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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
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
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
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