Hidden Tensor Structures

Classical electron theory with classical electromagnetic zero-point radiation (stochastic electrodynamics) is the classical theory which most closely approximates quantum electrodynamics. Indeed, in inertial frames, there is a general connection between classical field theories with classical zero-point radiation and quantum field theories. However, this connection does not extend to noninertial frames where the time parameter is not a geodesic coordinate. Quantum field theory applies the canonical quantization procedure (depending on the local time coordinate) to a mirror-walled box, and, in general, each non-inertial coordinate frame has its own vacuum state. In complete contrast, the spectrum of random classical zero-point radiation is based upon symmetry principles of relativistic spacetime; in empty space, the correlation functions depend upon only the geodesic separations (and their coordinate derivatives) between the spacetime points. It makes no difference whether a box of classical zero-point radiation is gradually or suddenly set into uniform acceleration; the radiation in the interior retains the same correlation function except for small end-point (Casimir) corrections. Thus in classical theory where zero-point radiation is defined in terms of geodesic separations, there is nothing physically comparable to the quantum distinction between the Minkowski and Rindler vacuum states. It is also noted that relativistic classical systems with internal potential energy must be spatially extended and can not be point systems. Based upon the classical analysis, it is suggested that the claimed heating effects of acceleration through the vacuum may not exist in nature.

We describe the simplest single–photon encoding schemes and introduce the concept of a quantum optical gate. These gates can be used to build up arbitrary entangled states of many initially separate single photons. Experimental realization of such a gate involves the development of nonlinear phase shift elements sensitice at the single quantum level. We report our experimental efforts using linear optical elements and non–classical sources where we are able to demonstrate interference and entanglement of initially separate single–photon pulses.

We present the fundamentals of a prequantum model with hidden variables of classical field type—prequantum classical statistical field theory (PCSFT). In some sense, this is the comeback of classical field theory, but with an extension to massive particles. All quantum averages (including correlations of entangled systems) can be represented as classical field averages and correlations. In the literature, entanglement of biparticle systems (in particular, biphotons) has been represented in the PCSFT framework. In this paper, we consider triparticle entanglement. It is well known that in conventional quantum mechanics, the cases of biparticle and triparticle entanglement are quite different. Roughly speaking, triparticle entanglement is not reducible to biparticle entanglement. The PCSFT approach to entanglement (as a correlation of classical signals) reflects this quantum situation. The PCSFT representations of correlations in biparticle and triparticle systems differ essentially. In particular, from the mathematical viewpoint the latter is fundamentally more complicated than the former.

Quantum information has been witnessing great science value and latent application since 1980's. The research work presented here consist of mainly two important parts: manipulations of multiphoton entanglement and atomic ensembles based quantum memory. In first part, the experimental technique multi-photon entanglement is further developed to study fundamental issues in quantum mechanics, remarkable applications to quantum communication and quantum computation. Specifically, we have demonstrated a bit-flip error-free transfer of quantum information, violation of Bell's inequality beyond Tsirelson's bound, teleportation of a two-qubit composite system, as well as the one-way computing by two-photon-four-qubit cluster state. To overcome un-scalability problem due to probabilistic feature in linear optical quantum information processing, we investigated in the second part the physics of atomic ensembles based quantum memory. We show that theoretically, entanglement between distant locations can be deterministically generated. The experimental work has thoroughly developed the necessary techniques and we have achieved deterministic single photon source, and interference of the photons from independent atomic ensembles, teleportation between photonic and atomic qubits, a novel way to create a robust entanglement between an atomic and a photonic qubit, and memory based entanglement swapping. We believe, the developed techniques here would dramatically facilitate progresses in many fields including global quantum communication, linear optical quantum computation and the foundations of quantum mechanics etc.

