QMM‐Enhanced Error Correction: Demonstrating Reversible Imprinting and Retrieval for Robust Quantum Computation

The ability to store information is of fundamental importance to any computer, be it classical or quantum. To identify systems for quantum memories which rely, analogously to classical memories, on passive error protection (`self-correction') is of greatest interest in quantum information science. While systems with topological ground states have been considered to be promising candidates, a large class of them was recently proven unstable against thermal fluctuations. Here, we propose two-dimensional (2D) spin models unaffected by this result. Specifically, we introduce repulsive long-range interactions in the toric code and establish a memory lifetime polynomially increasing with the system size. This remarkable stability is shown to originate directly from the repulsive long-range nature of the interactions. We study the time dynamics of the quantum memory in terms of diffusing anyons and support our analytical results with extensive numerical simulations. Our findings demonstrate that self-correcting quantum memories can exist in 2D at finite temperatures.

Quantum networks are composed of quantum nodes which coherently interact by way of quantum channels. They offer powerful capabilities for quantum computation, communication, and metrology. A generic requirement for these realizations is the capability to generate and store quantum states among multiple quantum nodes, and to disseminate these resources throughout the network via the quantum channels. In this thesis, I describe a series of experiments whereby single excitations in atomic ensembles are strongly coupled to optical modes and provide efficient means for the coherent control of entangled states between matter and light. By following the seminal proposal by Duan et al., we have generated measurement-induced entanglement of an excitation between two cold atomic ensembles. Using this system, we investigated the relationship for the global bipartite entanglement and local correlations in its subsystems. In addition, we achieved functional quantum nodes for entanglement distribution. Two pairs of remote ensembles at two quantum nodes were prepared into entangled states in a heralded and asynchronous fashion by the conditional controls of the entanglement. The quantum states of the ensembles were then distributed into polarization entangled states of photons. We also prepared an analogous quantum state and transferred the nonlocal coherence between two pairs of heralded entangled atomic ensembles, providing a step towards entanglement connection. Beyond such probabilistic approaches, we demonstrated an experiment where entanglement between two quantum memories is created by the reversible and deterministic mapping of an entangled state of light via dynamic electromagnetically induced transparency. This experiment opens novel prospects of integrating hybrid quantum systems by way of reversible quantum interfaces between light and matter. Then, we extended our work to multipartite quantum systems. We theoretically investigated the characterization of multipartite mode-entangled states by way of quantum uncertainty relations, and introduced theoretical tools to verify the entanglement orders in multipartite systems. In particular, we achieved entanglement for one delocalized photon among multiple optical modes (N > 2). Finally, we have achieved measurement-induced entanglement of spin waves among four quantum memories. The individual atomic components for the entangled W state of the four ensembles were then coherently converted into four propagating entangled beams of light via superradiant emissions. We observed the statistical and dynamic transitions for the multipartite entangled spin waves. Experiments described in this thesis thereby represent significant advances of experimental and theoretical capabilities to generate, store, transfer, and characterize entanglement of matter and light over quantum networks.

Developing quantum systems which are robust against noise are of prime importance to the realisation of quantum technologies. Without fault tolerance, we will never be able to preserve delicate quantum states for macroscopic time scales, a necessary requirement in the construction of scalable quantum computer. Topologically ordered models offer very beautiful mechanisms for preserving quantum states. In such models, quantum information is encoded globally over a degenerate topological Hilbert space which offers a natural robustness against local environmental noise. Remarkably, topological order is present in certain realistic condensed-matter systems. This provides a platform for accessing topological order in a laboratory. Moreover, considering condensed-matter systems enables us to combine topological features with other physical effects to enhance their behaviour. In this Thesis we study the physics of topologically ordered lattice models with defects. We seek practical applications of lattice defects for the realisation of a fault-tolerant quantum computer. The first result we present shows that anyonic data of point-like lattice defects, called twists, can be found by measuring the entanglement of the ground state of the host system. The data we learn relates to the capacity of a twist defect to perform quantum computational tasks. The second result in this Thesis concerns the dynamics of the qudit toric code model with line-like defects coupled to a thermal bath. We show we can entropically inspire fragile glassy dynamics in the system. Such dynamics qualitatively improve the coherence times of quantum information encoded in the ground state of the lattice. A novel way of achieving fault-tolerant quantum computation is by producing and manipulating twist defects of topologically ordered systems. In many ways, this paradigm of topological quantum computation is analogous to quantum computation using anyons. The first area of study in this Thesis extends the analogy between anyons and twists. Specifically, we show that the anyonic data of twists in Kitaev’s toric code model can be extracted

