Quantum Computation and Information Seminar 

I will address the role of quantum effects in photosynthesis. Exploring individual pigment-protein complexes (LH2) of a purple bacterium with coherent fs pulses it is observed that ultrafast quantum coherent energy transfer occurs under physiological conditions. Surprisingly quantum coherences between electronically coupled energy eigen-states persist at least 400 fs, and distinct, time-varying energy transfer pathways can be identified in each complex. Interestingly the single molecule approach allows to track coherent phase jumps between different pathways, which suggest that long-lived quantum coherence renders energy transfer robust in the presence of disorder.

The photosynthetic antenna complexes are efficient in energy transfer, yet such complexes are not designed to emit light and thus hard to observe at the level of individual units. We have developed nanofabrication methods to couple single pigment complexes resonantly to a gold nanoantenna. This way the fluorescence decay speeds up from nanosecond to picosecond timescale, the quantum efficiency is enhanced and up to 1000 times more emission is collected. Using the bright photon emission, we revealed that the bacterial LH2 complex with 27 bacteriochlorophylls coordinated in two rings of chromophores shows photon anti-bunching at ambient conditions, i.e. a bacterial complex acting as a non-classical single-photon emitter.

Quantum annealing has been proposed as a means to solve optimization problems using the laws of quantum mechanics. Despite many publications confirming the presence of quantum effects, especially entanglement, in D-Wave quantum annealing processors, the question of whether such effects can lead to a performance advantage still remains open. In this presentation, I start with introducing quantum annealing in general and the D-Wave implementation of it in particular. After a short review of some benchmarking attempts, I present the recent experimental results obtained in collaboration with Google and NASA. The data from the D-Wave II processor installed in NASA Ames clearly show that the processor employs multi-qubit coherent and incoherent tunneling to outperform all classical annealing approaches, including simulated annealing, path integral Monte Carlo, and spin vector Monte Carlo. I end with a brief description of our theoretical modeling of open quantum dynamics and show agreement between theoretical predictions and the experimental data.

In this work the cooperative $N^2$-effect is considered, that is the radiation whose power is ~$N^2$, where $N$ is the number of emitters which in this case is equal to the number of nonlinear coupled oscillators which model the electrons in a bunch. We consider two different models: in first case the predicted effect is the result of combining two others, namely Gunn-effect in GaAs and undulator-like radiation which can be produced by means of microstructure with grating (microundulator). In the second case, suggested effect is in a sense similar to Dicke superradiance, however it is not the spontaneous phase coherence arising in the ensemble of two-level atoms interacting via the emitted electromagnetic field, but rather, the result of interplay of another two effects. The first one is the ’pumping wave’ acting on the electrons and which is the result of undulator field, while the second is the backward effect of radiation which is produced by elec trons moving within such microundulator. As a result, the specific phase coherence (’synchronization’) develops in the ensemble of emitters and they start to generate as a single oscillating charge Ne, while the power of emitted radiation becomes ~$N^2$. It is very probable, that the effect can be used for the developing of a new semiconductor-based room temperature sources of the GHz and THz-radiation.

Quantum communication via satellite based systems could enable quantum communications, such as Quantum Key Distribution, over truly global scales. Furthermore, they would allow us to perform quantum science experiments on entangled photons at scales and velocities not possible no the ground, which could be interesting in the quest towards understanding the boundary of quantum mechanics and space time. I will intrude the Canadian mission proposal called QEYSSAt (Quantum Encryption and Science Satellite) is considered as a possible microsatellite system, and will implement a quantum analyzer and detector in space.   I will present our progress towards implementing a prototype of the payload, as well as ground based test and analysis of the expected performance for quantum communication between ground and space.

