Event Horizon, 24 Nov 2003 Quantum Computing Harnessing quantum mechanics for information technology...

Event Horizon, 24 Nov 2003

Quantum ComputingHarnessing quantum mechanics for

information technology

Andrew Fisher

UCL


Overview

• What’s different about a quantum computer?– How can quantum mechanics help with

information processing?– How can “quantum parallelism” make a difference

to the way computations are done?

• How might a quantum computer actually be built?

• What are we doing at UCL?


Why we need quantum mechanics for “more of the same”

• Moore’s Law (doubling of # transitors per chip every ~2 years) already takes mainstream electronics into regions where quantum mechanics is important– Transistors with “gate

lengths” of 10nm can already be fabricated

– Wave-like quantum properties of electrons become important on this lengthscale

– Transistors switchable by a single electron predicted by 2015 or so Quantum mechanics is crucial - but this is not

what we mean by quantum computing


How is quantum mechanics different?

A classical system is always (in principle) in a definite state; we “just” have to specify which one.

For example, to give a complete specification of the system of N particles, we “just” have to specify the positions and velocities (or positions and momenta) of all of them: 6N variables in all.

iv

ir

But for a quantum system this is not true…


How is quantum mechanics different? (2)

The state of a quantum system can involve many different possibilities simultaneously.

Examples:

A double slit experiment: particles pass through both slits to create interference pattern

A particle moving in a potential well: has a probability of being found at many different positions

The “spin” of a particle – for example an electron – can be both “up” and “down” simultaneously


Quantum mechanics and kets

ˆ ˆx y r i j

Mathematically, represent state of the system using kets (a notation introduced by Dirac).

Compare a two-dimensional vector:

A ket represents the state of a system, independently of the details of what coordinate system we use.

“Basis kets” – represent a complete set of possible states for system

“Basis vectors” – represent a complete set of possible directions


Quantum mechanics and information

Information is physics.

What does all this have to do with information processing?

It is not useful to separate abstract statements about information content and information processing from the physical representation of that information.

For example: we now know that computer science classification of problems into hard and easy depends on the physical laws used to process the information.


What is quantum computing?

Classical bits: 0 or 1

Quantum bits: 0 1 Superposition of 0 and 1

A quantum computer performs manipulations on information represented as quantum bits, just as a classical computer performs manipulations on information represented as classical bits.

A quantum computer could perform certain tasks (much) more efficiently than using any known algorithm on a classical computer. It would mark the transition from passively observing the quantum regime, to controlling it.

(qubits)


Overview







Why the advantage?

Have to specify much more information to give the state of a quantum system than of its classical analogue.

E.g. Three qubits: 000 , 001 , 010 , 011 , 100 , 101 , 110 , 111

Specifying general quantum state of N qubits requires 2N numbers:

000 001 010 011 100 101 110 111a b c d e f g h

Since quantum mechanics is linear, operations can, in effect, be performed on each member of this superposition in parallel.

Specifying general classical state requires three binary numbers


Quantum parallelism

1A2A

4A1 2 3 4A A A A A

2

1 2 3 4P A A A A 3A


Quantum gates

X Y Z

0 0 0

1 0 1

0 1 1

1 1 0

mod 2Z X Y

X Y

“Exclusive or” or “controlled not” gate:

CLASSICAL

x y x x y mod 2 00 00

01 01

10 11

11 10

QUANTUM

X

Y

00 01 10 11 00 01 11 10

And…

The bits are processed by means of logical gates


What could it do?

• A quantum computer could:– Factor large integers in a time exponentially faster than

any known classical algorithm, thereby making known public-key cryptography protocols vulnerable to attack

– Search a database of N items in a time proportional to – Efficiently simulate the behaviour of another quantum

system– Possibly run totally new algorithms that we cannot yet

conceive because they have no classical analogue– Lead to a new understanding of the transition between

quantum and classical physics: • When can a macroscopic system be put into a

superposition of quantum states?• The nature of quantum entanglement and nonlocality

N


What do we need?

Ability to perform any transformation on the state of the quantum bits (like any “rotation” of a vector). Needs, for example:

Arbitrary one-qubit manipulations

+At least one two-qubit manipulation

that is “non-trivial” in the sense that it produces quantum correlations

(entanglement) between the qubits0

1

( 0 1 ) / 2

( 0 1 ) / 2H

x y x x y mod 2 00 00

01 01

10 11

11 10

…all before decoherence sets in….0 1

20 (probability )

21 (probability )

(“Hadamard” gate)


A simple example

(0) 0, (1) 1

(0) 1, (1) 0

f f

f f

Is a particular coin we are given “fair” (heads on one side, tails on the other) or not (both sides the same)?

