Quantum Computation and Information Seminar 

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.

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.

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.

We introduce the concept of degree of quantumness in quantum synchronization, a measure of the quantum natu re of synchronization in quantum systems. Following techniques from quantum information to quantify the quantumness of a dynamics, we propose a measure based on the number of non-commuting observables that synchronize. The degree of quantumness is compatible with already existing synchronization measurements, and it captures different physical properties. We illustrate the definition in a quantum system consisting of two weakly interacting cavity-qubit systems, which are coupled via the exchange of bosonic excitations between the cavities, and the synchronization of the expectation values of the Pauli operators is studied. We additionally propose a feasible superconducting circuit system in which the experiment can be carried out. Finally, we briefly discuss the degree of quantumness in the synchronization between two quantum van der Pol oscillators.

Two quantum emitters, embedded in a linear waveguide, can relax towards bound states for resonant values of the interatomic distance. The stability of such states is studied, and their relevance for entanglement generation is analyzed.

We shall also discuss the role of quantum simulators. They are more focused than quantum computers, and easier to build. They can solve fundamental problems that are untractable by classical hardware. Like quantum computers, simulators simultaneously perform a number of computations by exploiting the superposition principle and entanglement. This is known as quantum parallelism and can lead to an exponential speedup of performance.

We consider the example of a discrete Abelian gauge theory, towards the realization of a quantum simulator for QED in one dimension. We analyze the role of the finiteness of the gauge fields and the properties of physical states, satisfying Gauss’s law.

Over the last decade, rapid developments in quantum optomechanics have led to an increasing level of control of mechanical systems down to the quantum level using a variety of system architectures. Possible applications range from quantum transducers, quantum memories and high-precision sensors to novel tests of the foundations of physics. In my talk, I will discuss recent developments in quantum optomechanics using trapped dielectric particles, the potential of using photonic crystals for particle trapping and control as well as developments towards future tests of the foundations of physics.

Technology based on memristors, resistors with memory whose resistance depends on the hist ory of the crossing charges, has lately enhanced the classical paradigm of computation with neuromorphic architectures. However, in contrast to the known quantized models of passive circuit elements, such as inductors, capacitors or resistors, the design and realization of a quantum memristor was still missing. Here, we introduce the concept of a quantum memristor as a quantum dissipative device, whose decoherence mechanism is controlled by a continuous-measurement feedback scheme, which accounts for the memory. Indeed, we provide numerical simulations showing that memory effects actually persist in the quantum regime. Our quantization method, specifically designed for superconducting circuits, may be extended to other quantum platforms, allowing for memristor-type constructions in different quantum technologies. The proposed quantum memristor is then, in the framework of quantum biomimetics, a building block for quantum neural network, quantum machine learning, quantum simul ations of non-Markovian systems and, in the long term, neuromorphic quantum computation.

I will introduce the concept of embedding quantum simulators, which allow for the implementation of unphysical ope rations in the lab. For instance, the complex conjugation of an unknown quantum state, a forbidden antilinear operation in quantum physics, could be realized via the use of an auxiliary qubit. This opens the possibility for measuring entanglement of an evolving quantum system with few observables and without the necessity of full tomography. Finally, I will explain how to adapt these ideas to different quantum platforms as trapped ions and superconducting circuits, among others.

The ability to distribute secret keys between two parties with information-theoretic security, that is regardless of the capacities of a malevolent eavesdropper, is one of the most celebrated results in the field of quantum information processing and communication. Indeed, quantum key distribution illustrates the power of encoding information on the quantum properties of light and has far-reaching implications in high-security applications. Today, quantum key distribution systems operate in real-world conditions and are commercially available. As with most quantum information protocols, quantum key distribution was first designed for qubits, the individual quanta of information. However, the use of quantum continuous variables for this task presents important advantages with respect to qubit-based protocols, in particular from a practical point of view, since it allows for simple implementations that require only standard telecommunication technology.

In this talk, I will explain the principle of continuous-variable quantum key distribution and explain how to prove security for such protocols.

