# Quantum Computation and Information Seminar

## Past sessions

### Approaches for Error Mitigation in Quantum Computing and Sensing

Current digital or logic-gate-based quantum computers and, indeed, those that will emerge within the next few years or so have limited numbers (20-200) of noisy qubits. This period has been dubbed the “noisy intermediate-scale quantum” era or NISQ era. Since fault-tolerant error correction procedures involve many physical qubits representing each logical qubit, it is difficult or not possible to apply them to non-trivial algorithms running on NISQ era computers. It is possible, however, to develop error mitigation strategies that either do not involve any extra qubits or perhaps just a limited number of extra ones. These approaches effectively replace the additional error-correcting qubits with additional runs of the quantum algorithm and extrapolation ideas. Such approaches also apply to estimates of quantum observables in general, including quantum sensing protocols such as Ramsey fringe measurements. Two such approaches developed by us are discussed.

This work was performed at the Center for Nanoscale Materials, a U.S. Department of Energy Office of Science User Facility, and supported by the U.S. Department of Energy, Office of Science, under Contract No. DE-AC02-06CH11357.

### Light-matter entanglement over 50km of optical fibre

When shared between remote locations, entanglement opens up fundamentally new capabilities for science and technology. Envisioned quantum networks use light to distribute entanglement between their remote matter-based quantum nodes. In this short talk, I will present our observation of entanglement between matter (a trapped ion) and light (a photon) over 50 km of optical fibre [1]: two orders of magnitude further than the state of the art and a practical distance to start building large-scale quantum networks. Our methods include an efficient source of ion-photon entanglement via cavity-QED techniques (0.5 probability on-demand fibre-coupled photon from the ion) and a single photon quantum frequency converter to the 1550 nm telecom C band (0.25 fibre-coupled device efficiency). Modestly optimising and duplicating our system could allow for 100 km-spaced ion-ion entanglement at rates over 1 Hz. Our results therefore show a path to entangling remote registers of quantum-logic capable trapped-ion qubits, and the optical atomic clock transitions that they contain, spaced by hundreds of kilometres.

1. Krutyanskiy, M. Meraner, J. Schupp, V. Krcmarsky, H. Hainzer, B. P. Lanyon. Light-matter entanglement over 50 km of optical fiber, arXiv:1901.06317.

The talk takes place in Sala de Formação Avançada, 2nd floor of the Physics Department building

### Quantum Simulation with quantum computers

In this seminar I will do 3 things.

First, I will review why the quantum many-body problem is very important and I will discuss the concept of exponential wall, that makes it intractable with conventional computing.

Second, I will discuss the use of digital quantum computers to tackle the many body problem. Specifically, I will review how the phase estimation algorithm can be used to obtain the eigenvalues of a very large class of Hamiltonians, including those of interest in the many body problem.

Finally, I will show our attempts to carry out actual quantum computations for quantum simulation of three simple model Hamiltonians (Zeeman, Ising, Hubbard) using IBM quantum hardware. I will discuss in some detail our approach for post-processing analysis and the challenges for digital quantum simulation with state of the art hardware.

### Continuous-time quantum walks in graphs

Quantum walks have been around for some time now, and there are just too many questions one could ask about them. In this talk, I shall focus on questions related to transport tasks in qubit networks modelled by simple graphs. We eventually hope to have a full understanding on how exactly the combinatorics of the graph might affect the quantum properties, but we will see that we are still very far away from achieving this goal — even for very simple questions.

### Information-theoretic key agreement and classical bound entanglement

Suppose Alice and Bob want to agree on a shared key which they want to keep secret from Eve, who can eavesdrop on their communication and has unlimited computational power. Towards this goal, we assume that all parties have access to correlated randomness. This is the setting of (classical) information-theoretic key agreement, which has been notoriously difficult to understand.

I will start by presenting some seminal results in this area. Then, I will briefly discuss a recent work where we characterize the asymptotic behavior of the secret-key rate (which measures how efficiently Alice and Bob can create shared secret bits) in an alternative setting where the honest parties can optimize the distribution of correlated randomness under some constraint. In contrast, even approximating the secret-key rate in the original setting with non-trivial correlated randomness appears to be a very hard problem.

