# 22nd Symposium on Quantum Information: Titles&Abstracts

## Vodola

**Qubit losses in topological quantum codes**

Quantum information is the generalisation of the classical information theory to quantum systems. If for a classical computer the bits are the fundamental units, quantum computers are built on quantum bits currently implemented in different physical systems (atoms, ions, molecules, Josephson junctions). However, these setups are so delicate that qubits can be corrupted by environmental noise and even be completely lost from the apparatus resulting in the partial or total loss of the information there memorised. In this talk, we will consider how losses can affect a particular class of quantum codes (the so-called color codes). We introduce a protocol for dealing with losses and we show that checking whether the logical information is still recoverable is equivalent to a generalised percolation process. We numerically compute the associated qubit loss thresholds and show that color codes are robust against qubit loss.

## Adesso

**Generic Emergence of Objectivity of Observables in Infinite Dimensions**

Phys. Rev. Lett. **121**, 160401 (2018)

Quantum Darwinism posits that information becomes objective whenever multiple observers indirectly probe a quantum system by each measuring a fraction of the environment. It was recently shown that objectivity of observables emerges generically from the mathematical structure of quantum mechanics, whenever the system of interest has finite dimensions and the number of environment fragments is large [F. G. S. L. Brandão, M. Piani, and P. Horodecki, Nat. Commun. **6**, 7908 (2015)]. Despite the importance of this result, it necessarily excludes many practical systems of interest that are infinite dimensional, including harmonic oscillators. Extending the study of quantum Darwinism to infinite dimensions is a nontrivial task: we tackle it here by using a modified diamond norm, suitable to quantify the distinguishability of channels in infinite dimensions. We prove two theorems that bound the emergence of objectivity, first for finite mean energy systems, and then for systems that can only be prepared in states with an exponential energy cutoff. We show that the latter class includes any bounded-energy subset of single-mode Gaussian states.

## Coecke

**Quantum compilation and natural language processing in one picture**

For well over a decade, we developed an entirely pictorial (and of course, formally rigorous) presentation of quantum theory [1], and it was recently shown that graphical reasoning by means of ZX-calculus can reproduce all equational reasoning in Hilbert space [2a, 2b]. In practical terms, it is currently for example being used as the core of quantum compilation [3], as it allows for easy translation between different computational models, allows for automation, and has outperformed any other method for circuit reduction. At the present, experiments are also being setup aimed at establishing the age at which children could effectively learn quantum theory in this manner. Meanwhile, the pictorial language has also been successful in the study of natural language [4] which induces new quantum algorithms [5], and we have started to apply it to model cognition, where we employ GPT-alike models [6]. In a recent development we are able to assign meaning to entire texts, which then looks like a quantum circuit, that reduces to a ZX-like diagram.

References:

We present the key ingredients of the pictorial language language as well as their interpretation across disciplines, and the applications mentioned above.

[1] BC & A. Kissinger (2017) Picturing Quantum Processes. A first course on quantum theory and diagrammatic reasoning. Cambridge University Press.

[2a] E. Jeandel, S. Perdrix & R. Vilmart (2017) A Complete Axiomatisation of the ZX-Calculus for Clifford+T Quantum Mechanics. arXiv:1705.11151

[2b] K. F. Ng & Q. Wang (2017) A universal completion of the ZX-calculus. arXiv:1706.09877

[3] https://cambridgequantum.com/2017/10/20/collaboration-with-university-of-oxford-computer-science-department/

[4] S. Clark, BC, E. Grefenstette, S. Pulman & M. Sadrzadeh (2013) A quantum teleportation inspired algorithm produces sentence meaning from word meaning and grammatical structure. arXiv:1305.0556

[5] W. Zeng & BC (2016) Quantum Algorithms for Compositional Natural Language Processing. arXiv:1608.01406

[6] J. Bolt, BC, F. Genovese, M. Lewis, D. Marsden & R. Piedeleu (2017) Interacting Conceptual Spaces I : Grammatical Composition of Concepts. arXiv:1703.08314

## Lamacraft

**Simulating unitary circuits of finite depth and infinite width with quantum channels**

We introduce a numerical approach simulate unitary circuits of finite depth and infinite width. The unitary dynamics is encoded in a (sequence of) quantum channels acting on an ancilla space. The spectra of the reduced density matrices of a half-infinite region and the ancilla coincide, allowing for efficient evaluation of the entanglement spectrum and Rényi entropies. We benchmark our method on random unitary circuits, where many analytic results are available.

## Bausch

**Undecidability of the Spectral Gap in One Dimension
**arXiv:1810.01858

The spectral gap problem – determining whether the energy spectrum of a system has an energy gap above ground state, or if there is a continuous range of low-energy excitations – pervades quantum many-body physics. Recently, this important problem was shown to be undecidable for quantum systems in two (or more) spatial dimensions: it is provably impossible to determine in general whether a system is gapped or gapless, a result which has many unexpected consequences for the physics of such systems. However, there are many indications that one dimensional systems are simpler than their higher-dimensional counterparts: for example, they cannot have thermal phase transitions or topological order, and there exist highly-effective numerical algorithms such as DMRG for gapped 1D systems, exploiting the fact that such systems obey an entropy area-law. Furthermore, the spectral gap undecidability construction crucially relied on aperiodic tilings, which are easily seen to be impossible in 1D. So does the spectral gap problem become decidable in 1D? In this paper we prove this is not the case, by constructing a family of 1D spin chains with translationally-invariant nearest neighbour interactions with undecidable spectral gap. This not only proves that the spectral gap of 1D systems is just as intractable, but also predicts the existence of qualitatively new types of complex physics in 1D spin chains. In particular, it implies there are 1D systems with constant spectral gap and unique classical ground state for all systems sizes up to an uncomputably large size, whereupon they switch to a gapless behaviour with dense spectrum.

## Wallden

**A single-device, device-independent pseudo-secret random qubits
**based on joint work with A. Cojocaru, L. Colisson and E. Kashefi arXiv:1802.08759

Abstract: We define the functionality of delegated pseudo-secret random qubit generator (PSRQG), where a classical client can instruct the preparation of a sequence of random qubits at some distant party. Their classical description is (computationally) unknown to any other party (including the distant party preparing them) but known to the client. We emphasize the unique feature that no quantum communication is required to implement PSRQG. Due to the fact that only the distant party has a quantum device, we can view such protocol as a single-device, device-independent protocol. The role of non-locality is replaced by the computational intractability of certain problems. We give a concrete protocol realising this functionality based on the hardness of the learning-with-errors problem. This enables classical clients to perform a class of quantum communication protocols with only a public classical channel with a quantum server. Important examples of such protocols include blind quantum computation, verifiable quantum computation and secure multiparty quantum computation.