states, in analogy to the stabilizer theory. A direct application of our resource theory is to bound the conversion rate between genuine non-Gaussian states. Finally, we give a protocol that probabilistically distills genuine non-Gaussianity—increases the genuine non-Gaussianity of resource states—only using free operations and postselection on Gaussian measurements, where our theory gives an upper bound for the distillation rate. In particular, the same protocol allows the distillation of cubic phase states, which enable universal quantum computation when combined with free operations.United States. Air Force Office of Scientific Research (Grant FA9550-14-1-0052
One-shot manipulation of dynamical quantum resources
We develop a unified framework to characterize one-shot transformations of
dynamical quantum resources in terms of resource quantifiers, establishing
universal conditions for exact and approximate transformations in general
resource theories. Our framework encompasses all dynamical resources
represented as quantum channels, including those with a specific structure --
such as boxes, assemblages, and measurements -- thus immediately applying in a
vast range of physical settings. For the particularly important manipulation
tasks of distillation and dilution, we show that our conditions become
necessary and sufficient for broad classes of important theories, enabling an
exact characterization of these tasks and establishing a precise connection
between operational problems and resource monotones based on entropic
divergences. We exemplify our results by considering explicit applications to:
quantum communication, where we obtain exact expressions for one-shot quantum
capacity and simulation cost assisted by no-signalling,
separability-preserving, and positive partial transpose-preserving codes; as
well as to nonlocality, contextuality, and measurement incompatibility, where
we present operational applications of a number of relevant resource measures.Comment: 5+10 pages. Made some changes in presentation and added minor
clarifications. Accepted in Physical Review Letter
Alchemy of quantum coherence: Arbitrary amplification in asymptotic and catalytic coherence manipulation
Quantum coherence is one of the fundamental aspects distinguishing classical
and quantum theories. Coherence between different energy eigenstates is
particularly important, as it serves as a valuable resource under the law of
energy conservation. A fundamental question in this setting is how well one can
prepare good coherent states from low coherent states and whether a given
coherent state is convertible to another one. Here, contrarily to intuitions
and previous expectations, we show that any low coherent state is convertible
to any high coherent state arbitrarily well, implying that one can increase the
amount of quantum coherence inexhaustibly. We demonstrate this remarkable
phenomenon in two operational settings: asymptotic and catalytic
transformations. For a variant of asymptotic coherence manipulation, the rate
of transformation becomes unbounded regardless of how weak the initial
coherence is. This particularly shows that the infinite rate of coherence
distillation can be accomplished for all coherent states. In a non-asymptotic
transformation with a catalyst -- a helper state that locally remains in the
original form after the transformation, we show that an arbitrary state can be
obtained from any low coherent states. Our protocol avoids the barrier of
quantum coherence in state conversion and allows us to amplify quantum
coherence infinitely. On its opposite side, we show that the aforementioned
amplification requires small but non-zero coherence, characterizing the
condition under which the anomalous power of coherence transformation is
enabled.Comment: 7+20 pages, 3 figure
Benchmarking one-shot distillation in general quantum resource theories
We study the one-shot distillation of general quantum resources, providing a
unified quantitative description of the maximal fidelity achievable in this
task, and revealing similarities shared by broad classes of resources. We
establish fundamental quantitative and qualitative limitations on resource
distillation applicable to all convex resource theories. We show that every
convex quantum resource theory admits a meaningful notion of a pure maximally
resourceful state which maximizes several monotones of operational relevance
and finds use in distillation. We endow the generalized robustness measure with
an operational meaning as an exact quantifier of performance in distilling such
maximal states in many classes of resources including bi- and multipartite
entanglement, multi-level coherence, as well as the whole family of affine
resource theories, which encompasses important examples such as asymmetry,
coherence, and thermodynamics.Comment: 8+5 pages, 1 figure. v3: fixed (inconsequential) error in Lemma 1
Fundamental limitations on distillation of quantum channel resources
Quantum channels underlie the dynamics of quantum systems, but in many
practical settings it is the channels themselves that require processing. We
establish universal limitations on the processing of both quantum states and
channels, expressed in the form of no-go theorems and quantitative bounds for
the manipulation of general quantum channel resources under the most general
transformation protocols. Focusing on the class of distillation tasks -- which
can be understood either as the purification of noisy channels into unitary
ones, or the extraction of state-based resources from channels -- we develop
fundamental restrictions on the error incurred in such transformations and
comprehensive lower bounds for the overhead of any distillation protocol. In
the asymptotic setting, our results yield broadly applicable bounds for rates
of distillation. We demonstrate our results through applications to
fault-tolerant quantum computation, where we obtain state-of-the-art lower
bounds for the overhead cost of magic state distillation, as well as to quantum
communication, where we recover a number of strong converse bounds for quantum
channel capacity.Comment: 15+25 pages, 4 figures. v3: close to published version (changes in
presentation, title modified; main results unaffected). See also related work
by Fang and Liu at arXiv:2010.1182
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