Reference: Entropy 17, 6072-6092 (2015), arXiv:1506.02888

By analyzing the key properties of black holes from the point of view of quantum information, we derive a model-independent picture of black hole quantum computing. It has been noticed that this picture exhibits striking similarities with quantum critical condensates, allowing the use of a common language to describe quantum computing in both systems. We analyze such quantum computing by allowing coupling to external modes, under the condition that the external influence must be soft-enough in order not to offset the basic properties of the system. We derive model-independent bounds on some crucial time-scales, such as the times of gate operation, decoherence, maximal entanglement and total scrambling. We show that for black hole type quantum computers all these time-scales are of the order of the black hole half-life time. Furthermore, we construct explicitly a set of Hamiltonians that generates a universal set of quantum gates for the black hole type computer. We find that the gates work at maximal energy efficiency. Furthermore, we establish a fundamental bound on the complexity of quantum circuits encoded on these systems, and characterize the unitary operations that are implementable. It becomes apparent that the computational power is very limited due to the fact that the black hole life-time is of the same order of the gate operation time. As a consequence, it is impossible to retrieve its information, within the life-time of a black hole, by externally coupling to the black hole qubits. However, we show that, in principle, coupling to some of the internal degrees of freedom allows acquiring knowledge about the micro-state. Still, due to the trivial complexity of operations that can be performed, there is no time advantage over the collection of Hawking radiation and subsequent decoding.

I will describe two architectures, quantum annealers and quantum circuits, that the Quantum AI team at Google is currently developing in order to accelerate tasks important for AI. Quantum annealers are a promising tool to find good solutions to hard combinatorial optimization problems. In recent benchmarking we were able to demonstrate that finite range quantum tunneling enables the D-Wave 2X quantum annealer to solve crafted benchmark problems $10^8$ times faster than thermal annealing that does not employ tunneling. We are now studying whether speedups are also available for generic problems such as Boolean satisfiability problems and find this is indeed the case. I will discuss the implications of these studies for the design of next generation quantum annealers. The second class of quantum processors we are developing are quantum circuits. Those were initially devised as an architecture to achieve digital error corrected quantum computation. In the near term however when the number of physical qubits is still small quantum circuits have to be operated as an analog device. Yet, with high fidelity gate operations and low measurement error it is possible to achieve quantum supremacy over all known classical algorithms with just about 50 qubits. The talk will conclude with an outlook how to apply quantum resources to enhance artificial intelligence. As an example of how to use quantum annealing in machine learning, I will describe learning from very noisy data. Using the quantum circuits we implemented what could be described as a quantum neural network. In a first application, we used such a circuit to calculate the energy surface of molecular hydrogen to chemical precision.

Atomic-scale logic and the minimization of heating (dissipation) are both very high on the agenda for future computation hardware. An approach to achieve these would be to replace networks of transistors directly by classical reversible logic gates built from the coherent dynamics of a few interacting atoms. Thus motivated, we show methods to realize the 3-bit Toffoli and Fredkin gates universal for classical reversible logic using a single time-independent 3-qubit Hamiltonian with realistic nearest neighbour two-body interactions. We also exemplify how these gates can be composed to make a larger circuit. We show that trapped ions may soon be scalable simulators for such architectures, and investigate the prospects with dopants in silicon.

Furthermore, we propose to use an array of large-spin quantum magnets for realizing a device which has two modes of operation: memory and data-bus. While the weakly interacting low-energy levels are used as memory to store classical information (bits), the high-energy levels strongly interact with neighboring magnets and mediate the spatial movement of information through quantum dynamics.

We investigate the prospects for using a spin chain of length $N$ as a probe for refrigeration and thermometry on a collection of identical qubits, all prepared in a thermal state $\chi(T)$ with temperature $T$. This requires a minimal degree of control -– one need only perform a swap operation between a single spin of the probe and the thermal qubits. Each swap operation either cools the thermal qubit, or leaves it the same, and the state of the probe incrementally gets closer to $\chi(T)\otimes N$. It is this latter property, which we call pseudo-thermalisation, that allows the probe to be used for thermometry. By measuring each spin with the observable for the thermal qubits' Hamiltonian, the statistics can be used to infer $T$ up to some arbitrary accuracy. We then propose an algorithm which, provided prior knowledge of $T$ and the dynamics of the probe, will allow for optimising the cooling process. We show that the presence of local dephasing on the spins, or an imperfection of the swap operation, reduces the entropy reduction possible and slows the rate of pseudo-thermalisation. However, the thermal qubits always remain thermal, with a temperature no greater than $T$.

The physics of many-body systems strongly depends on their dimensionality. With the realization of quantum wells for example, it has been possible to produce two-dimensional gases of electrons, which exhibit properties that dramatically differ from the standard three-dimensional case, some of them still lacking a full understanding.

During the last decade, a novel environment has been developed for the study of low-dimensional phenomena. It consists of cold atomic gases that are confined in tailor-made electromagnetic traps. The talk will discuss some experimental aspects of this research, including dynamical features like the emergence of coherence in the gas when it is rapidly cooled across the superfluid transition.

