C.-H. Tseng

QUANTUM SIMULATIONS ON A QUANTUM COMPUTER

We present a general scheme for performing a simulation of the dynamics of one quantum system using another. This scheme is used to experimentally simulate the dynamics of truncated quantum harmonic and anharmonic oscillators using nuclear magnetic resonance. We believe this to be the first explicit physical realization of such a simulation. {copyright} {ital 1999} {ital The American Physical Society }

Principles and Demonstrations of Quantum Information Processing by NMR Spectroscopy

Abstract. This paper surveys our recent research on quantum information processing by nuclear magnetic resonance (NMR) spectroscopy. We begin with a geometric introduction to the NMR of an ensemble of indistinguishable spins, and then show how this geometric interpretation is contained within an algebra of multispin product operators. This algebra is used throughout the rest of the paper to demonstrate that it provides a facile framework within which to study quantum information processing more generally. The implementation of quantum algorithms by NMR depends upon the availability of special kinds of mixed states, called pseudo-pure states, and we consider a number of different methods for preparing these states, along with analyses of how they scale with the number of spins. The quantum-mechanical nature of processes involving such macroscopic pseudo-pure states also is a matter of debate, and in order to discuss this issue in concrete terms we present the results of NMR experiments which constitute a macroscopic analogue Hardys paradox. Finally, a detailed product operator description is given of recent NMR experiments which demonstrate a three-bit quantum error correcting code, using field gradients to implement a precisely-known decoherence model.

Stochastic resonance and nonlinear response using NMR spectroscopy

We revisit the phenomenon of quantum stochastic resonance in the regime of validity of the Bloch equations. We find that a stochastic resonance behavior in the steady-state response of the system is present whenever the noise-induced relaxation dynamics can be characterized via a single relaxation time scale. The picture is validated by a simple nuclear magnetic resonance experiment on water.

Portable trap carries particles 5000 kilometers

Electrons suspended in a Penning trap were transported more than 5000 km, all the way across the continental United States. The magnetic field was provided by a persistent superconducting solenoid at 4.7 T which was not connected to any source of power during travel. The electric field was produced using ordinary 9 V batteries. A good vacuum, expected to be sufficient to keep antiprotons stored indefinitely, was maintained within the trap by keeping it at 4 K. Portable traps are of interest for experiments which require small numbers of antiprotons for precise studies, for acceleration to energies not available at the LEAR antiproton source, for experiments with large immovable detectors, and for possible medical applications. The portable apparatus is so similar to that used to contain low energy antiprotons, that the trip demonstrates the feasibility of transporting cold antiprotons over large distances in portable traps.

Extremely cold antiprotons for antihydrogen production

The possibility to produce, trap and study antihydrogen atoms rests upon the recent availability of extremely cold antiprotons in a Penning trap. Over the last five years, our TRAP Collaboration has slowed, cooled and stored antiprotons at energies 1010 lower than was previously possible. The storage time exceeds 3.4 months despite the extremely low energy, which corresponds to 4.2 K in temperature units. The first example of measurements which become possible with extremely cold antiprotons is a comparison of the antiproton inertial masses which shows they are the same to a fractional accuracy of 4×10−8. (This is 1000 times more accurate than previous comparisons and large additional increases in accuracy are anticipated.) To increase the number of trapped antiprotons available for antihydrogen production, we have demonstrated that we can accumulate or “stack” antiprotons cooled from successive pulsed injections into our trap.

A superconducting solenoid system which cancels fluctuations in the ambient magnetic field

Abstract An extra superconducting coil added to a standard, high-field solenoid results in a self-shielding solenoid system which utilizes flux conservation to passively shield an interior volume from changes in the ambient field, such as those from elevators or subways. For this first experimental demonstration, a highly homogeneous 6 T solenoid and an added coil were arranged in one of the geometries predicted to produce effective shielding. The fluctuations in the shielded high-field region are observed to be smaller than the fluctuations in the spatially uniform ambient magnetic field by a large factor of 156, confirming the general shielding principles presented earlier. This shielding is crucial for ongoing antiproton cyclotron resonance experiments and should be useful for nuclear magnetic resonance experiments and ion cyclotron resonance experiments and for other applications where high field and high stability are required simultaneously.

One-electron parametric oscillator

The parametric oscillation of a trapped electron is studied and used to measure enhanced spontaneous emission. Hysteresis in this motion provides a one bit memory to store information about excitations made with the electron “in the dark”.

Extremely cold antiprotons, for mass measurements and antihydrogen

Over the last five years, a series of experiments by our TRAP Collaboration has made it possible to slow, cool and store antiprotons at energies 1010 lower than was previously possible. Despite the extremely low energy, the storage time exceeds 3.4 months. The first example of measurements which become possible with extremely cold antiprotons is a comparison of the antiproton and proton inertial masses which shows they are the same to a fractional accuracy of 4×10−8. This is 1000 times more accurate than previous comparisons and large additional increases in accuracy are anticipated soon. The availability of low energy antiprotons opens other experimental possibilities as well, such as the production and study of trapped antihydrogen atoms. To increase the number of trapped antiprotons we have demonstrated that we can accumulate antiprotons from successive pulsed injections of antiprotons into the trap.

Geometric Algebra in Quantum Information Processing by Nuclear Magnetic Resonance

The relevance of information theoretic concepts to quantum mechanics has been apparent ever since it was realized that the Einstein-Podolsky-Rosen paradox does not violate special relativity because it cannot be used to transmit information faster than light [ 22, 39]. Over the last few years, physicists have begun to systematically apply these concepts to quantum systems. This was initiated by the discovery, due to Benioff [ 3], Feynman [ 25] and Deutsch [ 17], that digital information processing and even universal computation can be performed by finite state quantum systems. Their work was originally motivated by the fact that as computers continue to grow smaller and faster, the day will come when they must be designed with quantum mechanics in mind (as Feynman put it, “there’s plenty of room at the bottom”). It has since been found, however, that quantum information processing can accomplish certain cryptographic, communication, and computational feats that are widely believed to be classically impossible [ 5, 9, 19, 23, 40, 53], as shown for example by the polynomial-time quantum algorithm for integer factorization due to Shor [ 45]. As a result, the field has now been the subject of numerous popular accounts, including [ 1, 11, 37, 60]. But despite these remarkable theoretical advances, one outstanding question remains: Can a fully programmable quantum computer actually be built?