In the second part, I will focus on a conjecture with strong ties to the concept of bound entanglement from quantum information theory.

Namely, the conjecture asks whether “bound information” exists: Are there distributions of correlated randomness that “contain” secret bits which cannot be extracted via a key agreement protocol? In particular, it is believed that bound entangled quantum states lead to such classical distributions. To conclude, I will discuss how NOT to show bound information exists.

(Partially based on joint work with Daniel Jost and Ueli Maurer, ETH Zurich)

### Quantum-Proof Blockchain

Blockchain technology is now going through explosive development with the aim to build a new generation of revolutionary financial technology. The most successful example is new digital currency bitcoin. The fundamental building block in blockchain technology is actually cryptographic algorithms, which is why bitcoin is actually called a cryptocurrency. The main cryptographic algorithms used in blockchain technology are hash functions and elliptic curve digital signatures. As we all know, quantum computers are not such a significant threat to the security of Hash functions but it can be fatal to the elliptic curve digital signatures. In this presentation, we will first show how the quantum computers can threat the security of blockchain technology, in particular, why the existing blockchain technology used in bitcoins can not fundamentally avoid such a practical attack. Then we will explain the challenges we will face if if we just plug in existing post-quantum cryptographic solutions as a drop-in to replace the existing elliptic curve signatures, in particular, the key size problem and a few others. In the end, we will present some of the new solutions we have been developing to deal with these fundamental problems including a new type of proof of work algorithms, which, we believe, provide very viable solutions for the future long term secure blockchain technology.

### Classifying Quantum Entanglement through Topological Links

We present a classification scheme for quantum entanglement based on topological links. This is done by identifying a nonrigid ring to a particle, attributing the act of cutting and removing a ring to the operation of tracing out the particle, and associating linked rings to entangled particles. This analogy naturally leads us to a classification of multipartite quantum entanglement based on all possible distinct links for any given number of rings. We demonstrate the use of this new classification scheme for three and four qubits and its potential in the context of qubit networks.

### Seeing earthquakes and distributing entanglement on the international telecoms network

Detecting ocean-floor seismic activity is crucial for our understanding of the interior structure and dynamic behaviour of the Earth. However, 70% of the planet’s surface is covered by water and seismometers coverage is limited to a handful of permanent ocean bottom stations.

In the first part of this talk I discuss our recent results [1], where we showed that existing telecommunication optical fibre cables can detect seismic events when combined with state-of-the-art frequency metrology techniques by using the fibre itself as the sensing element. We detected earthquakes over terrestrial and submarine links with length ranging from 75 to 535 km and a geographical distance from the earthquake's epicentre ranging from 25 to 18,500 km. Implementing a global seismic network for real-time detection of underwater earthquakes requires applying the proposed technique to the existing extensive submarine optical fibre network.

In the second part of the talk I will discuss briefly how we distributed entanglement between Malta and Sicily [2] over the telecommunications network using polarisation-entangled photon pairs.

Note: Joint session with the Physics of Information Seminar.

### Engineering Quantum Causes

Are cause and effect objective facts about the world? Many philosophers doubt it. Physicists ground causation objectively in terms of Lorentz invariance: a central feature of quantum field theory. Yet the pioneers of quantum mechanics lamented the demise of classical causality and the violation of various Bell-like inequalities raise new questions. Nonetheless, advancing quantum communication technologies seek to exploit non classical quantum correlations to perform tasks impossible in a classical world. Quantum information theorists have recently discovered new quantum causal relations beyond Bell, yet the physical meaning of this discovery remains unclear. In this talk I will review some of the recent theories on classical and quantum causation and explain how ion trap quantum technologies might be used to engineer novel causal relations in a laboratory setting.

Joint session with the Physics of Information Colloquium.

