Quantum Quantum Architectures Architectures June 1, 2005 June 1, - - PowerPoint PPT Presentation

Quantum Quantum Architectures Architectures

June 1, 2005 June 1, 2005

Computing? Computing?

e of computing devices that exhibit quantu e of computing devices that exhibit quantu chanical behavior chanical behavior

ehavior of isolated ions ehavior of isolated ions Bose Bose-

• Einstein condensate in a magnetic well

Einstein condensate in a magnetic well hoton interactions hoton interactions ire and transistor interactions in the near future ire and transistor interactions in the near future

e computing model is largely unexplored computing model is largely unexplored

⊆ ⊆? QP ? QP ⊆ ⊆? NP ? NP

e usage model is still being debated usage model is still being debated

hy are Architects Involved hy are Architects Involved

e know what the “killer app” will be e know what the “killer app” will be

Error correction will be >99% of the work Error correction will be >99% of the work

e physicists don’t know computation e physicists don’t know computation

“Don’t worry, it’s polynomial...” “Don’t worry, it’s polynomial...”

e theorists don’t know physics e theorists don’t know physics

“Simplify the problem by removing communication...” “Simplify the problem by removing communication...”

short, architects can be the reality check short, architects can be the reality check

Identify physical bounds that supersede theoretical on Identify physical bounds that supersede theoretical on Determine what aspects of computation will be the m Determine what aspects of computation will be the mo challenging challenging

Outline Outline

hat makes quantum different? hat makes quantum different?

Quantum bits Quantum bits Operations and measurement Operations and measurement Decoherence Decoherence

hat will a quantum computer look like hat will a quantum computer look like uantum architecture research at UW uantum architecture research at UW

Current research: Simulation Current research: Simulation Building quantum wires Building quantum wires

Classical vs. Quantum Classical vs. Quantum

sic element: 0 or 1 sic element: 0 or 1 ts are independent ts are independent ata may be copied ata may be copied destroyed at will destroyed at will ata is static ata is static

n n Bits are continuous va

Bits are continuous va

n n Bits may be entangled

Bits may be entangled interfere interfere

n n Data may not be copie

Data may not be copie

n n Operations must be

Operations must be reversible reversible

n n Data

Data decoheres decoheres with t with t

Qubits Qubits: Quantum Bits : Quantum Bits

and and qubits qubits both have two states: 0 an both have two states: 0 an perposition: perposition:

ubit ubit may be in both states simultaneously may be in both states simultaneously

ase: ase:

ubit ubit may have a negative quantity of a st may have a negative quantity of a st

uantum States and Measuremen uantum States and Measuremen

e e qubit qubit probabilistically represents two states probabilistically represents two states a |0> + b |1> a |0> + b |1> ch additional ch additional quibit quibit doubles the number of sta doubles the number of sta a |00> + b |01> +c |10> + d |11> a |00> + b |01> +c |10> + d |11> easurement sends a easurement sends a qubit qubit into a classical stat into a classical stat is may alter the states of other is may alter the states of other qubits qubits

a |00> + b |11> (EPR state) a |00> + b |11> (EPR state)

easurement and Copy Protectio easurement and Copy Protectio

uantum data cannot be copied uantum data cannot be copied

Copying involves a read and a write Copying involves a read and a write “Reading” destroys the state “Reading” destroys the state

uantum data can be transferred uantum data can be transferred

One One qubit qubit can swap its state with another can swap its state with another Quantum state can be “teleported” over infinite Quantum state can be “teleported” over infinite distance (but the sender loses the data) distance (but the sender loses the data)

any quantum algorithms are probabilistic any quantum algorithms are probabilistic d involve iteration d involve iteration

Other Operations Other Operations

easurement: the only irreversible operati easurement: the only irreversible operati l other operations are reversible l other operations are reversible

2nd Law: Reversible operations conserve ener 2nd Law: Reversible operations conserve ener “Not” is reversible “Not” is reversible “And” and “Or” are not reversible “And” and “Or” are not reversible

• st “traditional” operations must produce
• st “traditional” operations must produce

ditional output ditional output

How do you make “+” reversible? How do you make “+” reversible? Scratch bits must be protected Scratch bits must be protected

Noise: Noise: Decoherence Decoherence

eoretical systems are “closed” eoretical systems are “closed”

No energy may enter the system unless explicitly No energy may enter the system unless explicitly introduced introduced

al systems can’t be completely isolated al systems can’t be completely isolated

Performing an op adds “noise” to a Performing an op adds “noise” to a qubit qubit Over time, Over time, qubits qubits will simply “ will simply “decohere decohere” ” At higher temperatures (higher energy), At higher temperatures (higher energy), decoherence decoherence

