GLORIA

GEOMAR Library Ocean Research Information Access

X

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften  (4)
  • 2015-2019  (4)
Material
Publisher
  • Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften  (4)
Person/Organisation
Language
Years
  • 2015-2019  (4)
Year
  • 1
    Online Resource
    Online Resource
    Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
    Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften ; 2019
    In:  Quantum Vol. 3 ( 2019-05-20), p. 142-
    Details
    In: Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 3 ( 2019-05-20), p. 142-
    Abstract: Quantum phases of matter are resources for notions of quantum computation. In this work, we establish a new link between concepts of quantum information theory and condensed matter physics by presenting a unified understanding of symmetry-protected topological (SPT) order protected by subsystem symmetries and its relation to measurement-based quantum computation (MBQC). The key unifying ingredient is the concept of quantum cellular automata (QCA) which we use to define subsystem symmetries acting on rigid lower-dimensional lines or fractals on a 2D lattice. Notably, both types of symmetries are treated equivalently in our framework. We show that states within a non-trivial SPT phase protected by these symmetries are indicated by the presence of the same QCA in a tensor network representation of the state, thereby characterizing the structure of entanglement that is uniformly present throughout these phases. By also formulating schemes of MBQC based on these QCA, we are able to prove that most of the phases we construct are computationally universal phases of matter, in which every state is a resource for universal MBQC. Interestingly, our approach allows us to construct computational phases which have practical advantages over previous examples, including a computational speedup. The significance of the approach stems from constructing novel computationally universal phases of matter and showcasing the power of tensor networks and quantum information theory in classifying subsystem SPT order.
    Type of Medium: Online Resource
    ISSN: 2521-327X
    URL: Journal
    URL: Article
    DOI: 10.22331/q
    DOI: 10.22331/q-2019-05-20-142
    Language: English
    Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
    Publication Date: 2019
    detail.hit.zdb_id: 2931392-2
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Online Resource
  • 2
    Online Resource
    Online Resource
    Anticoncentration theorems for schemes showing a quantum speedup
    Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften ; 2018
    In:  Quantum Vol. 2 ( 2018-05-22), p. 65-
    Details
    In: Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 2 ( 2018-05-22), p. 65-
    Abstract: One of the main milestones in quantum information science is to realise quantum devices that exhibit an exponential computational advantage over classical ones without being universal quantum computers, a state of affairs dubbed quantum speedup, or sometimes "quantum computational supremacy". The known schemes heavily rely on mathematical assumptions that are plausible but unproven, prominently results on anticoncentration of random prescriptions. In this work, we aim at closing the gap by proving two anticoncentration theorems and accompanying hardness results, one for circuit-based schemes, the other for quantum quench-type schemes for quantum simulations. Compared to the few other known such results, these results give rise to a number of comparably simple, physically meaningful and resource-economical schemes showing a quantum speedup in one and two spatial dimensions. At the heart of the analysis are tools of unitary designs and random circuits that allow us to conclude that universal random circuits anticoncentrate as well as an embedding of known circuit-based schemes in a 2D translation-invariant architecture.
    Type of Medium: Online Resource
    ISSN: 2521-327X
    URL: Journal
    URL: Article
    DOI: 10.22331/q
    DOI: 10.22331/q-2018-05-22-65
    Language: English
    Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
    Publication Date: 2018
    detail.hit.zdb_id: 2931392-2
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Online Resource
  • 3
    Online Resource
    Online Resource
    The boundaries and twist defects of the color code and their applications to topological quantum computation
    Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften ; 2018
    In:  Quantum Vol. 2 ( 2018-10-19), p. 101-
    Details
    In: Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 2 ( 2018-10-19), p. 101-
    Abstract: The color code is both an interesting example of an exactly solved topologically ordered phase of matter and also among the most promising candidate models to realize fault-tolerant quantum computation with minimal resource overhead. The contributions of this work are threefold. First of all, we build upon the abstract theory of boundaries and domain walls of topological phases of matter to comprehensively catalog the objects realizable in color codes. Together with our classification we also provide lattice representations of these objects which include three new types of boundaries as well as a generating set for all 72 color code twist defects. Our work thus provides an explicit toy model that will help to better understand the abstract theory of domain walls. Secondly, we discover a number of interesting new applications of the cataloged objects for quantum information protocols. These include improved methods for performing quantum computations by code deformation, a new four-qubit error-detecting code, as well as families of new quantum error-correcting codes we call stellated color codes, which encode logical qubits at the same distance as the next best color code, but using approximately half the number of physical qubits. To the best of our knowledge, our new topological codes have the highest encoding rate of local stabilizer codes with bounded-weight stabilizers in two dimensions. Finally, we show how the boundaries and twist defects of the color code are represented by multiple copies of other phases. Indeed, in addition to the well studied comparison between the color code and two copies of the surface code, we also compare the color code to two copies of the three-fermion model. In particular, we find that this analogy offers a very clear lens through which we can view the symmetries of the color code which gives rise to its multitude of domain walls.
    Type of Medium: Online Resource
    ISSN: 2521-327X
    URL: Journal
    URL: Article
    DOI: 10.22331/q
    DOI: 10.22331/q-2018-10-19-101
    Language: English
    Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
    Publication Date: 2018
    detail.hit.zdb_id: 2931392-2
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Online Resource
  • 4
    Online Resource
    Online Resource
    Guaranteed recovery of quantum processes from few measurements
    Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften ; 2019
    In:  Quantum Vol. 3 ( 2019-08-12), p. 171-
    Details
    In: Quantum, Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften, Vol. 3 ( 2019-08-12), p. 171-
    Abstract: Quantum process tomography is the task of reconstructing unknown quantum channels from measured data. In this work, we introduce compressed sensing-based methods that facilitate the reconstruction of quantum channels of low Kraus rank. Our main contribution is the analysis of a natural measurement model for this task: We assume that data is obtained by sending pure states into the channel and measuring expectation values on the output. Neither ancillary systems nor coherent operations across multiple channel uses are required. Most previous results on compressed process reconstruction reduce the problem to quantum state tomography on the channel's Choi matrix. While this ansatz yields recovery guarantees from an essentially minimal number of measurements, physical implementations of such schemes would typically involve ancillary systems. A priori, it is unclear whether a measurement model tailored directly to quantum process tomography might require more measurements. We establish that this is not the case.Technically, we prove recovery guarantees for three different reconstruction algorithms. The reconstructions are based on a trace, diamond, and ℓ 2 -norm minimization, respectively. Our recovery guarantees are uniform in the sense that with one random choice of measurement settings all quantum channels can be recovered equally well. Moreover, stability against arbitrary measurement noise and robustness against violations of the low-rank assumption is guaranteed. Numerical studies demonstrate the feasibility of the approach.
    Type of Medium: Online Resource
    ISSN: 2521-327X
    URL: Journal
    URL: Article
    DOI: 10.22331/q
    DOI: 10.22331/q-2019-08-12-171
    Language: English
    Publisher: Verein zur Forderung des Open Access Publizierens in den Quantenwissenschaften
    Publication Date: 2019
    detail.hit.zdb_id: 2931392-2
    Location Call Number Limitation Availability
    BibTip Others were also interested in ...
    Online Resource
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...