### D-Wave's Approach to Quantum Computing

Quantum computing promises to revolutionize computer technology as profoundly as the airplane revolutionized transportation. After dec ades of incubation, early generation quantum computers are finally appearing that allow people to begin experimentation in earnest. In this talk, I will describe D-Wave's approach to quantum computing, explain its pros and cons with respect to competing schemes, and give the rationale behind our design choices. Furthermore, I will give examples of how the native optimization and sampling capabilities of our quantum processor can be exploited to tackle problems in a variety of fields including healthcare, physics, finance, simulation, artificial intelligence, and machine learning.

### Mixing it up with atomic mixtures

Mixtures of ultracold atomic gases are an extremely versatile platform for the investigation of a wide variety of fundamental questions in ph ysics. In this talk, we will discuss first discuss their realization as done in our lab. We will then present their possible application to two rather distinct problems, the quantum simulation of dynamical gauge fields and the implementation of quantum heat engines.

### On Shannon entropy in quantum phase space : from entropic uncertainty relations to continuous majorization relations

Shannon differential entropy is a na tural uncertainty measure when considering a continuous-spectrum observable, such as a quadrature component of a mode of the electromagnetic field. I will show that it makes a very useful — though not yet fully explored — tool for the phase-space description of light. After a short survey on the entropic uncertainty relations generalizing the Heisenberg principle with differential entropies instead of variances, I will emphasize the notion of entropy power in this context and formulate new entropic uncertainty relations expressing the balance between multimode Gaussian projective measurements. This will lead me to discuss the differential entropy of a Wigner function, which, for states with non-negative such functions, yields a perfect uncertainty measure that is invariant under all Gaussian unitaries (symplectic transformations and displacements) and is saturated by all Gaussian pure states. I will then consider entropy-power inequalities for a beam splitter and finally discuss some conjectured continuous-variable majorization relations in phase space.

### Quantum and classical thermodynamic machines: work, power, cooling

Heat engine efficiency is limited by the Carnot bound. However, Scully et al. [Science 299, 862(2003)] bypassed this bound by allowing for extra heat input, and hence a higher hot-bath temperature, via coherence in the working fluid. In recent years, squeezed thermal baths have been claimed to yield extra heat input and hence surpass the Carnot bound [Rossnagel et al., PRL 112, 030602 (2014)]. However, the latter claim is unfounded, since squeezed baths transfer not just heat but also work to the working fluid, as shown by us [Gelbwaser-Klimovsky et al., NJP 18, 083012 (2016)]. Consequently, such engines are no longer heat engines but more like mechanical engines, and hence the Carnot bound is irrelevant to them. We have recently formulated a universal theory of any quantum or classical machines, fueled by arbitrary heat and work reservoirs [W. Niedenzu et al., Nature Commun. (2017)], which shows that what counts for maximal efficiency is the minimal loss of energy to the cold bath, which may be completely different from a Carnot bound if the baths are non-thermal. The crucial feature that allows for maximal work and power is maximized non-passivity (ergotropy) of the working fluid and/or the piston, as shown by us lately for a heat engine whose piston is squeezed by a pump [A. Ghosh et al., PNAS 2017]. Analogous considerations apply to cooling / refrigeration performance.

### The Emergence of Complex Quantum Networks

Complex network theory and quantum physics are being brought together to define and study a new subject: complex quantum networks.

But what exactly are complex quantum networks? And can they play a role in our understanding of fundamental science?

And what is their role in quantum technologies, namely in quantum computation and in quantum communications?

In this talk I will discuss what we know so far and what challenges lie ahead in this novel research domain.

Joint session with the Symposium on Complex Networks: from Classical to Quantum.

### How correspondents in orbit may realise Quantum Communications with ground and why

The paradigm shift that Quantum Communications represent vs. classical counterpart allows envisaging the global application of Quantum Information protocols as the cryptographic key distribution as well as of the use of the qubits as a probe for fundamental tests of Quantum Mechanics and Gravity on a scale beyond terrestrial limits.

Quantum Communications on planetary scale require complementary channels including ground and satellite links. As the former have progressed up to commercial stage using fiber-cables, it's crucial the study of links for space QC and eventually the demonstration of protocols such as quantum-key-distribution (QKD) and quantum teleportation along satellite-to-ground or intersatellite links.

