Scientific Progress and Accomplishments:

QUIC has had a productive year at MIT.  We have made significant progress in the areas of algorithms, devices, and error correction.

Algorithms: This year we devoted considerable resources towards designing algorithms for simple (few-bit) quantum computers.  The goal was to program quantum ‘microprocessors,’ with two or three quantum bits, to perform tasks that are not possible on classical devices.  We designed a two qubit version of the Deutsch-Jozsa algorithm, which can provide exponential speed-ups over classical computers.  Our version of this algorithm was performed by Ike Chuang and collaborators using nuclear magnetic resonance techniques, resulting in the experimental confirmation of the ability of quantum computers to perform calculations more rapidly than is possible classically.  In addition, we showed how simple sequences of quantum logic operations could be used to test fundamental quantum physics, by showing how few-bit quantum logic devices could be used to demonstrate a quantum heat engine, or ‘Maxwell's Demon,’ and to test quantum nonlocality by performing microscopic analogs of the Greenberger-Horne-Zeilinger experiment. Finally, we continued our work on quantum simulation to identify the ‘easiest’ quantum systems to simulate. (It should be noted that David Cory at MIT has managed to realize our quantum simulation procedures experimentally to make calcium fluoride crystals simulate large-scale quantum systems not found in nature).

Devices: We investigated a number of ‘non-standard’ techniques for quantum computation, including extending existing adiabatic passage techniques to many particles and to frequency domain methods.  In addition, we began a series of simple NMR experiments at the MIT Magnet Lab to test some of the algorithms described above.  We also investigated nonlinear versions of quantum mechanics and showed that if the usual (Weinberg) nonlinear quantum mechanics holds, then NP-complete and #P problems can be solved rapidly on a quantum computer.

Error Correction: We set forward a larger framework for quantum error correction by embedding it in a general theory of quantum feedback control.  We showed that if feedback control is implemented in a fully quantum-mechanically coherent fashion, then quantum systems can be controlled in ways that are not possible using ordinary ‘semiclassical’ feedback control.  We are working with Hideo Mabuchi at Caltech to look at feedback control in a quantum context, and have begun an experimental program to investigate quantum feedback using NMR.  In addition, we fulfilled one of the original QUIC goals by providing an in-principle solution to the analog quantum error correction problem.

Plans for the coming year:

We are continuing our work on quantum algorithm design to come up with useful algorithms that can be implemented on existing quantum ‘microprocessors’' and on the next generation of few-bit machines. We are investigating large-scale quantum simulations using NMR, both at the theoretical and the experimental level.

We will continue device development with the aim of providing accurate and stable quantum computation using quantum feedback control.  In addition, we will develop techniques for implementing quantum error correction and quantum feedback control using small-cavity electrodynamics.
 

List of Participating Scientific Personnel:

Seth Lloyd, Ph.D., Co-Principal Investigator, MIT
Personnel:
Post-Doctoral Fellow: Lorenza Viola
Graduate Students: Daniel Abrams, Rick Nelson, Hyuk-Sang Kwan, Yaakov Weinstein, Yun Kang
Visiting Associates: Murray Gell-Mann, Jean-Jacques Slotine

List of Manuscripts/Publications:

1. “Capacity of the Noisy Quantum Channel,” Physical Review A 55, R1613-1622, March 1997.
2. “Simulation of Many-Body Fermi Systems on a Universal Quantum Computer,” with Dan Abrams, Physical Review Letters 79, 2586-2589, 1997.
3. “Quantum-Mechanical Maxwell's Demon,” to appear in Physical Review A.
4. “Controllability and Observability of Quantum Systems,” submitted to Physical Review Letters, March 13, 1997.
5. “Analog Quantum Error Correction,” with J.J.E. Slotine, submitted to Physical Review Letters, December 15, 1997.
6. “Unconventional Quantum Computing Devices,” submitted to the proceedings of the Auckland Conference on Unconventional Computation.
7. “Universe as Quantum Computer,” Complexity 3, p. 32, 1997.
8. “Microscopic Analogs of the Greenberger-Horne-Zeilinger Experiment,” to appear in Physical Review A.