Quantum Memristors in Quantum Photonics

We propose a method to build quantum memristors in quantum photonic platforms. We firstly design an effective beam splitter, which is tunable in real-time, by means of a Mach-Zehnder-type array with two equal 50:50 beam splitters and a tunable retarder, which allows us to control its reflectivity. Then, we show that this tunable beam splitter, when equipped with weak measurements and classical feedback, behaves as a quantum memristor. Indeed, in order to prove its quantumness, we show how to codify quantum information in the coherent beams. Moreover, we estimate the memory capability of the quantum memristor. Finally, we show the feasibility of the proposed setup in integrated quantum photonics

Coherence and Entanglement in Two-Qubit Dynamics: Interplay of the Induced Exchange Interaction and Quantum Noise due to Thermal Bosonic Environment

We present a review of our recent results for the comparative evaluation of the induced exchange interaction and quantum noise mediated by the bosonic environment in two-qubit systems. We report new calculations for P-donor-electron spins in Si-Ge type materials. Challenges and open problems are discussed.Comment: Invited Review, 17 pages in LaTeX, with 4 EPS figure

Can biological quantum networks solve NP-hard problems?

There is a widespread view that the human brain is so complex that it cannot be efficiently simulated by universal Turing machines. During the last decades the question has therefore been raised whether we need to consider quantum effects to explain the imagined cognitive power of a conscious mind. This paper presents a personal view of several fields of philosophy and computational neurobiology in an attempt to suggest a realistic picture of how the brain might work as a basis for perception, consciousness and cognition. The purpose is to be able to identify and evaluate instances where quantum effects might play a significant role in cognitive processes. Not surprisingly, the conclusion is that quantum-enhanced cognition and intelligence are very unlikely to be found in biological brains. Quantum effects may certainly influence the functionality of various components and signalling pathways at the molecular level in the brain network, like ion ports, synapses, sensors, and enzymes. This might evidently influence the functionality of some nodes and perhaps even the overall intelligence of the brain network, but hardly give it any dramatically enhanced functionality. So, the conclusion is that biological quantum networks can only approximately solve small instances of NP-hard problems. On the other hand, artificial intelligence and machine learning implemented in complex dynamical systems based on genuine quantum networks can certainly be expected to show enhanced performance and quantum advantage compared with classical networks. Nevertheless, even quantum networks can only be expected to efficiently solve NP-hard problems approximately. In the end it is a question of precision - Nature is approximate.Comment: 38 page

Dangling-bond charge qubit on a silicon surface

Two closely spaced dangling bonds positioned on a silicon surface and sharing an excess electron are revealed to be a strong candidate for a charge qubit. Based on our study of the coherent dynamics of this qubit, its extremely high tunneling rate ~ 10^14 1/s greatly exceeds the expected decoherence rates for a silicon-based system, thereby overcoming a critical obstacle of charge qubit quantum computing. We investigate possible configurations of dangling bond qubits for quantum computing devices. A first-order analysis of coherent dynamics of dangling bonds shows promise in this respect.Comment: 17 pages, 3 EPS figures, 1 tabl

Topics in Quantum Dynamics and Coherence for Quantum Information Processing

We outline selected trends and results in theoretical modeling of quantum systems in support of the developing research field of quantum information processing. The resulting modeling tools have been applied to semiconductor materials and nanostructures that show promise for implementation of coherent, controlled quantum dynamics at the level of registers of several quantum bits (qubits), such as spins. Many-body field-theoretical techniques have been utilized to address a spectrum of diverse research topics. Specifically, the theory of decoherence and more generally the origin and effects of quantum noise and the loss of entanglement in quantum dynamics of qubits and several-qubit registers has been advanced. Qubit coupling mechanisms via the indirect exchange interaction have been investigated, and quantum computing designs have been evaluated for scalability. We outline general and specific research challenges, the solution of which will advance the field of modeling "open quantum systems" to further our understanding of how environmental influences affect quantum coherence and its loss during quantum dynamics

A strong direct product theorem for quantum query complexity

We show that quantum query complexity satisfies a strong direct product theorem. This means that computing $k$ copies of a function with less than $k$ times the quantum queries needed to compute one copy of the function implies that the overall success probability will be exponentially small in $k$. For a boolean function $f$ we also show an XOR lemma---computing the parity of $k$ copies of $f$ with less than $k$ times the queries needed for one copy implies that the advantage over random guessing will be exponentially small. We do this by showing that the multiplicative adversary method, which inherently satisfies a strong direct product theorem, is always at least as large as the additive adversary method, which is known to characterize quantum query complexity.Comment: V2: 19 pages (various additions and improvements, in particular: improved parameters in the main theorems due to a finer analysis of the output condition, and addition of an XOR lemma and a threshold direct product theorem in the boolean case). V3: 19 pages (added grant information

Experimental Quantum Fingerprinting

Quantum communication holds the promise of creating disruptive technologies that will play an essential role in future communication networks. For example, the study of quantum communication complexity has shown that quantum communication allows exponential reductions in the information that must be transmitted to solve distributed computational tasks. Recently, protocols that realize this advantage using optical implementations have been proposed. Here we report a proof of concept experimental demonstration of a quantum fingerprinting system that is capable of transmitting less information than the best known classical protocol. Our implementation is based on a modified version of a commercial quantum key distribution system using off-the-shelf optical components over telecom wavelengths, and is practical for messages as large as 100 Mbits, even in the presence of experimental imperfections. Our results provide a first step in the development of experimental quantum communication complexity.Comment: 11 pages, 6 Figure

Entanglement and Quantum Noise Due to a Thermal Bosonic Field

We analyze the indirect exchange interaction between two two-state systems, e.g., spins 1/2, subject to a common finite-temperature environment modeled by bosonic modes. The environmental modes, e.g., phonons or cavity photons, are also a source of quantum noise. We analyze the coherent vs noise-induced features of the two-spin dynamics and predict that for low enough temperatures the induced interaction is coherent over time scales sufficient to create entanglement. A nonperturbative approach is utilized to obtain an exact solution for the onset of the induced interaction, whereas for large times, a Markovian scheme is used. We identify the time scales for which the spins develop entanglement for various spatial separations. For large enough times, the initially created entanglement is erased by quantum noise. Estimates for the interaction and the level of quantum noise for localized impurity electron spins in Si-Ge type semiconductors are given.Comment: 12 pages, 9 figures; typos correcte