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Future quantum information processing devices will require the use of exotic quantum states, such as specially crafted entangled states, to achieve certain desired computations on demand.
In order to demonstrate non-trivial quantum computations experimentally, such as the synthesis of arbitrary entangled states, it will be useful to nderstand how to decompose a desired quantum computation into the shortest possible sequence of one-qubit and two-qubit gates. We contribute to this effort by providing a method to construct an optimal quantum circuit for a general two-qubit gate that requires at most 3 CNOT gates and 15 elementary one qubit gates. We then prove that these constructions are optimal with respect to the family of CNOT, y-rotation, z-rotation, and phase gates.
In this tutorial we discuss the quantum alternating operator ansatz (QAOA), which is a variational algorithm that can be used for approximate optimization of combinatorial problems with soft and hard constraints.We go through the design of the quantum circuit and its actual implementation in real hardware, discussing compilation issues such as gate synthesis and scheduling of all the required gates and qubit-swapping overhead.
In 1959, during a famous lecture entitled "There's Plenty of Room at the Bottom", Richard Feynman focused on the startling technical possibilities that would exist at the limit of miniaturization, that being atomically precise devices with dimensions in the nanometer range. A nanometer is both a convenient unit of length for medium to large sized molecules, and the root of the name of the new interdisciplinary field of "nanotechnology". Essentially, "nanoelectronics" denotes the goal of shrinking electronic devices, such as diodes and transistors, as well as integrated circuits of such devices that can perform logical operations, down to dimensions in the range of 100 nanometers. The thirty-year hiatus in the development of nanotechnology can figuratively be seen as a period of waiting for the bottom-up and atomically precise construction skills of synthetic chemistry to meet the top-down reductionist aspirations of device physics. The sub-nanometer domain of nineteenth-century classical chemistry has steadily grown, and state-of-the-art supramolecular chemistry can achieve atomic precision in non-repeating molecular assemblies of the size desired for nanotechnology. For nanoelectronics in particular, a basic understanding of the electron transport properties of molecules must also be developed. Quantum chemistry provides powerful computational methods that can accurately predict the properties of small to medium sized molecules on a desktop workstation, and those of large molecules if one has access to a supercomputer. Of the many properties of a molecule that quantum chemistry routinely predicts, the ability to carry a current is one that had not even been considered until recently. "Currently", there is a controversy over just how to define this key property. Reminiscent of the situation in high-Tc superconductivity, much of the difficulty arises from the different models that are used to simplify the complex electronic structure of real materials. A model-independent approach has been proposed, that sacrifices the plentiful molecular orbitals and Bloch functions of conventional approaches, for a single three-dimensional observable quantity, the electron momentum density Pi(sub rho). This quantity is simply the probability of any electron having momentum rho, multiplied by the total number of electrons in the system (the position of the electron is uncertain). We have explored the utility of this new approach in providing a fundamental understanding of the electron transport properties of molecules that have provi been nominated as candidates for components in the design of nanoelectronics; phenylene-ethynylene oligomers. Some of the molecular systems that have been studied are sketched below.
A bio-nanobattery is an electrical energy storage device that utilizes organic materials and processes on an atomic, or nanometer-scale. The bio-nanobattery under development at NASA s Langley Research Center provides new capabilities for electrical power generation, storage, and distribution as compared to conventional power storage systems. Most currently available electronic systems and devices rely on a single, centralized power source to supply electrical power to a specified location in the circuit. As electronic devices and associated components continue to shrink in size towards the nanometer-scale, a single centralized power source becomes impractical. Small systems, such as these, will require distributed power elements to reduce Joule heating, to minimize wiring quantities, and to allow autonomous operation of the various functions performed by the circuit. Our research involves the development and characterization of a bio-nanobattery using ferritins reconstituted with both an iron core (Fe-ferritin) and a cobalt core (Co-ferritin). Synthesis and characterization of the Co-ferritin and Fe-ferritin electrodes were performed, including reducing capability and the half-cell electrical potentials. Electrical output of nearly 0.5 V for the battery cell was measured. Ferritin utilizing other metallic cores were also considered to increase the overall electrical output. Two dimensional ferritin arrays were produced on various substrates to demonstrate the feasibility of a thin-film nano-scaled power storage system for distributed power storage applications. The bio-nanobattery will be ideal for nanometerscaled electronic applications, due to the small size, high energy density, and flexible thin-film structure. A five-cell demonstration article was produced for concept verification and bio-nanobattery characterization. Challenges to be addressed include the development of a multi-layered thin-film, increasing the energy density, dry-cell bionanobattery development, and selection of ferritin core materials to allow the broadest range of applications. The potential applications for the distributed power system include autonomously-operating intelligent chips, flexible thin-film electronic circuits, nanoelectromechanical systems (NEMS), ultra-high density data storage devices, nanoelectromagnetics, quantum electronic devices, biochips, nanorobots for medical applications and mechanical nano-fabrication, etc.