# New Approaches to Quantum Computing using Nuclear Magnetic Resonance Spectroscopy

## Abstract

The power of a quantum computer (QC) relies on the fundamental concept of the superposition in quantum mechanics and thus allowing an inherent large-scale parallelization of computation. In a QC, binary information embodied in a quantum system, such as spin degrees of freedom of a spin-1/2 particle forms the qubits (quantum mechanical bits), over which appropriate logical gates perform the computation. In classical computers, the basic unit of information is the bit, which can take a value of either 0 or 1. Bits are connected together by logic gates to form logic circuits to implement complex logical operations. The expansion of modern computers has been driven by the developments of faster, smaller and cheaper logic gates. As the size of the logic gates become smaller toward the level of atomic dimensions, the performance of such a system is no longer considered classical but is rather governed by quantum mechanics. Quantum computers offer the potentially superior prospect of solving computational problems that are intractable to classical computers such as efficient database searches and cryptography. A variety of algorithms have been developed recently, most notably Shor's algorithm for factorizing long numbers into prime factors in polynomial time and Grover's quantum search algorithm.more »

- Authors:

- Publication Date:

- Research Org.:
- Lawrence Livermore National Lab., CA (US)

- Sponsoring Org.:
- US Department of Energy (US)

- OSTI Identifier:
- 15007477

- Report Number(s):
- UCRL-ID-151370

TRN: US0401998

- DOE Contract Number:
- W-7405-ENG-48

- Resource Type:
- Technical Report

- Resource Relation:
- Other Information: PBD: 7 Feb 2003

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; ALGORITHMS; COMPUTERS; DEGREES OF FREEDOM; EFFICIENCY; JOSEPHSON JUNCTIONS; LOGIC CIRCUITS; NUCLEAR MAGNETIC RESONANCE; NUCLEI; OPTICS; POLYNOMIALS; QUANTUM MECHANICS; RESEARCH PROGRAMS; RESONANCE; SIMULATORS; SOLVENTS; SPECTROSCOPY; SPIN; TRANSISTORS

### Citation Formats

```
Colvin, M, and Krishnan, V V.
```*New Approaches to Quantum Computing using Nuclear Magnetic Resonance Spectroscopy*. United States: N. p., 2003.
Web. doi:10.2172/15007477.

```
Colvin, M, & Krishnan, V V.
```*New Approaches to Quantum Computing using Nuclear Magnetic Resonance Spectroscopy*. United States. doi:10.2172/15007477.

```
Colvin, M, and Krishnan, V V. Fri .
"New Approaches to Quantum Computing using Nuclear Magnetic Resonance Spectroscopy". United States. doi:10.2172/15007477. https://www.osti.gov/servlets/purl/15007477.
```

```
@article{osti_15007477,
```

title = {New Approaches to Quantum Computing using Nuclear Magnetic Resonance Spectroscopy},

author = {Colvin, M and Krishnan, V V},

abstractNote = {The power of a quantum computer (QC) relies on the fundamental concept of the superposition in quantum mechanics and thus allowing an inherent large-scale parallelization of computation. In a QC, binary information embodied in a quantum system, such as spin degrees of freedom of a spin-1/2 particle forms the qubits (quantum mechanical bits), over which appropriate logical gates perform the computation. In classical computers, the basic unit of information is the bit, which can take a value of either 0 or 1. Bits are connected together by logic gates to form logic circuits to implement complex logical operations. The expansion of modern computers has been driven by the developments of faster, smaller and cheaper logic gates. As the size of the logic gates become smaller toward the level of atomic dimensions, the performance of such a system is no longer considered classical but is rather governed by quantum mechanics. Quantum computers offer the potentially superior prospect of solving computational problems that are intractable to classical computers such as efficient database searches and cryptography. A variety of algorithms have been developed recently, most notably Shor's algorithm for factorizing long numbers into prime factors in polynomial time and Grover's quantum search algorithm. The algorithms that were of only theoretical interest as recently, until several methods were proposed to build an experimental QC. These methods include, trapped ions, cavity-QED, coupled quantum dots, Josephson junctions, spin resonance transistors, linear optics and nuclear magnetic resonance. Nuclear magnetic resonance (NMR) is uniquely capable of constructing small QCs and several algorithms have been implemented successfully. NMR-QC differs from other implementations in one important way that it is not a single QC, but a statistical ensemble of them. Thus, quantum computing based on NMR is considered as ensemble quantum computing. In NMR quantum computing, the spins with non-zero nuclear moments (spin 1/2 nuclei such as {sup 1}H or {sup 13}C) in an organic molecule dissolved in a solvent constitute the required qubits. The logic gates and algorithms correspond to set of instructions containing radio frequency (r.f) pulses and delays that manipulate the qubits and the final spectrum reflects the outcome of the algorithm. Three years ago, when we initiated proposal on NMR-QC, the foremost of the aim is to develop quantum computing as part of LLNL research programs and hence cultivate an interdisciplinary working group in the area of quantum computing. Our success in the proposal is in part responsible for the formation of the laboratory-wide exploratory group on ''quantum computing and information''. The PI's play an integral role in promoting the work performed using the LDRD funded project and hence acquire the attention within the lab as well outside. In specific goals of the project were to (a) develop experimental and sample based methods to improve the performance of NMR-QC, (b) define and estimate actual time cost or efficiency of a QCs, and (c) construct a comprehensive simulator of QC based on the principles of ensemble quantum computing. We were able to accomplish these goals and in particular we have reached some significant milestones in defining the QC efficiency and development of the QC-simulator. These developments have resulted to three publications.},

doi = {10.2172/15007477},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2003},

month = {2}

}