Since the mid-nineties of the 20th century it became apparent that one of the centuries’ most important technological inventions, computers in general and many of their applications could possibly be further enormously enhanced by using operations based on quantum physics. This is timely since the classical roadmaps for the development of computational devices, commonly known as Moore’s law, will cease to be applicable within the next decade due to the ever smaller sizes of the electronic components that soon will enter the quantum physics realm. Computations, whether they happen in our heads or with any computational device, always rely on real physical processes, which are data input, data representation in a memory, data manipulation using algorithms and finally, the data output. Building a quantum computer then requires the implementation of quantum bits (qubits) as storage sites for quantum information, quantum registers and quantum gates for data handling and processing and the development of quantum algorithms.

In this talk, the basic functional principle of a quantum computer will be reviewed. It will be shown how strings of trapped ions can be used to build a quantum information processor and how basic computations can be performed using quantum techniques. In particular, the quantum way of doing computations will be illustrated by analog and digital quantum simulations and the basic scheme for quantum error correction will be introduced and discussed. Scaling-up the ion-trap quantum computer can be achieved with interfaces for ion-photon entanglement based on high-finesse optical cavities and cavity-QED protocols, which will be exemplified by recent experimental results.

Understanding non-equilibrium dynamics of many-body quantum systems is crucial for many fundamental and applied physics problems ranging from de-coherence and equilibration to the development of future quantum technologies such as quantum computers, which are inherently non-equilibrium quantum systems.

One of the biggest challenges in probing non-equilibrium dynamics of many-body quantum systems is that there is no general approach to characterize the resulting quantum states. Using the full distribution functions of a quantum observable [1,2], and the full phase correlation functions allows us to study the relaxation dynamics in one-dimensional quantum systems and to characterize the underlying many body states.

Interfering two isolated one-dimensional quantum gases we study how the coherence created between the two many body systems by the splitting process slowly dies by coupling to the many internal degrees of freedom available. Two distinct regimes are clearly visible: for short length scales the system is characterized by spin diffusion, for long length scales by spin decay [3]. The system approaches a pre-thermalized state [4], which is characterized by thermal like distribution functions but exhibits an effective temperature over five times lower than the kinetic temperature of the initial system.  A detailed study of the correlation functions reveals that these thermal-like properties emerge locally in their final form and propagate through the system in a light-cone-like evolution [5]. Furthermore we demonstrate that the pre-thermalized state is connected to a Generalized Gibbs Ensemble and that its higher order correlation functions factorize. Finally we show two distinct ways for subsequent evolution away from the pre-thermalized state. One proceeds by further de-phasing, the other by higher order phonon scattering processes.  In both cases the final state is indistinguishable from a thermally relaxed state.  We conjecture that our experiments points to a universal way through which relaxation in isolated many body quantum systems proceeds if the low energy dynamics is dominated by long lived excitations.

Supported by the Wittgenstein Prize, the Austrian Science Foundation (FWF) SFB FoQuS: F40-P10 and the EU through the ERC-AdG QuantumRelax

[1] A. Polkovnikov, et al. PNAS 103, 6125 (2006); V. Gritsev, et al., Nature Phys. 2, 705 (2006);
[2] S. Hofferberth et al. Nature Physics 4, 489 (2008);  
[3] M. Kuhnert et al. Phys. Rev. Lett 110, 090405 (2013);
[4] M. Gring et al., Science 337, 1318 (2012); D. Adu Smith et al. NJP 15, 075011 (2013);
[5] T. Langen et al. Nature Physics 9, 640–643 (2013).

A quantum phase transition may occur in the ground state of a system at zero temperature when a controlling field or interaction is varied. The resulting quantum fluctuations which trigger the transition produce scaling behavior of various observables, governed by universal critical exponents. A particularly interesting class of such transitions appear in systems with quantum impurities where a non-extensive term in the free energy becomes singular at the critical point. Curiously, the notion of a conventional order parameter which exhibits scaling at the critical point is generically missing in these systems. We here explore the possibility to use the Schmidt gap, which is an observable obtained from the entanglement spectrum, as an order parameter. A case study of the two-impurity Kondo model confirms that the Schmidt gap faithfully captures the scaling behavior by correctly predicting the critical exponent of the dynamically generated length scale at the critical point.