We shall report on the extension of the Quantum Communications and Technologies to long distances, on the surface of the Earth as well as from the Earth to an orbiting terminal in Space. This is influenced by hurdles as the large losses, the effects on the optical propagation of the turbulent medium and the relative motion of terminals. Nevertheless, it was possible to demonstrate the Quantum Communications with Low-Earth-Orbit satellites using polarization degree of freedom to encode the qubits.

Temporal modes were used to demonstrate the quantum interference along a Space channel will be also described.

The recent results on the extension to Space of the Gedanken experiment proposed by John Wheeler on the wave-particle duality, then about the very nature of the quantum entities, will be described.

### On the Security of Semi-Quantum Key Distribution

A semi-quantum key distribution protocol is presented and its proof of security is detailed.

### Tests of Quantum Mechanics and Gravitation with Atom Interferometry

Recent de Broglie wave interference experiments with atoms have achieved wavepacket separations as large as 54 cm over time intervals of 2 sec. These experiments, and their impact on gravitational and quantum physics, will be discussed.

Joint session with the Physics of Information Colloquium and Lisbon Training Workshop on Quantum Technologies in Space.

### Navigating a Maze Using Quantum-Walk Searches

Quantum searches are used to localize a specific element within the Hilbert space. Usually such element is a base state, or a small subspace of the Hilbert space. We expand this set by searching for a path in a maze between two specific vertices using quantum walks. A particular type of maze we use is a chain of connected stars. We show, that having $M$ stars, each of them containing $N$ spikes, we can find the whole path in $O(M N^{1/2})$ steps. Standard choice of the initial state in a large, albeit phase-modulated superposition leads to the usual Grover search. However, such state is usually hard to prepare and a choice of a localized state is preferred. In such case we show, that it is possible to find the path with the same efficiency (up to a multiplicative constant) successively, by starting on the first star and uncovering successive stars by short searches of $O(N^{1/2})$ steps.

### Quantum communication onboard the International Space Station

Models of quantum systems on curved space-times lack sufficient experimental verification. Some speculative theories suggest that quantum properties, such as entanglement, may exhibit entirely different behavior to purely classical systems. By measuring this effect or lack thereof, we can test the hypotheses behind several such models. For instance, as predicted by Ralph and coworkers [T C Ralph, G J Milburn, and T Downes, Phys. Rev. A, 79(2):22121, 2009, T C Ralph and J Pienaar, New Journal of Physics, 16(8):85008, 2014], a bipartite entangled system could decohere if each particle traversed through a different gravitational field gradient. We propose to study this effect in a ground to space uplink scenario. We extend the above theoretical predictions of Ralph and coworkers and discuss the scientific consequences of detecting/failing to detect the predicted gravitational decoherence. We present a detailed mission design of the European Space Agency's (ESA) Space QUEST (Space - Quantum Entanglement Space Test) mission, and study the feasibility of the mission schema.

### Effect of acceleration on quantum states

In this talk, we discuss the influence of acceleration on quantum states. We start by studying the effects of acceleration on fermionic Gaussian states of localized modes of a Dirac field. Thereby we formulate the action of the transformation to an accelerated frame as a fermionic quantum channel and discuss the entanglement of the vacuum, as well as the entanglement in Bell states. After that, we discuss collective dynamics of accelerated atoms interacting with a massless scalar field via an Unruh-deWitt type interaction. Therefore, we derive the general Hamiltonian describing such a system and employ a Markovian master equation. In particular, we report the emergence of superradiance and entanglement between two-level atoms. Finally, we briefly outline a proposal for an experimental setup for a quantum simulation of this system using Bose-Einstein condensates.

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Supported by: Phys-Info (IT), SQIG (IT), CeFEMA and CAMGSD, with funding from FCT, FEDER and EU FP7, specifically through the Doctoral Programme in the Physics and Mathematics of Information (DP-PMI), FCT strategic projects PEst-OE/EEI/LA0008/2013 and UID/EEA/50008/2013, IT project QuSim, project CRUP-CPU CQVibes, the FP7 Coordination Action QUTE-EUROPE (600788), and the FP7 projects Landauer (GA 318287) and PAPETS (323901).