Slide1: Quantum Computers
That Fix Themselves Dave Bacon
Caltech
Department of Physics
Institute for Quantum Information
Slide2: The Enemy?
Slide3: 57 Nobel Prizes 27 Nobel Prizes 0.01 Nobel Prizes / Capita 0.005 Nobel Prizes / Capita Caltech MIT “lies, damn lies, and statistics.” – Leonard Henry Courtney Quantum Computing Mecca Quantum Computing Mecca The California Tech
Slide4: Castor canadenis Caltech
Slide5: The Quantum Computing Roadmap NIST Boulder Ions
Slide6: Have We Learned Anything? 1941 – First programmable electronic calculator.
mechanical relays.
1943 – ENIAC.
18000 vacuum tubes: “nature abhors the vacuum tube.”
1947 – Bell labs develops the transistor.
1952 – G. W. Dummer proposes manufacturing electronic equipment in one
block with no connecting wires.
1959 – Texas Instruments and Fairchild Semiconductor invent the integrated
circuit.
1964 – first IBM 360 series (the concept of an “architecture”)
1964 – Integrated circuit which cost $1000 in 1959 now costs $10. Moore
describes his law. 1972 – Intel 8008 and 8 bit microprocessor.
1975 – First personal computer the Altair.
1982 – IBM PC introduced. Personal computer revolution begins.
Slide7: History Only Teaches Me Physics ordered
regular
reducible turbulent
complex
not reducible Interacting Isolated What happens when many units (defined isolated) interact? Computers are strange beasts in this world:
built from parts which order and are regular
reductionist’s dream come true
yet:
complexity of computer running a program is high
algorithmic complexity implies reduction cannot be
compressed beyond running the algorithm Platyputor
Slide8: The Physics Guarantee What is the phase of matter corresponding to the computer? PRACTICAL QUESTION (as opposed to philosophical) There are distinct PHYSICAL reasons why robust classical
computation is possible. not all physical systems are equally good for computation:
there exists systems whose PHYSICS guarantees
their ability to enact robust classical computation. This talk: (1) this point of view for classical computers
(2) attempts to port these ideas to a quantum computer Are there (or can we engineer) physical systems whose
PHYSICS guarantees robust quantum computation? Rant mode ON
Slide9: Two Paths Coding: majority vote of
current Transistor Hard Drive Error correction: amplification Coding: majority vote of
magnetism Error correction: local energy
minimization Fault-tolerant: macro applied
field. Fault-tolerant: conducting / insulating phase transition More than storage?
Slide10: A Dynamic Ising Model Ising model Dynamic Ising model
Slide11: Reminder two-level system radiatively coupled to a thermal reservoir: “heating” “cooling” “non-dissipative”
Slide12: A Dynamic Ising Model Ising model Dynamic Ising model (Metropolis update)
Slide13: Storage and Manipulation Compare 1D and 2D Ising models at different temperatures for
a) storage of information
b) manipulation of information Storage in thermal state (infinite time - ensemble is thermal) 1D Ising 2D Ising 1st attempt: Criticism: (1) thermodynamic limit taken (N infinite)
(2) what if relaxation to equilibrium takes a long time?
Slide14: 2nd attempt: 1D Ising Relaxation to thermal Imperfect preparation Storage 2D Ising
Slide15: Manipulation Flipping spins is imperfect 1D Ising 2D Ising 1D Ising
temperature less than gap
manipulation error must be small
2D Ising
temperature less than critical temp
self correcting
Slide16: Self Fixing
Slide17: Two Paths Coding: majority vote of
current Transistor Hard Drive Error correction: amplification Coding: majority vote of
magnetism Error correction: local energy
minimization Fault-tolerant: macro applied
field. Fault-tolerant: conducting / insulating phase transition More than storage?