One of the biggest obstacles to building a large scale quantum computer is the high qubit cost of protecting quantum information. For two-dimensional architectures, the surface code has long been the leading candidate quantum memory, but can require upwards of a thousand physical qubits per logical qubit to reach algorithmically-relevant logical error rates. In this work, we introduce a hierarchical memory formed from surface codes concatenated into high-density parity check codes. These yoked surface codes are arrayed in a rectangular grid, with parity checks (yokes) measured along each row, and optionally along each column, using lattice surgery. Our construction assumes no additional connectivity beyond a nearest-neighbor square qubit grid operating at a physical error rate of 10−3. At algorithmically-relevant logical error rates, yoked surface codes use as few as one-third the number of physical qubits per logical qubit as standard surface codes, enabling moderate-overhead fault-tolerant quantum memories in two dimensions.

Data compression is a ubiquitous aspect of modern information technology, and the advent of quantum information raises the question of what types of compression are feasible for quantum data, where it is especially relevant given the extreme difficulty involved in creating reliable quantum memories. We present a protocol in which an ensemble of quantum bits (qubits) can in principle be perfectly compressed into exponentially fewer qubits. We then experimentally implement our algorithm, compressing three photonic qubits into two. This protocol sheds light on the subtle differences between quantum and classical information. Furthermore, since data compression stores all of the available information about the quantum state in fewer physical qubits, it could allow for a vast reduction in the amount of quantum memory required to store a quantum ensemble, making even today's limited quantum memories far more powerful than previously recognized.

By the birth of Quantum Physics, many new areas were opened for research and development in the world of science and technology. One such field is Quantum Computing and Communication where there is room for all that was once a dream in the field of computing and communication. Ultra high speed, immunity to eavesdropping, security, and name it and it may be possible. This paper gives a brief review of what is happening in the field of quantum computing and communication. We try to give an idea on polarization, quantum entanglement and their use in quantum communication and also briefly explain quantum communication networks, teleportation over optic fiber cables, quantum cryptography, quantum based satellite communication and quantum memory.

An essential component of any quantum computer is the quantum memory, the content of which is a pure quantum state. A program to study the quantum memory is initiated here, where the spatial variables are of central importance. The presence of the spatial variables makes it possible to apply the powerful and well-developed theory of scattering: The fundamental operations of writing on, reading and resetting the quantum memory are all performed through scattering from the memory. The requirement that the quantum memory must remain in a pure state after scattering implies that the scattering is of a special type, and only certain incident waves are admissible. Models based on the coupled-channel Schrodinger equation for potential scattering are formulated, where there is indeed the required large collection of admissible incident waves. On the basis of these models, certain types of decoherence are unavoidable. Such decoherence and the necessity of using the relativistic Schrodinger equation are discussed. One of the implications of quantum memory is the possible lack of security for the quantum key distribution in quantum cryptography.

This thesis is a summary of my research work during the last few years of my Ph.D. The main system of research is quantum memory based on cold atomic ensembles. Flying photons can be used to transmit quantum information over long distances, and quantum memories based on cold atomic ensembles can act as carriers for local storage and manipulation of quantum information, so it is of great significance to study cold atomic quantum memories for construction of global quantum networks. In this thesis, based on previous work, we further scrutinize the factors that will affect the performance metrics of quantum memory such as retrieval efficiency, and then we combine these analysis with some innovative experimental techniques, which will enable us to finally realize a highly retrievable quantum memory with intrinsic retrieval efficiency up to 90% and overall measured retrieval efficiency up to 40%. Based on this efficient quantum memory, we optimize the experimental loading time for preparing cold atomic ensembles, the number of experimental trials in each loading and other timing parameters, so that the experimental detection brightness of photons can support our experimental study of multiple quantum memories.

