**Nanomedicine,
Volume I: Basic Capabilities**

**©
1999 Robert A. Freitas Jr. All Rights
Reserved.**

Robert A. Freitas Jr., Nanomedicine, Volume I: Basic Capabilities, Landes Bioscience, Georgetown, TX, 1999

**10.2.4.2 Quantum Computers**

Digital computers manipulate discrete units of information, with data strings stored as binary digits, or bits. Any two-state physical system (e.g., high or low voltages in semiconductor circuits) can represent these bits. Similarly, a quantum computer would use quantum states of atomic or molecular systems to store data. For example, the states of a hydrogen atom could be assigned such that a wavefunction corresponding to a state of hydrogen would represent a bit of data. Shining laser light on the atoms would trigger processing the data by inducing transitions between electronic states.

Quantum systems, however, exhibit a peculiar phenomenon known
as superposition, in which several discrete states can be processed by a single
physical system at once, crudely analogous to the musical effect of a single
note being made up of many different harmonics.^{1259}
Superposition gives quantum systems the potential to be enormously more powerful
than conventional computers. Since more than one state can be supported, quantum
bits, or qubits, may store a mixture of many bits of data at the same time.
A superposition of N qubits can store 2^{N} binary digits. An operation
on these mixtures is massively parallel, effectively performing many calculations
simultaneously. For example, photons interacting with an atom in a superposition
of states drive all the states in the superposition, producing another superposition
corresponding to all solutions of the original states. The advantage over conventional
computers is not merely linear, but exponential: A conventional processor operates
sequentially on 64-bit numbers, but a quantum computer with 64 qubits would
simultaneously operate on the full set of 2^{64} (~10^{19})
binary values. An N-qubit quantum computer could model an N-body system in real
time^{6}; in contrast, the number of operations
required by a conventional computer to perform such a simulation increases exponentially
with the number of bodies.

Since the early 1980s, theoretical interest in quantum computing
has developed rapidly.^{6,1996-2004,2013}
Many groups have begun designing quantum computational architectures and constructing
physical quantum gates and devices. In 1995, one group at NIST made a controlled
NOT gate of two qubits from a cooled beryllium ion in a radio-frequency trap,^{2005}
while a French group used single photons trapped in quantum cavities to control
cesium atom states.^{2006} In 1999,
experiments began on an analog quantum computer using electrons floating on
liquid helium.^{3276} Others work
with NMR techniques,^{2007,2008,2014}
storing data not in electron states but in nuclear spins, which are less susceptible
to perturbations.^{2002} Resonance
effects between proton and electron spins in hydrogen atoms can make AND and
NOT gates, hence NAND gates, from which all Boolean computers can be made. It
has been suggested that by encoding the amplitudes of a couple of thousand electron
states in a superposition, large amounts of data could be written onto a single
atom (see Section 10.2.4.3). The discovery of certain
error-correcting procedures,^{2003}
since verified experimentally,^{2141}
was another important breakthrough. Unlike conventional devices, it is not possible
to simply check that qubits are in the right states, because the act of measuring
destroys the coherence. But Shor^{2009}
proved that information can be reliably stored and read from a several qubit
system even if one of the bits is corrupted, and it has been shown that error
correction can be applied during the computation process itself.^{2010}
This opens the door to many-qubit systems; by 1998, two groups had already performed
4-bit sums, and one group had demonstrated a 2-qubit device.^{2329}
Quantum game theory has also been investigated.^{2867}

Last updated on 24 February 2003