Slide18: No Quantum Transistor Quantum Cloning Machine “A single quantum cannot be cloned,” Wootters and Zurek, Nature, 1982
Slide19: The Quantum
Hard Drive? (Kitaev) Do there exist (or can we engineer) quantum systems whose
physics guarantees fault-tolerant quantum computation? 1. Coherence preserving. 2. Accessible Fault-Tolerant
Operations 3. Universality “self-correcting”
Slide20: Old School Error Fix “cold” ancilla “hot” ancilla If criteria holds, then fixing procedure possible prepare out compute Competition between errors and cooling Quantum error correcting code Error correcting criteria:
Slide21: Into The Fray Strongly Interacting Many Body Quantum System Thermodynamic limit guarantees robustness Hamiltonian energy
eigenstates Barnes and Warren, PRL 85, 856 (2000) [but is only “classical”]
Slide22: Quantum Error Correcting
Order Parameters Encoded quantum information The quantum information is
still here. How do we see it? diagnose fix measure encoded info j
Slide23: A Simple Start [4,2,2] quantum error detecting code: “To be an Error and to be Cast out is Part of [Nature’s] Design.” -William Blake
Slide24: Supercoherence ZZ ZZ XX XX 1 2 3 4 4 qubit system System Hamiltonian:
Slide26: Supercoherence ALL single qubit errors take degenerate ground state to higher energy levels.
Single qubit errors change value of (S1,S2) and hence take ground state to higher energy level. FORBIDDEN D. Bacon, Ph.D. thesis, U.C. Berkeley, 2001
Slide27: system bath ~ HI = perturbative system-bath coupling HI energy small compared to Esys and Ebath implies decoherence dominated by pathways that conserve unperturbed energies (essentially rotating wave approximation) “cooling” “heating” “non-dissipative” Making Decoherence Work Hard
Slide28: two-level atom radiatively coupled to a thermal reservoir: “heating” “cooling” “non-dissipative” At low bath temperatures, heating disappears…….. Supercoherence
made all quantum errors “heating”!
Slide29: 1 2 3 4 Four spin systems with equal strength exchange interactions
between all spins: In a Few Years Time… Supercoherent qubit single P atoms in Silicon
exchange controlled by voltage
mediated barriers Bacon, Brown, and Whaley, PRL 87, 247902 (2001) DiVincenzo, Bacon, Kempe, Burkard, and Whaley, Nature 408, 399 (2001) See: Hellberg, quant-ph/0304150 (2003)
Slide30: Supercoherence
As the First Step To
Achieving the Threshold
For Fault-Tolerant
Quantum Computation?
Slide31: Mysterious Extra Slide
Slide32: Ladder Qubits 1 2 i-1 i i+1 n n-1 n-2 n-3 1 2 qubit (i,2) qubit (i,1) The Hamiltonian Z Z Z Z X X X X X X X X X X X X D. Bacon, Ph.D. thesis, U.C. Berkeley, 2001
Slide33: Basis Change i i+1 1 2 Z Z Z Z X X X X X X X X X X X X New basis:
Slide34: Everybody’s Favorite Ising + transverse field transverse
field
only Ising + transverse field transverse
field
only
Slide35: Grounded X X k 1 2 Z Z Z Ground state is two-fold degenerate
Slide36: Detect and Correct Z Z Z Z X X X X X X X X X X X X
Slide37: Into the 2nd Dimension ZZ ZZ XX XX ZZ ZZ ZZ ZZ XX XX XX XX i i+1 i-1 j-1 j j+1
Slide38: ZZ ZZ XX XX XX Tic-Tac-“DOH!” XX ZZ ZZ ZZ XX XX ZZ ZZ ZZ ZZ XX XX XX XX
Slide39: Subsystem Codes
Slide40: Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z Z X X X X X X X X X X X X X X
Slide41: Into the Third Dimension YY YY ZZ ZZ YY XX XX XX XX ZZ ZZ YY YY XX ZZ
Slide42: Logical Operators
Slide43: Errors ZZ ZZ YY YY ZZ ZZ ZZ ZZ YY YY YY YY i i+1 i-1 j-1 j j+1
Slide44: Wherefore Art Toric Codes?
Slide45: Summary Learn from our past! Let physics do the work! Towards self-correcting quantum memories Supercoherence as first step?
Slide46: Fin Error correcting codes classical
quantum Fault-tolerance local structures giving rise
to global robustness (CA) Representation theory identification of qubits
and logical operations Geometry, Topology? Statistical Physics theory of strongly interacting
quantum systems Real Physics physical implementation
optical lattices, donor
electrons, superconducting
circuits, etc. Naturally Fault-Tolerant Quantum Computation