Since the pioneering work of Onsager and Ramsey in the 1940s and '50s, physical states at negative (absolute) temperatures have attracted the curiosity of researchers and shown how science can challenge common sense. In negative-temperature regimes, the temperature is above infinity and high-energy states are more populated than low-energy ones.

After many years elapsed since the first experimental evidences of negative temperatures in quantum nuclear-spin systems, recent experiments have realized a negative temperature state in a system of ultracold bosons trapped in optical lattice, modeled by a Bose-Hubbard Hamiltonian.

I will discuss the statistical behavior of a semi-classical limit of the Bose-Hubbard model, namely the Discrete Nonlinear Schroedinger Equation. By monitoring the microcanonical temperature, it is possible to show that there exists a parameter region where the system evolves towards a state characterized by a finite density of spatially localized nonlinear excitations (discrete breathers) and a negative temperature. Such a state persists over very long (astronomical) times since the convergence to equilibrium becomes increasingly slower as a consequence of a coarsening process.

I will also discuss possible mechanisms for the generation of negative-temperature states in experimental setups.

Commitment schemes are fundamental primitives in cryptography. In particular, a Bit Commitment (BC) scheme allows one user, Alice, to choose a bit value $b=\{0,1\}$, and upon request prove to a second user, Bob, that the value she chose was indeed b. The protocol is said to be secure if Alice is unable to change her mind once the choice is made, and Bob is unable to discover Alice’s choice until she willingly presents her proof. Unfortunately, there are no unconditionally secure BC protocols, meaning that the security of BC protocols relies on some assumptions. In the classical world, these assumptions are of computational nature. In this work, we present a BC protocol which makes use of quantum mechanical phenomena, and whose security is based on technological limitations rather than computational hardness. Furthermore, we carefully analyse the effects of noise throughout the entirety of the protocol, and prove that, in a sense, it is always advantageous for a cheating Alice to introduce extra noise prior to her measurements.

A promising platform for quantum information processing is that of silicon impurities, where the quantum states are manipulated by magnetic resonance. Such systems, in abstraction, can be considered as a nucleus of arbitrary spin coupled to an electron of spin one-half via an isotropic hype rfine interaction. We therefore refer to them as "nuclear-electronic spin systems". The traditional example, being subject to intensive experimental studies, is that of phosphorus doped silicon (Si:P) which couples a spin one-half electron to a nucleus of the same spin, with a hyperfine strength of 117.5 MHz. More recently, bismuth doped silicon (Si:Bi) has been suggested as an alternative instantiation of nuclear-electronic spin systems, differing from Si:P by its larger nuclear spin and hyperfine strength of 9/2 and 1.4754 GHz respectively. Here we develop a model that is capable of predicting the magnetic resonance properties of nuclear-electronic spin systems, which has proven to be in good agreement with experiments. Furthermore, we show that the larger nuclear spin and hyperfine strength of Si:Bi, compared with that of Si:P, offer advantages for quantum information processing by providing magnetic field-dependent two-dimensional decoherence free subspaces, called optimal working points or clock transitions, which have been identified to exist in Si:Bi, but not Si:P.

Optomechanics has attracted a lot of interest recently due to the combined control of light and mechanical modes. Spontaneous optomechanical self-organization was observed in a variety of non-linear systems such as atomic ensembles in a cavity [1].

