Quantum computation in continuous time using dynamic invariants

We introduce an approach for quantum computing in continuous time based on the Lewis-Riesenfeld dynamic invariants. This approach allows, under certain conditions, for the design of quantum algorithms running on a nonadiabatic regime. We show that the relaxation of adiabaticity can be achieved by processing information in the eigenlevels of a time dependent observable, namely, the dynamic invariant operator. Moreover, we derive the conditions for which the computation can be implemented by time independent as well as by adiabatically varying Hamiltonians. We illustrate our results by providing the implementation of both Deutsch-Jozsa and Grover algorithms via dynamic invariants.     

Nanoscale superconducting quantum bits

Various physical systems were proposed for quantum information processing. Among those nanoscale devices appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. These systems combine intrinsic coherence of the superconducting state with control possibilities of single-charge circuits. In the regime where the typical charging energy dominates over the Josephson coupling, the low-temperature dynamics is limited to two states differing by a Cooper-pair charge on a superconducting island. In the opposite regime of prevailing Josephson energy, the phase (or flux) degree of freedom can be used to store and process quantum information. Under suitable conditions the system reduces to two states with different flux configurations. Several qubits can be joined together into a register. The quantum state of a qubit register can be manipulated by voltage and magnetic field pulses. The qubits are inevitably coupled to the environment. However, estimates of the phase coherence time show that many elementary quantum logic operations can be performed before the phase coherence is lost. In addition to manipulations, the final state of the qubits has to be read out. This quantum measurement process can be accomplished using a single-electron transistor for charge Josephson qubits, and a d.c.-SQUID for flux qubits. Recent successful experiments with superconducting qubits demonstrate for the first time quantum coherence in macroscopic systems.     

Universality of black hole quantum computing

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.     

Equivalent programmable quantum processors

Programmable quantum circuits, or processors, have the advantage over single-purpose quantum circuits that they can be used to perform more than one function. The inputs of a quantum processor consist of two quantum states, the first, the data register, is a state on which an operation is to be performed, and the second, the program, determines the operation to be performed on the data. In this paper we study how to determine whether two different quantum processors perform the same set of operations on the data. We define an equivalence between quantum processors that is quite natural in a circuit model of quantum information processing. Two processors are equivalent if one can be converted into the other by inserting fixed unitary gates at the input and the output of the program register. We then use this definition to find a necessary condition for two processors to be equivalent. We also study the beam splitter as an example of a quantum processor and find that this example suggests that as well as there being an equivalence relation on processors, there may also be a partial ordering.     

Typical Unpreparability of Quantum States with Quantum Circuit Model

The quantum entanglement is an interesting resource in quantum information processing, especially in measurement-based quantum computing. However, most quantum states may be too entangled to be prepared efficiently in terms of quantum circuit theory, in that high values of the geometric measure of entanglement preclude states from holding a polynomial quantum preparation circuit. We prove that this phenomenon experiences occurs in a dramatic majority of all states using a novel circuit tree-state correspondence. This work highlights new aspects of the roles both entanglement and quantum circuit theory play for quantum information processing.     

Computing with a single qubit faster than the computation quantum speed limit

The possibility to save and process information in fundamentally indistinguishable states is the quantum mechanical resource that is not encountered in classical computing. I demonstrate that, if energy constraints are imposed, this resource can be used to accelerate information-processing without relying on entanglement or any other type of quantum correlations. In fact, there are computational problems that can be solved much faster, in comparison to currently used classical schemes, by saving intermediate information in nonorthogonal states of just a single qubit. There are also error correction strategies that protect such computations.     

Scalable quantum information transfer between nitrogen-vacancy-center ensembles

We propose an architecture for realizing quantum information transfer (QIT). In this architecture, a LC circuit is used to induce the necessary interaction between flux qubits, each magnetically coupling to a nitrogen-vacancy center ensemble (NVCE). We explicitly show that for resonant interaction and large detuning cases, high-fidelity QIT between two spatially-separated NVCEs can be implemented. Our proposal can be extended to achieve QIT between any two selected NVCEs in a large hybrid system by adjusting system parameters, which is important in large scale quantum information processing.     

Continuous‐variable quantum information processing

Observables of quantum systems can possess either a discrete or a continuous spectrum. For example, upon measurements of the photon number of a light state, discrete outcomes will result whereas measurements of the light's quadrature amplitudes result in continuous outcomes. If one uses the continuous degree of freedom of a quantum system for encoding, processing or detecting information, one enters the field of continuous‐variable (CV) quantum information processing. In this paper we review the basic principles of CV quantum information processing with main focus on recent developments in the field. We will be addressing the three main stages of a quantum information system; the preparation stage where quantum information is encoded into CVs of coherent states and single‐photon states, the processing stage where CV information is manipulated to carry out a specified protocol and a detection stage where CV information is measured using homodyne detection or photon counting.     

Experimental investigations of the problem of the quantum jump with the help of superconductor nanostructures

The quantum theory, that we now know, arose in the process of sharp disputes between its creators. One of the results of these disputes was the emergence in recent years of fundamentally new areas of investigation and technology – quantum information and quantum computing. One of the subjects of controversy between the creators of quantum theory was the quantum jump. We draw the attention to the possibility of experimental investigation of this problem with the help of quantum superconductor nanostructures. The first results of experiments are presented, the paradoxicality of which indicates the relevance of the problem.     

Quantum computing based on space states without charge transfer

An implementation of a quantum computer based on space states in double quantum dots is discussed. There is no charge transfer in qubits during a calculation, therefore, uncontrolled entanglement between qubits due to long-range Coulomb interaction is suppressed. Encoding and processing of quantum information is merely performed on symmetric and antisymmetric states of the electron in double quantum dots. Other plausible sources of decoherence caused by interaction with phonons and gates could be substantially suppressed in the structure as well. We also demonstrate how all necessary quantum logic operations, initialization, writing, and read-out could be carried out in the computer.     

