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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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