We are looking in a single mirror scheme where a single pump beam and a mirror placed after the atomic cloud induce spontaneous self-organization observed on a plane transverse to the beam propagation. Previous investigations that showed continuous symmetry breaking on both translation and rotation relied on spatial modulation on the internal states of the atoms. Recently it was predicted that dipole forces alone could induce the same kind of transverse self-organization based on the atomic density without an intrinsic optical non-linearity [2]. We report on the observation of spontaneous self-structuring in cold atoms released from a magneto-optical trap [3]. Two mechanisms come into play in this experiment: the already known internal states non-linearity and the new optomechanical non-linearity. We identify regimes where each mechanism is dominant as well as the mixed case by comparing the structures in both the pump and in a probe beam sent a few tens of microseconds after pump extinction. In the optomechanical dominant regime, we observe in the probe the dynamical growth and decay of atomic structures in the order of magnitude comparable to the atomic motion at ultracold atoms temperatures.

References

1. H. Ritsch et al. Rev. Mod. Phys. 85, 553–601 (2013)
2. E. Tesio et al. Phys. Rev. A 86 031801(R) (2012)
3. G. Labeyrie et al. Nature Photon. 8 321–325 (2014)

Quantum decoherence is seen as an undesired source of irreversibility that destroys quantum resources. Quantum coherences are a property that vanishes at thermodynamic equilibrium. Away from equilibrium, quantum coherences challenge the classical notions of a thermodynamic bath in a Carnot engines, affect the efficiency of quantum transport, lead to violations of Fourier's law, and can be used to dynamically control the temperature of a state. However, the role of quantum coherence in thermodynamics is not fully understood.

We will show that the relative entropy of a state with quantum coherence with respect to its decohered state captures its deviation from thermodynamic equilibrium. As a result, changes in quantum coherence can lead to a heat flow with no associated temperature, and affect the entropy production rate. From this, we derive a quantum version of the Onsager reciprocal relations that shows that there is a reciprocal relation between thermodynamic forces from coherence and quantum transport. Quantum decoherence can be useful and offers new possibilities of thermodynamic control for quantum transport and to understand transport in photosynthetic complexes.

Under certain assumptions, it is possible to define for an open quantum system many key thermodynamic quantities, such as the internal energy, entropy, exchanged heat and work. By means of these quantities, the zeroth, first and second law of thermodynamics can also be given a consistent formulation.

A brief introduction on the dynamics of open quantum systems will be given, together with a review of the concepts of positivity and complete positivity in relation with entanglement.

Afterwards, it will be shown how to define the law of thermodynamics, and specifically the second one in terms of positivity of the internal entropy production, and the connections with complete positivity of the dynamics. Such techniques have been applied to a concrete case, namely a model for a quantum pumping process in a noisy environment. The master equation originally proposed for this model turns out to provide a non-completely positive dynamics, and it was found that, in certain conditions, this fact can lead to consequences from a thermodynamical point of view, such as violations of the second law.

Complete positivity, beside guaranteeing a physically consistent description when entanglement is taken into account, seems then to gain an important role in relation to thermodynamics.

We study quantum walks in different network structures. We model the quantum transport by a tight-binding hamiltonian with site-energies disorder, and the interaction with the environment by pure dephasing noise. Furthermore, we introduce losses and a trapping site in the structure and calculate numerically the transport efficiency to this site. We find that optimal efficiency is achieved when the time-scale associated with dephasing matches that of the site-to-site hopping.

The quantum-mechanical description of coherent light, as produced by lasers, gives rise to an intrinsic noise, known as quantum noise, optical noise or shot noise. Several protocols have been proposed to exploit this physical phenomenon to obtain secure data encryption and key distribution, including AlphaEta. Here we focus on the cryptographic aspects of a variant presented by Barbosa [PRA 2003] and propose an improvement, which is inspired on the concept of a pool of randomness as used by random bit generators in operating systems. This research in progress is a colaboration with Gabriel Almeida and Geraldo A. Barbosa.