• ccurs more quickly
• ccurs more quickly

e will need massive cooling systems e will need massive cooling systems y usable quantum system will require error y usable quantum system will require error

rror Correction is Crucial rror Correction is Crucial

ror correcting codes are available ror correcting codes are available

Operations exist for computing on encoded dat Operations exist for computing on encoded data Since Since qubits qubits cannot be read, an error correction cannot be read, an error correction routine manipulates the coded bits to fix errors routine manipulates the coded bits to fix errors

ror correction must often be applied ror correction must often be applied cursively to error correction routines cursively to error correction routines e Threshold Theorem e Threshold Theorem

An error rate of 10 An error rate of 10-

• 4

4 per op can be tolerated

per op can be tolerated This error rate requires nearly continuous error This error rate requires nearly continuous error correction correction

To Summarize... To Summarize...

uantum bits are awesome uantum bits are awesome

...except that no one has really done anything ...except that no one has really done anything amazing with them (yet) amazing with them (yet) …because measurement really hurts …because measurement really hurts

• ring and moving data will be difficult
• ring and moving data will be difficult

Decoherence Decoherence limits storage and transit time limits storage and transit time

e know what quantum computers will do e know what quantum computers will do

Error correcting...all the time Error correcting...all the time

rforming computation in the presence of rforming computation in the presence of

Outline Outline

hat makes quantum different? hat makes quantum different?

Quantum bits Quantum bits Operations and measurement Operations and measurement Decoherence Decoherence

hat will a quantum computer look like hat will a quantum computer look like uantum architecture research at UW uantum architecture research at UW

Current research: Simulation Current research: Simulation Building quantum wires Building quantum wires

Pick a Technology Pick a Technology

hat device technology will be used? hat device technology will be used?

Who knows... Who knows...

evelop first order assumptions evelop first order assumptions

Classical control of quantum gates Classical control of quantum gates Silicon to interface and control Silicon to interface and control

n n Provides rough size constraints

Provides rough size constraints

Individual control of quantum bits Individual control of quantum bits

ck a likely technology that fits ck a likely technology that fits

For example, ion traps For example, ion traps

Consider Building Blocks

• nsider Building Blocks

Processor: Computation Processor: Computation

Several sets of universal gates exist Several sets of universal gates exist Different device technologies can more easily implem Different device technologies can more easily implem some gates than others some gates than others Measurement and “zero” creation is also important Measurement and “zero” creation is also important

emory: Storage emory: Storage

Storage is difficult because of Storage is difficult because of decoherence decoherence Constant error correction may be performed Constant error correction may be performed

n n Decoherence

Decoherence-

• free subspaces are being researched

free subspaces are being researched

Hence, memory looks a lot like the processor Hence, memory looks a lot like the processor

Interconnect: Communication Interconnect: Communication

reger reger-

• Stickles and

Stickles and Balensiefer Balensiefer

e computer is a grid of traps and wires e computer is a grid of traps and wires ch trap has a flexible gate that can perform ch trap has a flexible gate that can perform easurement or a quantum op easurement or a quantum op mmunication is performed by moving ions mmunication is performed by moving ions

Outline Outline

hat makes quantum different? hat makes quantum different?

Quantum bits Quantum bits Operations and measurement Operations and measurement Decoherence Decoherence

hat will a quantum computer look like hat will a quantum computer look like uantum architecture research at UW uantum architecture research at UW

Current research: Simulation Current research: Simulation Building quantum wires Building quantum wires Representing quantum algorithms Representing quantum algorithms

mulating Quantum Compute ulating Quantum Compute

nt work by nt work by Kreger Kreger-

• Stickles,

Stickles, Balensiefer Balensiefer, and O , and O compare architectures, performance data is n compare architectures, performance data is n ulation is the only choice ulation is the only choice

Fully” simulating a quantum system takes exponential Fully” simulating a quantum system takes exponential y modeling only reliability, can be done in linear time y modeling only reliability, can be done in linear time

e Simulation Infrastructu e Simulation Infrastructur

n error correction compiler error correction compiler

Takes a quantum algorithm for one specific inpu Takes a quantum algorithm for one specific inpu Produces a fault tolerant version of the algorithm Produces a fault tolerant version of the algorithm

device scheduler device scheduler

Takes a program and an architecture Takes a program and an architecture Produces a static operation and communication Produces a static operation and communication schedule schedule

reliability simulator reliability simulator

Takes a scheduled application and architecture Takes a scheduled application and architecture Produces performance and reliability metrics Produces performance and reliability metrics

