DARPA ITO Sponsored Research

1997 Project Summary
Bulk Quantum Computation with NMR
Stanford University

Project Website: http://feynman.stanford.edu/nmrqc -- Additional project information provided by the performing organization
Objective: The focus of this research program is to investigate and to develop an enabling technology for the near-term realization of practical computing systems based on the non-classical dynamical behavior of quantum scale systems. Such systems offer orders-of-magnitude improvement in computing power beyond foreseeable technology. Through a collaborative engineering and basic science effort, recent results demonstrating the possibility of quantum computation with bulk systems will be leveraged to accomplish the following objectives:
  • Demonstrate basic quantum gates and circuits using NMR techniques
  • Laboratory implementation of quantum algorithms, and tests of fitness for quantum computation
  • Experimental application of quantum error correction codes
  • Development of robust quantum algorithms which tolerate errors
  • Design and construct a desktop scale quantum computer and ultimately, a solid-state microminiaturized system
  • Develop and implement an optimizing "quantum compiler" and language to program quantum computers

Approach: Quantum Gates, Circuits, and Algorithms using NMR - Bulk quantum computation is a radically different approach which, in contrast to trapped ion and cavity-QED implementations, allows quantum computation to be performed using ordinary liquids at room temperature. Applying these methods to nuclear magnetic resonance, and using a simple molecule in solution, a quantum controlled-NOT gate has been realized. Quantum bits (qubits) are represented as nuclear spins, which have long coherence times due to their natural isolation from the external world, and fiducial input states are created using state labeling techniques. Cascading elementary gates will provide an exciting opportunity to experimentally explore quantum algorithms immediately.

Error Correction - Quantum computers, though inherently digital in nature, are notoriously susceptible to errors due to decoherence: leakage of quantum information to the environment. This reality can be countered by application of error correction techniques, which restore the system to a set of standardized states. Methods which generalize known classical error correction codes to work on quantum systems have been discovered, but these codes are complicated; the simplest requires five qubits to encode one. Practical quantum computers require simple, expedient codes which are short and easy to encode and decode, and target real-world errors like those resulting from T1 and T2 processes in NMR. Such codes will be developed and their application will be explored using high-field NMR techniques in the laboratory.

Robust Quantum Algorithms - Quantum computation can be made reliable at the expense of intermixing quantum error correction techniques with quantum algorithms. This is currently the subject of serious theoretical investigations; however, it can also be seen that algorithms such as Shor's quantum factoring algorithm actually use decoherence as an integral part of their procedures. In fact, simulated annealing provides an excellent classical example of the usefulness of controlled loss (heating and cooling via coupling to an external reservoir). Application of such notions toward quantum computation would provide a way to perform quantum computation with decohering systems, and thus achieve a natural robustness. These algorithms would provide practical means for accomplishing quantum computation with current technology, such as NMR.

Quantum Signature Tests - Given a black box, what distinctive signature would its dynamics have which certifiably demonstrate its capacity to perform quantum (vs. classical) computation? From the theoretical point of view, an NMR quantum computer can be treated as a black box, as can other physical implementations. For the purposes of quantum computation, what is most important is the existence of an exponential number of degrees of freedom which are manipulated by a polynomial number of "knobs." A suitability benchmark will be designed to test for this relationship, and implemented on an NMR quantum computer.

Quantum Computer Compiler - Quantum algorithms are implemented with quantum circuits, which are networks of abstract elements such as the controlled-NOT and square-root-of-NOT gates. An important application, which will complement network design and simulation tools, is the "back-end" compiler, which outputs actual control instructions optimized for a particular physical machine model, such as an ion trap or NMR spectrometer. Depending on the experimental configuration, many simplifications can be made, and due to the imperfect nature of current experiments, such optimizations may be crucial to practical operation. For example, sequential single qubit rotations can be combined using the rules of SU(2) Lie algebra. At present, simple quantum circuits are hand-coded into pulse sequences for NMR quantum computation. An optimizing compiler will be developed to automate this important function.

Desktop Quantum Computer - Quantum computers will not be practically useful until they are either large enough to out-perform the best classical computers, or physically small enough to be useful as integrated co-processors. A technological opportunity afforded by the invention of bulk quantum computers is the development of such a quantum co-processor. As a step in this direction, a desktop scale quantum computer will be designed and implemented, using permanent magnet NMR techniques, and targeted multi-qubit molecules. Ultimately, the envisioned system is a solid-state quantum computer, realized by modern semiconductor materials technology using micromachining of complex quantum structures.

Recent FY-97 Accomplishments: New Start
FY-98 Plans:

Cascade multiple quantum gates

Experimentally demonstrate a superfast quantum algorithm

Characterize quantum error correction code performance

Implement quantum computer compiler

Technology Transition: New Start
Principal Investigator: James Harris
Paul Allen Center for Integrated Systems
Rm. 328
Stanford, CA 94305-4075
(650) 723-9775
(650) 723-4659 fax

Neil Gershenfeld
MIT Media Lab, Rm. E 15-495
20 Ames St.
Cambridge, MA 02139-4307
(617) 253-7680
(617) 258-7168 fax

Ruth Kaempf
Stanford University
Sponsored Projects Office M/C 4125
Stanford, CA 94305-3027
650 723-4740
650 723-0810 fax