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Quantum Computing Hardware Implementation Methods: A Survey over Categories

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Abstract

In this paper, we conduct a comprehensive survey of quantum hardware implementation methods with an assessment to categorize them, manifest them under an even scheme, and indicate their weaknesses, strengths, differences and similarities. Those quantum hardware implementation methods are categorized into five groups according to the basic elements they are using: Nuclear Magnetic Resonance (NMR), ion traps, all optical, super conducting, and quantum dots. We compare these methods to indicate the method with the most promising potential.
1
Quantum Computing Hardware Implementation
Methods: A Survey over Categories
Reem Alataas & Khaled Elleithy
Computer Science & Engineering Department
University of Bridgeport
Bridgeport, CT
ralataas@bridgeport.edu & elleithy@bridgeport.edu
Abstract In this paper, we conduct a
comprehensive survey of quantum hardware
implementation methods with an assessment to
categorize them, manifest them under an even
scheme, and indicate their weaknesses, strengths,
differences and similarities. Those quantum
hardware implementation methods are
categorized into five groups according to the
basic elements they are using: Nuclear Magnetic
Resonance (NMR), ion traps, all optical, super
conducting, and quantum dots. We compare
these methods to indicate the method with the
most promising potential.
Index Terms—Quantum computing, hardware,
nuclear magnetic resonance, ion traps, all optics,
super conducting, quantum dots.
I. I
NTRODUCTION
Why build a quantum computer? Because it’s not
there, since the implementation of quantum
computing machines represents a formidable
challenge to the communities of engineers and
applied physicists. However, there is some hope in
sight: quite recently, some simple quantum devices
consisting of a few qubits have been successfully
built and tested.
Different implementation methods are used
including ion traps, Nuclear Magnetic Resonance
(NMR) spectroscopy, optics, Josephson junction,
and quantum dots. In this paper, we survey a variety
of proposed quantum computing quantum hardware
implementation methodologies using the taxonomy
framework proposed by Van Meter, 2006 in [1].
This paper structure is as follows: quantum
hardware implementation methods are discussed in
section II. The different implementation methods
categories are discussed in the subsections of that
section. Finally, we provide the conclusions in
section III.
II. Q
UANTUM
H
ARDWARE
I
MPLEMENTATION
M
ETHODS
Despite the experimental problems of
implementing quantum devices, theoretical
physicists have tried to conceive some
implementations for quantum algorithms. We
present five technologies: NMR, ion traps, all
optical, super conducting, and quantum dots. These
systems were chosen for their near and long term
implementation capabilities. In the following
subsections, we will briefly discuss each technology
and its architectural implications.
A. NMR
Nuclear Magnetic Resonance (NMR) quantum
computing uses the spin states of molecules as
qubits. NMR differs from other implementations of
quantum computers in that it uses an ensemble of
systems, i.e. molecules. The ensemble is initialized
to be the thermal equilibrium state. In mathematical
parlance, this state is given by the density matrix [2]:
where H is the Hamiltonian matrix of an
individual molecule and
where k is the Boltzmann constant and T the
temperature.
2
In the following subsections, we will go through
solution NMR, All-Silicon NMR, and Kane Solid-
State NMR.
1. Solution NMR
Probably the most complete demos of quantum
computation to date are the solution NMR
experiments [3]. In an NMR system, the qubit is
denoted by the spin of the nucleus of an atom. When
placed in a magnetic field, that spin processes, and
the spin can be deployed via microwave radiation. In
solution NMR, a carefully planned molecule is used.
Some of the atoms in the molecule have nuclear
spins, and the frequency of radiation to which they
are disposed varies depending on their position in
the molecule, so that different qubits are addressed
by frequency. Many copies of the molecule are held
in a liquid solution; each molecule is a separate
quantum computer, run independently, with the
large numbers providing adequate signal strength for
readouts. This is the canonical ensemble system [4].
Strengths Weaknesses
Good decoherence time,
room temperature
operation, and advanced
experimental
verification.
Slow gates, poor
scalability, and difficult
concurrent operations.
2. All-Silicon NMR
Ladd et al. have proposed an all-silicon NMR-
based quantum computer which stores qubits in the
nuclear spin of 29Si (spin 1/2 nucleus) laid down in
a line across a micromechanical bridge of spin 0
nuclei (28Si and 30Si). This is an ensemble system;
105 copies are required to get satisfactory signal for
measurement. Readout is done via magnetic
resonance force microscopy (MRFM), reading
oscillations of the bridge. Initialization is done via
electrons whose spins are set with polarized light.
