Reversing the usual direction of simulation, the QRST says that noiseless quantum channels can efficiently simulate noisy ones, in the presence of shared entanglement between sender and receiver. The theorem has long been known to hold for some channels on all sources, and about a year ago Shor showed that it holds for all channels on known IID sources. Recently Devetak and Winter have extended the latter result to include all separable sources, known or unknown. Whether the QRST holds for all channels on nonseparable sources remains open.

To observe or control a quantum system, one must interact with it via an interface. In this talk I present simple universal quantum interfaces---quantum input/output ports consisting of a single qubit that interacts with a system. I will show that under very general conditions the ability to observe and control the qubit on its own implies the ability to observe and control the system itself. The interface can also be used as a quantum communication channel, and multiple quantum systems can be connected by interfaces to become an efficient universal quantum computer. Experimental realizations are proposed, and implications for controllability, observability, and quantum information processing are explored.

Work done in collaboration with M. L.. Terraciano, F. M. Dimler, W. P. Smith and J. E. Reiner and supported by NSF and NIST.

We define "reciprocal logic gates" in both classical and quantum context. In addition to invertibility, these obey the following "action--reaction" criterion (assume for simplicity two inputs, x and y, and two outputs, x' and y'): The mutual information between x and y' conditional on y equals the mutual information between y and x' conditional on x. Intuitively, the "amount of influence" of signal x on y must equal that of signal y on x.

We discuss the existence of nontrivial reciprocal gates, the preservation of reciprocity on composition of such gates, and their computation universality. In conclusion, like the invertibility constraint, this additional physically-motivated criterion further restricts the structure of networks capable of useful computation, but (unlike the linearity constraint) does not arrive to "kill" computation universality. In sum, there is still room to make logic primitives closer to physics.

However, even in this highly restricted (and much more easily implemented) special case of quantum computing, we can still show that a ballistic (self-contained, and still mostly coherent) variation of the scheme still in fact provides polynomial cost-efficiency advantages for most general-purpose computations, excluding only the small minority of tasks that are either totally serial, or totally parallelizable and very loosely-coupled. This general advantage is due simply to the near-reversibility (low rate of entropy generation) in the ballistic evolution of a well-isolated quantum system. Given the existence of both fundamental and practical bounds on attainable entropy flux densities, the improved entropic efficiency can be demonstrated to boost theoretical performance on, in fact, the majority of computational applications that require tightly-coupled parallelism. Because of the generality of this advantage, we can even argue that this approach, called reversible computing, can reasonably be anticipated to have a greater overall practical economic impact than the more difficult, full-quantum approach, which presently appears somewhat more limited in its potential applications.

In this talk, I will outline the basic technological and architectural requirements for reversible computing, and show how to analyze and optimize the system-level cost-efficiency gains that can be attained using this approach. Given the raw decoherence rate of a particular device mechanism, I show how to optimize other design parameters including the redundancy factor (physical qubits per logical bit) of the logic encoding, the speed of the logic transitions, and the degree of logical reversibility of an arbitrary target computation emulated using Bennett¡¦s spacetime-efficient algorithm. With these parameters simultaneously optimized, I show that improvements in cost-efficiency on the order of 1,000„e that of contemporaneous irreversible computing can be projected for general-purpose desktop-scale applications by the middle of the century.

I also discuss particular technological strategies for implementing the requirement of ballistic, self-contained evolution, which is not a requirement for traditional quantum algorithms, which place no limits on dissipation in the control system. I will also demonstrate a simple new mechanical model of self-timed, 3D, ballistic computation that avoids a variety of defects that were present in earlier models of reversible computing.

It has been known for a long time that the thermodynamic limit kBTln2 on the energy dissipation per logic operation can be overcome by physically and logically reversible circuits. However, explicit experimental demonstration of this is still lacking, and would be highly desirable both in its own right and in view of strong interest in inherently reversible quantum computation. In this work, we analize a few gates including ``negative-inductance SQUID``, that are suitable for the experimental demonstration of reversible information processing in Josephson-junction circuits, and present results of its theoretical and experimental analysis.

A single current biased Josephson junction (CBJJ) is a promising candidate for a solid-state superconducting qubit. The effective coupling strength of two (or more) capacitively coupled CBJJ's may be actively controlled by varying each junction's applied bias current, thus bringing the junctions in or out of resonance. Active tuning of the coupling of qubits provides a powerful mechanism for manipulating quantum states. We numerically compute the energy levels and macroscopic quantum states of the nonlinear coupled-qubit Hamiltonian to guide the engineering of this coupled qubit system. Necessary for the challenge of high fidelity quantum computing, our methods incorporate the effects of tunneling and higher energy states, including the continuum states. Recently, experimental evidence for the macroscopic quantum mechanics of this system in very close agreement with our numerical predications has been seen.

Based on a quantum analysis of two capacitively coupled current-biased Josephson junctions, we have identified two fundamental (universal) two-qubit evolutions, equivalent to controlled-phase and swap gates. By design, these gates take advantage of extra states in the two-junction Hilbert space. Numerical solutions of the time-dependent Schroedinger equation demonstrate that these operations can be performed with good fidelity.

I will review the basic physics of quantum antidots in the i=1 and f =1/3 QH states, and then discuss the experimental determination of the quasiparticle coherence time in a QAD ``molecule". The invariance of quasiparticle charge has been demonstrated in recent experiments. In these experiments, the Laughlin quasiparticle charge has been found to be e*=e/3 \pm 1.2%, independent of temperature, tunneling current and conductance in a wide range of experimental parameters. Thus our experimental results imply robustness of Laughlin quasiparticles localized on QADs, and we conclude that it is possible to control and manipulate fractional quasiparticles in QAD devices in a manner similar to electrons in quantum dots.

The objective of future research is to study possibility of using the controlled transport of FQH quasiparticles in structures with multiple antidots to perform quantum logic operations. The most important question to be answered by the future work is to what extent the topological nature of the statistical phase of fractionally charged quasiparticles helps to alleviate the decoherence problem in quantum computation. The future research should result in a detailed understanding of topological quantum computation and should clarify issues relevant to its eventual practical implementation using FQH systems.

The degree to which a pure quantum state is entangled can be characterized by the distance or angle to the nearest unentangled state. This geometric measure of entanglement, already present in a number of settings (Shimony [1] and Barnum and Linden [2]), is explored for bipartite and multipartite pure and mixed states. It is determined for arbitrary two-qubit mixed states and for generalized Werner and isotropic states, and is also applied to certain multipartite mixed states [3,4]. The physical meaning of the geometric measure of entanglement is also investigated via connections with the notion of entanglement witnesses [5].