In Search of a Magic Bottle of Error-Be-

Gone

Dave BaconCaltech

Department of PhysicsInstitute for Quantum Information

Decoherence

errosol

The FutureVisualize 2040:

Experimentalists all just thought

what will a quantum computer look like?

Ion Traps

Optical Lattices

Josephson Junctions

Linear Optics + a

bit

ElectronSpins

Quantum Architecture?

Fault Tolerant QuantumArchitecture?

At the lowest level we must perform quantum errorcorrection and use fault-tolerant techniques.

What is the “best” way to do this?

Today’s talks on quantum error correction will drastically influence what a quantum computer looks like…

“Best?”Objection: BEST depends on strengths and weaknesses

of particular physical implementations

physical implementation

gate speedsgate accuraciesgate costsforms of decoherencedecoherence timesshuttling speedsshuttling accuraciescooling ratescalibration errorsdegree of parallelismgeometric constraintsfabrication constraints

theory brain trust

quantum architecture specification

plans suitable for founding qIntel

Two Paths

even today TWO styles are emerging

concatenation local codes

Concatenation

1 qubit

n qubits

qubitsprobabilityof failure

p

cp2

n2 qubits c(cp2)2

nk qubits (cp) /c2k

1

2

k

0

level

exponential decreasein # qubits if

p<1/c=pthresh

A quantum circuit with k gates

can be simulated with error probability e

using O(k poly(log(k/e))) gates

on hardware whose components fail with probability p less than some threshold pthresh

under caveats A, B, C, D,…

Threshold Theorem

faulty componentsalmost certainly not faulty

Concatenation and LocalityConcatenation is hierarchical

how to merge with local bare qubits?

despite: moving or swapping qubits creates error rate proportional to distance moved

THERE IS STILL A THRESHOLD THEOREM

Daniel Gottesman, 1999

Are there non-hierarchical ways todo fault-tolerant quantum computation?

Kitaev’s Toric Codes

qubits on links

plaque operatorsvertex operators

syndrome measurementsinvolve only four qubit localmeasurements!

2 encoded qubits

BUT: diagnosing erroris not a local process.

1 encoded qubit

Local CodesCan we find a fully local code?

syndrome+

diagnosis and correction+

fault-tolerant

In 4 dimensions there is a fully local code(sit down silly string theorists)

Physics and Toric Codes

qubits on links

plaque operatorsvertex operators

2 encoded qubits

ground state is the toric code!

energy required to excite outof code: at low temperatureswe can freeze out errors.

error correction still needed

The Physics GuaranteeWhat is the phase of matter corresponding to the computer?

There are distinct PHYSICAL and DYNAMICAL reasons why robust classical computation is possible.

not all physical systems are equally good for computation:there exist systems whose PHYSICS guaranteestheir ability to enact robust classical computation.

Rant mode ON

In Practice

Coding: majority vote of current

Integrated CircuitHard Drive

Error correction: amplificationfault-tolerance guaranteed by conducting-insulatingphase transition

Coding: majority vote of magnetism

Error correction: local energyminimization

The Physics GuaranteeWhat is the phase of matter corresponding to the computer?

There are distinct PHYSICAL and DYNAMICAL reasons why robust classical computation is possible.

not all physical systems are equally good for computation:there exist systems whose PHYSICS guaranteestheir ability to enact robust classical computation.

Rant mode ON

Are there (or can we engineer) physical systems whosePHYSICS guarantees robust quantum computation?

What is the phase of matter corresponding to thequantum computer?

The Quantum Hard Drive?Do there exist (or can we engineer) quantum

systems whosephysics guarantees fault-tolerant quantum

computation?1. Coherence preserving.

2. Accessible Fault-Tolerant Operations

3. Universality

“self-correcting”

Kitaev’s Codes hint that this is possible (in <4D!)

Rant mode shutting down

What Will a QC Look Like?

concatenationEngineering?

local codesPhysics?

Rant mode OFF

CuBits