Operations are done via microwave radiation
directed at the device [1].
Strengths Weaknesses
Longest known
decoherence time;
Slow gates,
measurement still being
designed.
3. Kane Solid-State NMR
Kane has suggested a solid-state NMR system
with excellent scalability, built on VLSI techniques
for control [6]. Then, others suggested that
teleportation may be required to move qubits long
distances even for error correction, and progress in
fabrication has been made. In this system, individual
phosphorus atoms are embedded in a silicon
substrate, and standard photolithography techniques
are used to build control structures on the surface.
The qubit is held in the spin of the phosphorus
nucleus, and interactions between neighboring
qubits are mediated by electrons coupled to the
nuclei via hyperfine interactions. The shape of the
electron wave function is controlled via the control
structures built on the Si surface; the distance
between neighboring P atoms and the accuracy of
aligning the control gates to the P impurities will
determine the quality of qubit interactions.
Strengths Weaknesses
Long coherence time; Difficult fabrication,
creating adequate
overlap in electron wave
functions.
B. Ion Trap
One of the few systems that explicitly separate
storage areas from interaction areas is the scalable
ion trap [7]. In ion trap systems, qubits are usually
stored in the energy levels of individual ions. Early
ion trap experiments featuring small numbers of ions
held in a single trap have given way to a large
system of interconnected, individually controllable
traps. In the scalable trap system, the ions are
literally moved around using magnetic fields until
they reach locations in the system designated for
operations, as shown in Figure 3. Small numbers of
ions are brought together and formed into chains to
execute multi-qubit gates. Gates are effected by
laser pulses, and readout is also accomplished by
laser pulses creating fluorescence (interpreted as a 1)
or not (0), depending on the state of the atom. Gate
times are moderate; speed can be traded off against
fidelity in the range of 14-100kHz. Overall system
performance will likely be driven by ion movement
3
times (which naturally depend on distance and
topology), times for creating and splitting chains of
atoms, time to cool atoms heated by the movement
process, and multiplexing of gate operations. The
movement operations are unlikely to allow a gate
rate in excess of 20kHz.
Strengths Weaknesses
Scalability of storage; Slow gates; limitations
on concurrent operations
and measurements.
C. All Optical
All-optical systems come in two flavors: those
that depend on nonlinear effects to execute gates,
and those in which the only necessary nonlinearity is
measurement, known as Linear Optics Quantum
Computation (LOQC). Research on all-optical
systems has focused on photon sources capable of
generating precise numbers of photons with the
necessary timing precision, gates based on
measurement, and high-quality single-photon
detectors [11]. Measurement-based gates are
inherently probabilistic in nature, though it has been
shown that these gates can be built into a scalable
feed-forward network. Much of the current
experimental work is focusing on this approach, and
individual gates have been shown to work.
Jitter and skew are likely to be managed by
“stopped light,” created by electromagnetically-
induced transparency.
Strengths Weaknesses
Well-understood physics
and easy fabrication;
Photon losses; for
nonlinear systems, weak
nonlinear effects give
poor gate quality; high
resource requirements
for probabilistic gates.
D. Super Conducting
Super conducting devices come in three flavors:
represent qubits using charge, using flux, and using
phase; most of the information in the tables applies
to all three. Fabrication is done using conventional
electron-beam lithography and shadow evaporation
of Al onto a SiNx insulating substrate. In the charge
qubit, a sub-micron size superconducting box
(essentially, a small capacitor) is coupled to a larger
superconducting reservoir. In a superconductor,
electrons move in pairs known as Cooper pairs.
The qubit representation is the number of Cooper
pairs in the box, controlled to be either zero or one,
or a superposition of both. Similarly, for the flux
qubit, Cooper pairs are introduced into a
superconducting ring, where they circulate and
induce a quantized magnetic flux. Because the flux
qubit has slower gate times but a relatively even
longer coherence time, experimental efforts appear
to be shifting toward the flux qubit approach [1].
In one proposed scalable form of the charge qubit
it is possible to address any two qubits and couple
them. This is done through a shared inductance. In
this case, the restriction of operations involving only
neighboring qubits in a linear array is removed, but
execution is limited to one gate at a time.