Equivalent to asking…

Is a particular binary function that we are given “balanced” (equally likely to give 0 or 1) or “constant” (always gives same result)

(0) 0, (1) 0

(0) 1, (1) 1

f f

f f

Balanced: Constant:

Classically: must look at both sides of coin (evaluate function twice)


The Deutsch-Josza algorithm

1 2

H

H

0

1

H

0 3

0 top bottom0 1

1

top bottom

0 1 0 1

2 2

2

top bottom

top bottom

0 1 0 1 (if constant)

2 2

0 1 0 1 (if balanced)

2 2

f

f

3 topbottom

topbottom

0 10 (if constant)

2

0 11 (if balanced)

2

f

f

x

y

x

( )y f x

Measure:

0→constant

1→balanced

…with just one function evaluation!

fU

http://www.esi-topics.com/enc/interviews/Dr-David-Deutsch.jpg


Overview







The ‘DiVincenzo Checklist’

Must be able to• Characterise well-defined set of quantum states to use as qubits• Prepare suitable states within this set• Carry out desired quantum evolution (i.e. the computation)• Avoid decoherence for long enough to compute• Read out the results

And ideally• Transport qubits• Interconvert stationary and flying qubits


Some actual or proposed quantum computers

Liquid-state NMR (“quantum computing in a coffee cup” - has factored 15)

Ion traps

Lattices of cold atoms

Bose-Einstein condensates

Atom/photon interactions in cavities (“cavity QED”)

Superconducting circuits


The solid state: pros and cons for quantum computing

• Potential advantages:– Scalability– Silicon compatibility– Microfabrication (and nanofabrication)– Possibility of ‘engineering’ structures– Interaction with light (quantum communication)

• Potential disadvantage:– Much stronger contact of qubits with environment,

so (usually) much more rapid decoherence



Must be able to• Characterise well-defined set of quantum states to use as qubits• Prepare suitable pure states within this set• Carry out desired quantum evolution• Avoid decoherence for long enough to compute• Read out the results



What are the qubits?

• Many different particles in solids (electrons and nuclei) whose states can be used

• There are also collective excitations that only occur in many-particle systems

• Possible systems for qubits include:– Nuclear spins

– Nuclear (atomic) displacements

– Electron spins

– Electron charges

– Correlated many-electron states


Timescales

• Can arrange these roughly according to strength of the qubit interactions with one another (and with the environment)

Nuclear spins

Collective electron excitations

Atomic motions

Electron spins

Electron charges

Weaker interactions Stronger interactions

Faster operation (good)

Faster decoherence (bad)


Many-particle states: superconductors

• Superconductors are an example of a macroscopic quantum state

• Coherence extending over large distances• Use magnetic field (flux) through a

superconducting ring as the qubit….

Superconducting loop with small ‘weak link’ of normal material (SQUID)

Field Field

0 1


Many-particle states: superconductors

• Superconductors are an example of a macroscopic quantum state

• Coherence extending over large distances• …or use a small ‘Cooper pair box’ containing

variable number of superconducting electrons

‘

0 1N electrons (N+2) electrons

Box connected to reservoir of superconducting electrons by ‘weak link’


Coherence of qubits in superconductors

Oscillating population of ‘single Cooper pair box’ as two quantum processes interfere

Experiment

Theory

Nakamura et al. Nature 398 786 (1999)


Engineering the quantum states

Vion et al Science 296 886 (2002)

By working at “saddle-point” where system is insensitive to noise…

…get quantum quality factor Q~25,000

Entanglement of two qubits recently demonstrated in a similar system (Mooij et

al, Delft)


Nuclear spins - the Kane proposal

• Qubit is spin of 31P nucleus embedded in silicon crystal

• Evolution and measurement of qubits performed by controlling individual electron states nearby

Si

V=0

Magnetic field





Si

V>0+ + + +

Magnetic field





Si

VJ<0- - - - -





Si

VJ>0+ + + +



• Readout performed by transferring qubits to electrons and measuring small changes in the shape of the electron distribution

Si

+ + + +- - - - -

Electron cannot transfer



• Readout performed by transferring qubits to electrons and measuring small changes in the shape of the electron distribution

Si

+ + + +- - - - -

Electron transfers



A-gates J-gates

20 nm

Now good progress on

some fabrication

issues (Clark et al 2002)


Overview








Must be able to• Characterise well-defined set of quantum states to use as qubits• Prepare suitable pure states within this set• Carry out desired quantum evolution• Avoid decoherence for long enough to compute• Read out the results



Is there another way?