Preliminary Results Preliminary Results

ror correction is less effective than we assum ror correction is less effective than we assum

Correcting errors requires that bits be moved Correcting errors requires that bits be moved

e Threshold Theorem is optimistic e Threshold Theorem is optimistic

Realistic execution constraints (communication) limit Realistic execution constraints (communication) limit acceptable error rate acceptable error rate The realistic threshold is four orders of magnitude wo The realistic threshold is four orders of magnitude wo

antum computer size will be limited by the er antum computer size will be limited by the er te of the underlying technology te of the underlying technology

The further bits have to move, the lower the rate has The further bits have to move, the lower the rate has t be be

ilding a Quantum Wire (Oski ilding a Quantum Wire (Oski

get technology is Kane’s silicon ion get technology is Kane’s silicon ion-

• tra

tra

• ns are embedded into silicon traps
• ns are embedded into silicon traps
• Spin of 31P holds quantum state

Spin of 31P holds quantum state

• Ions spaced

Ions spaced ≤ ≤ 20nm apart for quantum effect to o 20nm apart for quantum effect to o

• ≤

≤ 1.5Kelvin for reasonable coherence time 1.5Kelvin for reasonable coherence time

• cal magnetic field arbitrates gates
• cal magnetic field arbitrates gates
• Controlled by “classical” pins

Controlled by “classical” pins

• Driven by high frequency (10

Driven by high frequency (10-

• 100Mhz) clock

100Mhz) clock

• Gated by “lower” frequency (0.01

Gated by “lower” frequency (0.01 – – 10Mhz) clock 10Mhz) clock

A A Short Short Quantum Wire Quantum Wire

nstructed from swap gates nstructed from swap gates

Unless the particle that holds the quantum state physically moves, the information “flows” in discrete steps from particle to particle. Each step requires 3 quantum controlled-not operations, effectively performing a “swap” of the quantum states.

rchitecture of a Long Wir rchitecture of a Long Wire

EPR Generator

Teleporation Unit Teleporation Unit Entropy Exchange Purification Coded Tele- Portation

Classical control channel Quantum EPR channel R channel

Two Possible Wires Two Possible Wires

• rt range: swapping
• rt range: swapping-
• channel

channel

“Pitch matching” causes structural concerns “Pitch matching” causes structural concerns

n n Qubits

Qubits are 20nm apart, so control is limited to 5nm are 20nm apart, so control is limited to 5nm

n n @ 1.5 Kelvin, cannot drive an AC current

@ 1.5 Kelvin, cannot drive an AC current

n n Other dimensions must be increased to > 100nm

Other dimensions must be increased to > 100nm

Length is limited due to Length is limited due to decoherence decoherence

ng range: teleportation ng range: teleportation-

• channel

channel

Length is arbitrary Length is arbitrary Many additional structures are required Many additional structures are required Bandwidth is constrained by EPR pair productio Bandwidth is constrained by EPR pair productio

presenting Quantum Computati resenting Quantum Computati

lop an alternative notation for quantum computing lop an alternative notation for quantum computing

presentation: dealing with groups of bits is ha presentation: dealing with groups of bits is ha

nsure operations are insensitive to state space size nsure operations are insensitive to state space size troduce shorthand for common entangled states troduce shorthand for common entangled states acilitate computation on large, highly entangled states acilitate computation on large, highly entangled states

asoning: interesting states are difficult to iden asoning: interesting states are difficult to iden

entify quantum properties explicitly entify quantum properties explicitly efine operations by the quantum properties they induc efine operations by the quantum properties they induc avor local transformations over global ones avor local transformations over global ones

An Example: EPR Pairs An Example: EPR Pairs

atrix notation:

H(x) → x 0 : x 0 + x1 || x1 : x 0 CNot(x,y) → x 0 : x 0y || x1 : x qubit p ⇒ p0 qubit q ⇒ q0 H(p) on p0 ⇒ p0 + p1 CNot(p,q) on (p0 + p1)q0

        =                                  =       ⊗             =          −    1 2 1 1 1 2 1 1 1 1 2 1 1 1 , 1 1 2 1 1 1 1 1

In the algebra:

The High Order Bits The High Order Bits

uantum architecture is a wide uantum architecture is a wide-

• open field
• pen field

We can’t even agree how to build wires! We can’t even agree how to build wires!

chitects have an important role chitects have an important role

We act as intermediaries between the physicist We act as intermediaries between the physicist and algorithm designers and algorithm designers

you know how to do error correction well, you know how to do error correction well, u could become famous u could become famous