A different proposal links neighboring qubits in a
one-dimensional structure with nearest-neighbor-
only gates, but potentially may allow concurrent
gates on independent qubits.
Strengths Weaknesses
Very fast gates,
advanced experimental
demonstration,
straightforward
fabrication.
Low coherence time
relative to measurement
time, sensitivity to
background charge
fluctuations and local
magnetic fields.
E. Quantum Dot
A “quantum dot,” as used in quantum
information processing, is a lithographically-defined
structure that confines electrons at the boundary
layer between two materials, creating a two-
dimensional electron gas (2DEG). By varying the
surrounding electrical potential, individual electrons
can be positioned in a small area, called the quantum
dot. A qubit can be defined based on the number of
electrons in a quantum dot or the spin or energy
levels of a single electron held in a quantum dot.
Several quantum dot devices are under
development; one experimentally advanced
approach uses a pair of quantum dots as a dual-rail
4
encoded logical qubit, with a single electron in the
left dot representing a logical 0, and the electron in
the right dot representing a logical 1. Another
approach uses a linear array of single-electron
quantum dots, and encodes the qubit in the spin of
the excess electron [15].
In a third approach, the only operation needed is
an exchange between two neighboring qubits,
accomplished by lowering the electrical potential
and allowing the electrons to tunnel. This is easier to
accomplish than precise control of a magnetic field,
which would be required in order to affect other
gates on specifically addressable bits.
Perhaps the biggest disadvantage of this approach
is that exchange-only computation requires encoding
a single logical qubit onto multiple physical qubits.
A CNOT, for example, requires each logical qubit to
be encoded in three physical qubits, and the
exchange times must be controlled fairly precisely.
TheCNOT on neighboring logical qubits requires 19
exchange operations [DiVincenzo et al. 2000],
though Myrgren and Whaley [2003] have found
interesting optimizations that allow non-neighbor
operations to be effected in 28% fewer total
operations than the obvious formulation of repeated
use of the 19-exchange CNOT.
Continued compiler work may reduce the
encoded execution time penalty further, though the
important storage penalty remains.
Strengths Weaknesses
Advanced fabrication
Low
coherence time
III. C
ONCLUSION
In this paper, quantum hardware implementation
methods were considered. The usefulness of the
different methods was regarded. According to our
survey, the best implementation method was super
conducting followed by solution NMR.
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Symposium on , vol.5, no., pp. V-777- V-780
vol.5, 25-28 May 2003
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... Elleithy en la International Conference on Quantum Information Science and Engineering realizada en Berlin, Alemania, en mayo de 2013 [2]. Más recientemente, la Academia Nacional de Ciencias, Ingeniería y Medicina de los EEUU publicó una revisión del progreso y las perspectiva del área [75], mientras que Jazaeri et al. presentan una revisión de plataformas de computación cuántica basadas en Silicio [53]. ...
Book
Se realizó una discusión detallada de correlaciones cuánticas en estados de sistemas bipartitos de qubits y de un importante conjunto de cuantificadores, centrados en la familia de los llamados Estados Bell Diagonal (BD) [13]. Para el entrelazamiento se presentó la Concurrencia [45] como cuantificador bona fide de la misma. Se realizó un cuidadoso estudio de las denominadas Discordias Cuánticas, tanto la introducida por Ollivier y Zurek [79] como por Henderson y Vedral [42], que denotaremos QD, como también de las tres Discordias Geométricas (DG) conocidas, i.e. Distancia de Hilbert-Schmidt [19], Distancia de Traza [80] y Distancia de Bures [98], y se presentaron los cálculos analíticos de éstas para los estados BD. Igualmente se realizaron los cálculos analíticos para los cuantificadores relacionados con las denominadas Correlaciones Cuánticas Localmente Asequibles (LAQC) [72] para la familia de los estados BD [3]. Finalmente se estudió la dinámica disipativa de tres tipos de correlaciones cuánticas, e.g. entrelazamiento, QD y LAQC, para los estados de Werner [109] bajo la aproximación Born-Markov en el formalismo de los Operadores de Kraus [57]. Palabras claves: Teoría de Información Cuántica, Estados Bell Diagonal, Estados de Werner, Correlaciones Cuánticas, Entrelazamiento, Discordia Cuántica, Decoherencia, Operadores de Kraus.
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