We discuss progress towards the development of on-chip quantum networks of multiple spin qubits in nitrogen vacancy (NV) centers in diamond. This talk will describe NV-nanocavity systems in the strong Purcell regime with optical quality factors approaching 10,000 and electron spin coherence times approaching milliseconds; implantation of NVs with nanometer-scale apertures into the cavity field maximum; hybrid on-chip networks for integration of multiple functional NV-cavity systems; and techniques for high-yield integration of superconducting nanowire single photon detectors on-chip. 

There is great interest in designing photonic devices capable of disorder-resistant transport and information processing. In this work we propose to exploit 3D integrated photonic circuits in order to realize 2D discrete-time quantum walks in a background synthetic gauge field, for both the single and many walker case. The gauge fields are generated by introducing the appropriate phase shifts between waveguides. Polarization-independent phase shifts lead to an Abelian or magnetic field, a case we describe in detail. We find that, in the disordered case, the magnetic field enhances transport due to the presence of topologically protected chiral edge states which do not localize. Polarization-dependent phase shifts lead to effective non-Abelian gauge fields, which could be adopted to realize Rashba-like quantum walks with spin-orbit coupling. Our work introduces a flexible platform for the experimental study of multi-particle quantum walks in the presence o f synthetic gauge fields, which paves the way towards topologically robust transport of many-body states of photons.

Continuous observation of an oscillator results in quantum back-action, which limits the knowledge acquired by the measurement. A careful balance between the information obtained and the back-action disturbance leads to the standard quantum limit of precision. This limit can be surpassed by a measurement with strength modulated at twice the oscillator frequency, resulting in a squeezed state of the oscillator motion, as proposed decades ago by Braginsky and colleagues. We have recently implemented such a measurement experimentally using a collective spin of an atomic ensemble precessing in a magnetic field as an oscillator [1]. The oscillator initially prepared nearly in the ground state is stroboscopically coupled to an optical mode of a cavity. A measurement of the output light results in a 2.2 dB squeezed state of the oscillator. The demonstrated spin-squeezed state of 10⁸ atoms with an angular spin variance of 8∙10^-10 rad² allowed us to achieve 150 femtoT/√Hz magnetic field sensitivity.

An even more striking notion is the back-action evasion in both quadratures for the continuous measurement on a mechanical oscillator entangled with the atomic spin oscillator [2]. Such measurement does not violate quantum mechanics, but still provides a way to detect disturbances on the oscillator trajectory which are way below those set by the standard Heisenberg uncertainty bound by using a negative mass reference system [3]. Experimental demonstration of this ABATE (Atomic Back-action Eater) principle will be discussed.

References

[1] G. Vasilakis, H. Shen, K. Jensen, M. Balabas, D. Salart, B. Chen, and E. S. Polzik. Nature Physics, doi:10.1038/nphys3280 (2015).

[2] K. Hammerer, M. Aspelmeyer, E.S. Polzik, P. Zoller.  Phys. Rev. Lett. 102, 020501 (2009).

[3] E.S. Polzik and K. Hammerer.  Annalen der Physik. 527, No. 1–2, A15–A20 (2015).

GaAs based quantum dots have played a pioneering role in the experimental development of electron spin qubits. However, one challenge is decoherence due to the unavoidable interaction of the electrons with nuclear spins.

I will discuss experiments that elucidate the role of quadrupolar coupling and g-factor anisotropy for this decoherence channel and thus complete our understanding of the intricate dynamics arising from the coupling to nuclear spins, known as the central spin problem. Contrary to what one might expect when considering spin diffusion, we find that quadrupolar effect degrade coherence via decorrelating transverse nuclear field that are coupled to the electron in second order.

In a second part, I will discuss how careful tuning of gate operations can lead to high gate fidelities ($\gt 98\%$ experimentally, $\gt 99.8 \%$ predicted based on best measured coherence time) in the face of real life experimental constraints.  Our feedback-based tuning method is of particular relevance for encoded spin qubits that employ several spins to encode a single qubit in order to simplify control or decoherence suppression as these are often not well suited for standard Rabi control.

I will conclude with an outlook of how a scalable quantum computer based on semiconductor spin qubits might look like and what challenges have to be overcome to reach that long term goal.

I will talk about using cold atoms as probe to test gravity. In particular, I will focus on the technology being developed at Birmingham to push quantum gravity sensors towards application.

The exploration of quantum effects in biology is an emerging field of research that concerns itself with the experimental and theoretical exploration of quantum phenomena in biological systems. In this lecture I aim to bring out design principles that nature may be exploiting to make use of quantum effects and I will develop in particular one underlying theme - the dynamics of quantum dynamical networks in the presence of an environment and the fruitful interplay that the two may enter. I will aim to demonstrate that this interplay has a wider relevance for biology.