(English) Future networks for quantum communication will require a new form of technology in order to operate over long distances. The no-cloning theorem precludes the use of amplification, so quantum repeater schemes have been proposed to achieve long-distance quantum communication through the distribution of entanglement. A key device for this setup is a quantum memory, which is required in order to store entanglement and synchronise its distribution. Among the many physical systems than can be used as a quantum memory, rare-earth ion-doped crystals stand out due to their long coherence times and potential for multiplexing and integration. This thesis reports the use of one such system, Pr3+:Y2SiO5, as a quantum memory using the atomic frequency comb (AFC) protocol. Building on previous work, we improved the performance of the memory to be able to demonstrate light-matter entanglement with a telecommunications wavelength photon and the quantum memory, for both a bulk memory and an integrated version. To measure light-matter entanglement, we use photon pairs generated through cavity-enhanced spontaneous parametric down conversion, where one photon (the signal) is stored in the memory and the other (the idler) is at a telecommunications wavelength. These photon pairs exhibit energy-time entanglement, which we analyse in the time basis using fibre- and AFC-based Mach-Zehnder interferometers. In the first experiment, we demonstrate light-matter entanglement where the bulk quantum memory is used with on-demand retrieval via storage in a spin-wave. We measure interference fringes with average visibilities of 89(2)% for AFC storage, and 70(3)% for spin-wave storage, sufficient to demonstrate entanglement. This is the first such demonstration using an on-demand multimode solid-state memory and telecom photon. We show that entanglement is maintained for up to 47.7 µs of storage. These results were made possible through improvements in the AFC efficiency and the noise filtering. Furthermore, we perform on-demand storage and retrieval of up to 30 temporal modes. We take the next step towards implementing our system in a real world scenario by measuring entanglement over a distance. To do so, we send the idler photons through both optical fibre spools and deployed fibre in the metropolitan area of Barcelona, Spain, while the photon detection still occurs in the same lab. The resulting visibilities (80% or higher) demonstrate that the photonic qubit does not decohere during transmission through the optical fibre. We then decouple the photon creation and detection by measuring non-classical correlations between signal photons detected in the lab, and idler photons detected 16 km away (44 km in fibre) in a different location. The final experiment uses a fibre-integrated memory for light-matter entanglement. We use a Pr3+:Y2SiO5 crystal containing a Type I laser-written waveguide, interfaced directly with optical fibre. The fibre-integration allows for improved transmission and AFC efficiency compared to a free-space coupled waveguide memory. To analyse the performance of the memory, we demonstrate non-classical correlations for storage times up to 28 µs. We perform qubit tomography in the time basis for storage times of 3 and 10 µs, measuring two-qubit fidelities of 86(2)% and 86(4)%, respectively, demonstrating storage of entanglement. These experiments demonstrate the potential of our system for use as part of a quantum repeater, with many opportunities for further improvement to the storage time, efficiency, and multiplexing capability.

Coherently converting the frequency and temporal waveform of single and entangled photons will be crucial to interconnect the various elements of future quantum information networks. Of particular importance is the quantum frequency conversion of photons emitted by material systems able to store quantum information, so-called quantum memories. There have been significant efforts to implement quantum frequency conversion using nonlinear crystals, with non-classical light from broadband photon-pair sources and solid-state emitters. However, solid state quantum frequency conversion has not yet been achieved with long-lived optical quantum memories. Here we demonstrate an ultra-low-noise solid state photonic quantum interface suitable for connecting quantum memories based on atomic ensembles to the telecommunication fibre network. The interface is based on an integrated-waveguide nonlinear device. We convert heralded single photons at 780 nm from a rubidium-based quantum memory to the telecommunication wavelength of 1,552 nm, showing significant non-classical correlations between the converted photon and the heralding signal.

In quantum information science, photons are the best candidate for transmitting information, and atoms are the best candidate for storing information. The combination of these two systems provides a fascinating future for practical applications of the quantum information concepts. The work presented in this thesis mainly consists of two parts. The first part is about manipulation of entangled photons, including the demonstration of a nondestructive CNOT gate, the creation of narrowband entangled photons through cavity-enhanced spontaneous parametric down-conversion, and the realization of interference between narrowband photon sources. The second part is about manipulation of atomic ensembles. The main purpose for this part is to extend the quantum communication distance using the concept of quantum repeater. Within this part, the experimental work includes, the extension of storage lifetime of quantum memories to 1 ms by increasing the wavelength of stored spinwave, the realization of entanglement assisted spinwave interferometer, the demonstration of efficient entanglement swapping with quantum memories, and the realization of quantum teleportation between atomic ensembles.