State space representation of flexible structure dynamics in air flow

In this course we will concentrate on (nonlinear) stochastic partial differential equations (SPDEs) of evolutionary type. All kinds of dynamics with stochastic influence in nature or man-made complex systems can be modeled by such equations. As we shall see from the examples at the end of this section, the state spaces of their solutions are necessarily infinite dimensional, such as spaces of (generalized) functions. In this course the state spaces, denoted by H, will be mostly separable Hilbert spaces, sometimes separable Banach spaces.

The paper deals with the exact controllability of a semilinear system in a separable Hilbert space. A bounded linear part is considered and a linear control introduced. The state space is compactly embedded in a Banach space and the nonlinear term is continuous in its state variable in the norm of the Banach space. An infinite sequence of finite dimensional controllability problems is introduced and the solution is obtained by a limiting procedure. To the best of our knowledge, the method is new in controllability theory. An application to an integro-differential system in euclidean spaces completes the discussion.

We show that every quantum computation can be described by a probabilistic update of a probability distribution on a finite phase space. Negativity in a quasiprobability function is not required in states or operations. Our result is consistent with Gleason's theorem and the Pusey-Barrett-Rudolph theorem.

Quantum computers can solve certain problems more efficiently than any possible conventional computer. Small quantum algorithms have been demonstrated on multiple quantum computing platforms, many specifically tailored in hardware to implement a particular algorithm or execute a limited number of computational paths. Here we demonstrate a five-qubit trapped-ion quantum computer that can be programmed in software to implement arbitrary quantum algorithms by executing any sequence of universal quantum logic gates. We compile algorithms into a fully connected set of gate operations that are native to the hardware and have a mean fidelity of 98 per cent. Reconfiguring these gate sequences provides the flexibility to implement a variety of algorithms without altering the hardware. As examples, we implement the Deutsch-Jozsa and Bernstein-Vazirani algorithms with average success rates of 95 and 90 per cent, respectively. We also perform a coherent quantum Fourier transform on five trapped-ion qubits for phase estimation and period finding with average fidelities of 62 and 84 per cent, respectively. This small quantum computer can be scaled to larger numbers of qubits within a single register, and can be further expanded by connecting several such modules through ion shuttling or photonic quantum channels.

Fault-tolerant quantum computers that can solve hard problems rely on quantum error correction1. One of the most promising error correction codes is the surface code2, which requires universal gate fidelities exceeding an error correction threshold of 99 per cent3. Among the many qubit platforms, only superconducting circuits4, trapped ions5 and nitrogen-vacancy centres in diamond6 have delivered this requirement. Electron spin qubits in silicon7-15 are particularly promising for a large-scale quantum computer owing to their nanofabrication capability, but the two-qubit gate fidelity has been limited to 98 per cent owing to the slow operation16. Here we demonstrate a two-qubit gate fidelity of 99.5 per cent, along with single-qubit gate fidelities of 99.8 per cent, in silicon spin qubits by fast electrical control using a micromagnet-induced gradient field and a tunable two-qubit coupling. We identify the qubit rotation speed and coupling strength where we robustly achieve high-fidelity gates. We realize Deutsch-Jozsa and Grover search algorithms with high success rates using our universal gate set. Our results demonstrate universal gate fidelity beyond the fault-tolerance threshold and may enable scalable silicon quantum computers.

Quantum Communications promise advances in cryptography, quantum computing and clock synchronisation, among other emerging applications. However, communication based on quantum phenomena requires an extreme level of isolation from external disturbances, complicating the co-propagation of quantum and classical signals. The challenge is greater when deploying networks that are both heterogeneous (e.g., multiple vendors) and installed in production facilities, given that this type of infrastructure already supports networks loaded with their own requirements. Moreover, to achieve a broad acceptance among network operators, the joint management and operation of quantum and classical resources, compliance with standards, and legal and quality assurance need to be addressed. This article presents solutions to the aforementioned challenges validated in the Madrid quantum network during the implementation of the projects CiViC and OpenQKD. This network was designed to integrate quantum communications in the telecommunications ecosystem by installing quantum-key-distribution modules from multiple providers in production nodes of two different operators. The modules were connected through an optically-switched network with more than 130 km of deployed optical fibre. The tests were done in compliance with strict service level agreements that protected the legacy traffic of the pre-existing classical network. The goal was to ensure full quantum-classical interoperability at all levels, while limiting the modifications to optical transport and encryption and complying with relevant standards. This effort is intended to lay the foundation for large-scale quantum network deployments.