In many areas of science (e.g. physics, chemistry, quantum information) controlled modification and in particular efficient transfer of population between quantum states is wanted. Many schemes are known that allow varying the usually thermal population distribution. Of particular interest are means for selective and efficient transfer of population from quantum state \(i\) to quantum state \(f\). “Efficient” means that nearly 100% of the population residing initially in state \(i\) reaches state \(f\). This also implies high selectivity as no other quantum state receives population. Traditional techniques such as Raman scattering, optical pumping or stimulated emission pumping fail to reach the goal. Spontaneous emission, which channels population into other levels,is a main problem. STIRAP solves that problem through a surprisingly simple, but at first glance very puzzling, sequence of radiative interactions: The quantum system is first exposed to the radiation field which connects the final state with an intermediate state (thus, it does not couple to the quantum state which carries initially the population) before the second radiation field couples the initial state to the same intermediate one. The basic phenomena and the physics building blocks of this process, the concept of which is now applied in very many areas, are presented and explained.

To create a useful quantum information process we always have to deal with the demons of decoherence and a highly demanding control. An answer to reduce the control needed in the qubits interaction is the use of scattering of one flying qubit with a static qubit. In a solid state scenario, the experimental development of quantum electron optics allows to manipulate the path of just one electron in a ballistic regime. In this way, the flying qubit can be implemented with a ballistic electron spin, and the static one with a magnetic impurity or a quantum dot spin. In this talk we discuss the very interesting advantages and the different disadvantages of this proposal. Then we show how the extraordinary properties of graphene, in particular the Klein tunnelling, could overcome this problems and help to implement low-error two-qubit logic gates.

In this talk I will present and discuss a few recent biophysics methodologies that have opened up the way to study a series of new biological questions ranging to single molecule studies to control of read out of neuronal network activity. The topics will include amongst others such-super resolution microscopy, single molecule techniques and optogenetics. I will introduce the basics of the methods followed by case examples of their application in specific biological or biophysical questions. In addition I will point out to a few recent developments a physics based approach to biological questions has led to the discovery of new principles that are now leading to the new field of quantum biology, where non-trivial quantum effects such as quantum coherence are thought to be generated through dynamic interactions with relevance for biological function.

We will cover two important notions in quantum cryptography and give their concrete examples: quantum hardcores and quantum public-key cryptosystems. 1) Hardcore functions have played an essential role in building a secure cryptosystem. They are closely associated with the list-decodability of certain codes. We establish a close relationship between quantum hardcore functions and quantum list-decoding. From three classical codes, we construct three new quantum hardcore functions for quantum one-way functions. 2) A private-key cryptosystem requires a large number of keys whereas a public-key cryptosystem needs only a single encoding key for all senders. To develop a large scale quantum network in a near future, it is thus desirable to build an efficient public-key quantum cryptosystem. We present the first quantum public-key cryptosystem that withstands any eavesdropper’s chosen plaintext quantum attack if a certain graph-theoretic problem cannot be solved efficiently by quantum computers.

Integrated photonic circuits have a strong potential to perform quantum information processing. Indeed, the ability to manipulate quantums states of light by integrated devices may open new perspectives both for fundamental tests of quantum mechanics and for novel technological applications. Within this framework we have developed a directional coupler, fabricated by femtosecond laser waveguide writing, acting as an integrated beam splitter able to support polarization-encoded qubits. As following step we addressed the implementation of quantum walk. This represents one of the most promising resources for the simulation of physical quantum systems, and has also emerged as an alternative to the standard circuit model for quantum computing. Up to now the experimental implementations have been restricted to single particle quantum walk, while very recently the quantum walks of two identical photons have been reported. For the first time, we investigated how the particle statistics, either bosonic or fermionic, influences a two-particle discrete quantum walk. Such experiment has been realized by adopting two-photon entangled states and integrated photonic circuits. As following step we have exploited this technology to simulate the evolution for disordered quantum systems observing how the particle statistics influences Anderson localization. Finally we will discuss the perspectives of optical quantum simulation: the implementation of the boson sampling to demonstrate the computational capability of quantum systems and the development of integrated architecture with three-dimensional geometries.