High performance quantum memory for quantized states of light is a building block of quantum information technology. Despite great progresses of optical quantum memories based on interactions of light and atoms, physical features of these memories still cannot satisfy requirements for applications in practical quantum information systems, since all of them suffer from trade off between memory efficiency and excess noise. Here, we report a high-performance cavity enhanced electromagnetically induced transparency memory with warm atomic cell in which a scheme of optimizing the spatial and temporal modes based on the time-reversal approach is applied. The memory efficiency up to 67 ± 1% is directly measured and atom interaction, and a noise level close to quantum noise limit is simultaneously reached, which enable the high fidelity quantum memory. Thus, the realized quantum memory platform is ready to be applied in quantum information systems.

I present quantum nano-photonic devices based on nanophotonic resonators coupled to rare-earth-ions in crystals. The rare-earth ions exhibit long coherence times on optical transitions, which makes them suitable for optical quantum memories. We demonstrate a high-fidelity nanophotonic quantum memory based on a mesoscopic rare-earth ensemble coupled to a photonic crystal cavity. The nanocavity enables >95% spin polarization for efficient initialization of the atomic frequency comb memory, and time-bin-selective readout via enhanced optical Stark shift of the comb frequencies. Besides ensemble memories, single rare-earth-ions coupled to nano-resonators can be used as single optically addressable quantum bits where the quantum state is mapped on their Zeeman or hyperfine levels with long coherence time. Our solid-state nano-photonic quantum light-matter interfaces can be integrated with other chip-scale photon source and detector devices for multiplexed quantum and classical information processing at the nodes of quantum networks.

Quantum teleportation is one of the most basic quantum protocols, which transfers an unknown quantum state from one location to another through local operation and classical communication by using shared quantum entanglement without physical transfer of the information carrier. And it has been widely used in various quantum information protocols such as entanglement swapping, quantum repeaters, quantum gate teleportation, quantum computation based on measurement, and quantum teleportation networks, which have important application value in quantum computation and quantum information. Quantum teleportation is a naturally bipartite process, in which an unknown quantum state can only be transmitted from one node to another. With the further development of quantum information research, it is necessary to transfer quantum states or quantum information among more and more nodes. Multipartite quantum protocols are expected to form fundamental components for larger-scale quantum communication and computation. A bipartite quantum teleportation should be extended to a multipartite protocol known as a quantum teleportation network. In this paper, a multifunctional quantum teleportation network is proposed theoretically. We first propose a special method of constructing four-partite quantum resources in continuous variables (CVs), and based on this, construct two different types of CV quantum teleportation networks. One type of network contains just one quantum teleportation process consisting of a sender, a receiver and two controllers. In this type of network, the unknown quantum state can be recovered at any other node according to the requirement after the measurement in the input node, which enriches the transfer direction and transfer mode of the unknown quantum state. And meanwhile, the two controllers can control the transfer of a quantum state from the sender to the receiver by restricting the sender and receiver’s access to their information, which makes the quantum teleportation network controllable. The other type of network has two quantum teleportation processes, each containing only a sender, a receiver and no controllers, which increases the number of quantum states that can be transmitted. Then we analyze the dependence of the fidelity of each quantum teleportation network on different physical parameters, and compare the characteristics, advantages and disadvantages among different types of quantum teleportation networks. The scheme for constructing a multifunctional quantum teleportation network in this paper shows some advantages, such as the greater number of quantum nodes, diversity of types, simple operation procedure. And all these advantages provide a broader application prospect for establishing larger and more complex quantum information networks in the future and quicken the pace of the application of quantum information.

Quantum states are inherently fragile, making their storage a major concern for many practical applications and experimental tests of quantum mechanics. The field of quantum memories is concerned with how this storage may be achieved, covering everything from the physical systems best suited to the task to the abstract methods that may be used to increase performance. This review concerns itself with the latter, giving an overview of error correction and self-correction, and how they may be used to achieve fault-tolerant quantum computation. The planar code is presented as a concrete example, both as a quantum memory and as a framework for quantum computation.