One of the primary driving forces behind the explosion of interest in quantum computing has been the realization that it is possible to construct working quantum information processing devices using a wide variety of existing techniques from nuclear magnetic resonance, quantum optics, atomic and molecular physics, and solid-state physics. Work by Ekert, Deutsch, Divincenzo and Lloyd in the early 1990s showed that essentially any quantum system that can be coherently controlled, and that exhibits nonlinear interactions between degrees of freedom, can be made to perform quantum computations in principle. Since 1995, a wide variety of quantum information processing devices have been designed, constructed, and operated, many of them by members of the MIT quantum computing group.

At the current time, there is no one best system for quantum information processing. Room temperature NMR systems exhibit a high degree of coherent controllability, and have been the systems of choice so far for performing proof-of-principle demonstrations of quantum computation. They do not exhibit entanglement, however, and are not scalable beyond about ten quantum bits. Ion trap quantum computers have recently been scaled beyond their initial size of two or three quantum bits, but the successful systems constructed and operated by Wineland and Monroe at NIST have proved difficult to replicate. Cavity quantum electrodynamic quantum computers pioneered by Kimble at Caltech and the Innsbruck group exhibit great promise for integrated quantum computation and quantum communications (the `quantum internet'), but have proved difficult to implement.

Today, experimentalists from a variety of backgrounds are entering the field of quantum computation, and a new generation of concepts for quantum computation and quantum communications is being explored. Particularly promising are a variety of proposals for solid-state quantum computing, including Kane's proposal to use atoms embedded in lithographed circuits, and Mooij's proposals for performing quantum computation using electron spins in semiconductors, and Mooij's demonstration (with Orlando and Lloyd) of superconducting quantum qubits.

In Cambridge, the Cavendish Laboratory's Semiconductor Physics Group have growth, processing and measurement capabilities for a wide variety of semiconductor technologies. Their most recent research program has developed a number of electronic devices and measurement techniques which allow non-invasive detection of single electron and many electron processes. These technologies allow the opportunity to pursue four different proposals to create a quantum processor: the creation of arrays of laterally patterned quantum dots; the production of accurately doped and designed SiGe heterostructures; the detection of hyper fine interactions in the quantum Hall regime; and the use of electrons trapped in the minima of surface acoustic waves (SAW).

In this background, the CU/MIT workshop identified a number of emerging areas in which the joint expertise of research at Cambridge and at MIT could make a significant contribution. In particular, the following projects aim to build prototype solid state quantum information processors over a four year period:

• using electrons trapped in surface acoustic waves;
• using donor atoms in semiconductor materials;
• using planar electrostatically defined arrays of quantum dots;
• constructing arrays of superconducting quantum bits;
• investigating the use of abelian anyons such as quantum Hall effect quasiparticles to perform quantum logic.

The CMI collaboration will help them to grow, process and measure the relevant devices, and to simulate their operation numerically. These projects will use existing equipment or purchase it using separate funds.

Like classical computers, quantum computers can be connected together by communication lines to form a network. MIT has an existing significant MURI experimental effort to construct a quantum internet. The proposed work under CMI will address aspects of the quantum internet not covered under existing grants. In particular, CU possesses a strong group in the theory of quantum communications and quantum cryptography. This group will collaborate with the MIT group to develop communication protocols and applications for the quantum internet, including quantum file transfer protocols, quantum routing routines, and distributed quantum communication methods. Although the experimental work at MIT aims to construct a simple three node network, with two-qubit cavity QED quantum computers at each node, it is not too early to investigate applications and architectures for more complicated networks. Applications to quantum cryptography will be discussed in detail below.

One of the most powerful ways to address quantum information processing is in terms of geometric control. Methods of quantum control are essential for performing quantum logic and for attaining reliable operation of quantum computers and quantum communication systems. The application of geometric control methods to quantum computation was first suggested by Lloyd, and by Deutsch et al. The extensive use of geometric techniques for programming NMR quantum computers was pioneered by Cory and Havel. Havel and Doran propose to extend these techniques to develop powerful new error-resistant algorithms for NMR quantum computation. Specifically, they will perform a geometric algebra analysis of coherent dipole-dipole interactions between nuclear spins, and develop error correction techniques for dipolar interactions. They will perform theoretical and experimental NMR analyses of dilute crystals of molecules to show how they can exhibit quantum entanglement.

A second application of geometric methods is to the problem of preventing and correcting errors. Researchers at MIT (Chuang, Lloyd) and elsewhere have developed a set of symmetry-based methods for protecting quantum information processing systems from errors. These methods go under a variety of names --- decoherence-free subspaces, noiseless subspaces, bang-bang control --- but their underlying mathematics is similar. Each of these techniques relies on symmetries, either existing or induced, in the interaction of the quantum information processing system with its environment. Recent work by Knill, Laflamme, and Viola has suggested an approach for unifying these methods with conventional quantum error correction codes. The framework is that of group representation theory. Lloyd, Cory, Kent, Johnson and Suhov will generalize this approach and will develop and implement experimentally new examples of symmetric quantum error protection.

Room-temperature nuclear magnetic resonance has proved itself over the last five years to be a highly effective method of demonstrating basic quantum algorithms and quantum information processing tools. Although room-temperature NMR systems do not exhibit entanglement and are limited by scaling considerations to on the order of ten quantum bits, the highly precise control of NMR systems allows the accurate performance of hundreds or thousands of basic quantum logic operations on those bits. The group of Cory (together with collaborators at Los Alamos) and Chuang's group have performed the lion's share of NMR quantum computations in the USA over the last five years. These groups together with their extensive equipment resources will make possible the demonstration of fundamental algorithms and effects developed as part of the CU-MIT collaboration.