With recognition of quantum computer's enormous computational ability, it is of paramount importance to develop fault-tolerant quantum computing systems for their practical use. Recently, it has been shown that fault-tolerant systems can be achieved using a small set of basic quantum operations. This, however, incurs technical difficulties in finding an optimal sequence of basic operations toward a specific target computation and may limit possible quantum computations. In this work, we aim to achieve arbitrary target quantum computations under the restriction of four universal quantum gates of Pauli-X, -Y, -Z and SWAP. We develop two gate-sequence search methods based on the fidelity measure and deep neural networks. We verify the performance of our proposed methods through numerical results comparing total search space and the number of searched nodes.

One of the current trends in quantum computing is the application of algebraic topological methods in the design of new algorithms and quantum computers, giving rise to topological quantum computing. One of the tools used in it is the Yang-Baxter equation whose solutions are interpreted as universal quantum gates. Lately, more general Yang-Baxter equations have been investigated, making progress as two-spectral equations and Yang-Baxter systems. This paper intends to apply these new findings to the field of topological quantum computation, more specifically, the proposition of the two-spectral Yang-Baxter operators as universal quantum gates for 2 qubits and 2 qutrits systems, obtaining 4x4 and 9x9 matrices respectively, and further elaboration of the corresponding Hamiltonian by the use of computer algebra software Mathematica® and its Qucalc package. In addition, possible physical systems to which the Yang-Baxter operators obtained can be applied are considered. In the present work it is demonstrated the utility of the Yang-Baxter equation to generate universal quantum gates and the power of computer algebra to design them; it is expected that these mathematical studies contribute to the further development of quantum computers

Holonomic quantum computation exploits a quantum state's non-trivial,\nmatrix-valued geometric phase (holonomy) to perform fault-tolerant computation.\nHolonomies arising from systems where the Hamiltonian traces a continuous path\nthrough parameter space have been well-researched. Discrete holonomies, on the\nother hand, where the state jumps from point to point in state space, have had\nlittle prior investigation. Using a sequence of incomplete projective\nmeasurements of the spin operator, we build an explicit approach to universal\nquantum computation. We show that quantum error correction codes integrate\nnaturally in our scheme, providing a model for measurement-based quantum\ncomputation that combines the passive error resilience of holonomic quantum\ncomputation and active error correction techniques. In the limit of dense\nmeasurements we recover known continuous-path holonomies.\n

This work studies pulse based variational quantum algorithms (VQAs), which are designed to determine the ground state of a quantum mechanical system by combining classical and quantum hardware. In contrast to more standard gate based methods, pulse based methods aim to directly optimize the laser pulses interacting with the qubits, instead of using some parametrized gate based circuit. Using the mathematical formalism of optimal control, these laser pulses are optimized. This method has been used in quantum computing to optimize pulses for quantum gate implementations, but has only recently been proposed for full optimization in VQAs. Pulse based methods have several advantages over gate based methods such as faster state preparation, simpler implementation and more freedom in moving through the state space. Based on these ideas, we present the development of a novel adjoint based variational method. This method can be tailored towards and applied in neutral atom quantum computers. This method of pulse based variational quantum optimal control is able to approximate molecular ground states of simple molecules up to chemical accuracy and is able to compete with the gate based variational quantum eigensolver in terms of total number of quantum evaluations. The total evolution time T and the form of the control Hamiltonian Hc are important factors in the convergence behavior to the ground state energy, both having influence on the quantum speed limit and the controllability of the system.