Quantum photonic network on chip

We provide an overview of quantum photonic network on chip. We begin from the discussion of the pros and cons of several material platforms for engineering quantum photonic chips. Then we introduce and analyze the basic building blocks and functional units of quantum photonic integrated circuits. In the main part of this review, we focus on the generation and manipulation of quantum states of light on chip and are particularly interested in some applications of advanced integrated circuits with different functionalities for quantum information processing, including quantum communication, quantum computing, and quantum simulation. We emphasize that developing fully integrated quantum photonic chip which contains sources of quantum light, integrate circuits, modulators, quantum storage, and detectors are promising approaches for future quantum photonic technologies. Recent achievements in the large scale photonic chips for linear optical computing are also included. Finally, we illustrate the challenges toward high performance quantum information processing devices and conclude with promising perspectives in this field.     

Hadamard NMR spectroscopy for two-dimensional quantum information processing and parallel search algorithms

Hadamard spectroscopy has earlier been used to speed-up multi-dimensional NMR experiments. In this work, we speed-up the two-dimensional quantum computing scheme, by using Hadamard spectroscopy in the indirect dimension, resulting in a scheme which is faster and requires the Fourier transformation only in the direct dimension. Two and three qubit quantum gates are implemented with an extra observer qubit. We also use one-dimensional Hadamard spectroscopy for binary information storage by spatial encoding and implementation of a parallel search algorithm.     

Efficient Scheme for One-Way Quantum Computing in Thermal Cavities

We propose a practical scheme for one-way quantum computing based on efficient generation of 2D cluster state in thermal cavities. We achieve a controlled-phase gate that is neither sensitive to cavity decay nor to thermal field by adding a strong classical field to the two-level atoms. We show that a 2D cluster state can be generated directly by making every two atoms collide in an array of cavities, with numerically calculated parameters and appropriate operation sequence that can be easily achieved in practical Cavity QED experiments. Based on a generated cluster state in Box⁽⁴⁾ configuration, we then implement Grover’s search algorithm for four database elements in a very simple way as an example of one-way quantum computing.     

Strong chaos of fast scrambling yields order: Emergence of decoupled quantum information capsules

The information loss problem in black hole evaporation is one of fundamental issues. Its resolution requires more profound understanding of information storage mechanism in quantum systems. In this Letter, we argue that when multiple unknown parameters are stored in large entangled qudits, strong chaos generated by fast scrambling in high temperature limit yields an ordered information storage structure with decoupled quantum information capsules (QICs). A rotational isometry emerges in the quantum Fisher information metric. The isometry is expected to be observed in future experiments on cold atoms in a pure entangled state. We provide a QIC speculation of black hole evaporation.     

Nuclear magnetic resonance for quantum computing: Techniques and recent achievements

Rapid developments in quantum information processing have been made, and remarkable achievements have been obtained in recent years, both in theory and experiments. Coherent control of nuclear spin dynamics is a powerful tool for the experimental implementation of quantum schemes in liquid and solid nuclear magnetic resonance(NMR) system,especially in liquid-state NMR. Compared with other quantum information processing systems, the NMR platform has the advantages such as the long coherence time, the precise manipulation, and well-developed quantum control techniques,which make it possible to accurately control a quantum system with up to 12-qubits. Extensive applications of liquid-state NMR spectroscopy in quantum information processing such as quantum communication, quantum computing, and quantum simulation have been thoroughly studied over half a century. This article introduces the general principles of NMR quantum information processing, and reviews the new-developed techniques. The review will also include the recent achievements of the experimental realization of quantum algorithms for machine learning, quantum simulations for high energy physics, and topological order in NMR. We also discuss the limitation and prospect of liquid-state NMR spectroscopy and the solid-state NMR systems as quantum computing in the article.     

Electric field control of exciton states in quantum dot molecules

Semiconductor nanostructures have attracted considerable interest during the recent years in view of the potential application in quantum information processing. In particular, quantum dots have been suggested to fulfill an essential requirement for quantum computation: controllable interaction that couples two quantum dot qubits. Previous experiments on two vertically aligned quantum dots have demonstrated the formation of coupled exciton states. We show that this coupling between two In_0.60Ga_0.40As/GaAs quantum dots can be tuned by an electric field applied along the molecule axis. This controllable coupling in such a relatively simple configuration could be implemented in a solid-state-based quantum device.     

Entangled Bell states of two electrons in coupled quantum dots—phonon decoherence

We demonstrate coupling and entangling of quantum states in a pair of vertically aligned self assembled quantum dots by studying the dynamics of two interacting electrons driven by external electric field. The present entanglement involves the spatial degree of freedom for the two electrons system. We show that system of two interacting electrons initially delocalized (localized each in one dot) oscillate slowly in response to electric field, since the strong Coulomb repulsion makes them behaving so. We use an explicit formula for the entanglement of formation of two qubit in terms of the concurrence of the density operator. In ideal situations, entangled quantum states would not decohere during processing and transmission of quantum information. However, real quantum systems will inevitably be influenced by surrounding environments. We discuss the degree of entanglement of this system in which we introduce the decoherence effect caused by the acoustic phonon. In this entangled states proposal, the decohering time depends on the external parameters.     

Photonic quantum information processing

Information processing with light is ubiquitous, from communication, metrology and imaging to computing. When we consider light as a quantum mechanical object, new ways of information processing become possible. In this review I give an overview of how quantum information processing can be implemented with single photons, and what hurdles still need to be overcome to implement the various applications in practice. I will place special emphasis on the quantum mechanical properties of light that make it different from classical light, and how these properties relate to quantum information processing tasks.