Would really like to control coupling of qubits without presence of nearby electrodes and associated electromagnetic fluctuations

Our proposal (Stoneham et al., UCL): use real transitions in a localized state to drive gate:

Ground state

(no interaction)

Excited state

(interaction present)

Exploit properties of point defect systems conveniently occurring in Si

Our proposal: basic idea• Qubits are S=1/2 electron spins which must be controlled by

one- and two-qubit gates

• The spins are associated with dopants (desirable impurities)– Chosen so they do not ionise thermally at the working

temperatures (“deep donors”)

• The dopants are spaced 7-10nm to have negligible interactions in the “off” state

Silicon

Dopants

Basic Ideas (Continued)…

• Uniquely, the distribution of dopant atoms is disordered– A disordered distribution is desirable for system reasons– Dopants do not have to be placed at precise sites

Silicon

Dopants

• The new concept is to control the spins producing the A-gates and J-gates using laser pulses

• Another major new concept is separation of the storing of Quantum information from the control of Quantum interactions

Silicon

Source of Control Electron

Donors carrying Qubit Spins

Control gate by laser-induced electron transfer

ALL GATES OFF

Controlling Spins

Gate addressed by combination of position and

energy

ONE GATE ON

ALL GATES OFF

Silicon

Source of Control Electron

Donors carrying Qubit Spins

Control gate by laser-induced electron transfer

ALL GATES OFF

Controlling Spins

Gate addressed by combination of position and

energy

Many different charge transfer events possible

Different laser wavelengths

allow discrimination

ONE GATE ON

Configuring the Device…When we have made a device…

The solution… We shall configure each device, just as hard disks are configured

There are also analogies with communications networks

…we shall not know in advance which are which!

• Some qubit atoms will be too close to use as gates- These may be useful to move quantum information around

• Some qubit atoms will be at useful spacings

• Some qubit atoms will be too distant (hence useless)

Silicon

Dopants


Can one achieve entanglement?

• Experimental demonstrations for related systems:– Optically-induced many-spin entanglement

demonstrated in quantum wells:• Bao, Bragas, Furdyna, Merlin 2003 Nature Materials 2 175

(also 2003 Sol State Comm 127 771)

– Entanglement demonstrated in bulk spin systems via macroscopic properties:

• Ghosh, Rosenbaum, Aeppli, Coppersmith 2003 Nature 425 48.


Macroscopic properties (magnetic susceptibility) of LiHo0.045Y0.955F4 showing effects of

entanglement. Ghosh, Rosenbaum, Aeppli, Coppersmith 2003 Nature 425 48


Advantages and challenges

• Advantages:– Compatibility with CMOS– Coupling mechanism does not

rely on a small energy scale, so potential for high-temperature operation if single-qubit decoherence OK

– An interface with photons (“flying qubits”) built in from the beginning

– Take advantage of natural inhomogeneity to address individual gates

• Challenges:– Initialization cannot be done

using B-field if operate at high T– Must ensure no ‘residual’

entanglement between control particle and qubits (gate timing)

– Readout mechanisms– Connectivity of gates– Fabrication and demonstration

experiments (London Centre for Nanotechnology)

New £3.5M Basic Technology project

at UCL, 2003-7


To watch

• The Basic Technology project

• Other quantum-information related projects in the CMMP group and in the new London Centre for Nanotechnology

• The new IRC in Quantum Information Processing (CMMP group and Sougato Bose involved)


Thanks:

• Several colleagues at UCL:– Marshall Stoneham– Thornton Greenland– Gabriel Aeppli– Joe Gittings– Robbie Rodriguez

• Members of informal ‘quantum logic gate club’ (Oxford/Cambridge/HP/UCL/IC/Bristol…)

• EPSRC and Basic Technology programme (£)


To find out more…

• About the field in general:– Gerald Milburn “The Feynman Processor” (Perseus 1998)– “Feynman lectures on computation” (Penguin 1999)– Michael Nielsen and Isaac Chuang “Quantum computation

and quantum information” (CUP 2000; for the serious – and advanced – student!)

• About our Basic Technology project:– Our paper: Stoneham, Fisher and Greenland J. Phys. Cond.

Matt. 15 L447 (2003) (find it on http://www.iop.org)– Nature news article (31 July 2003 – see also

http://www.nature.com))• About the LCN:

– LCN website http://www.london-nano.ucl.ac.uk

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