let's build a quantum computer!
TRANSCRIPT
Andreas DewesAcknowledgements go to "Quantronics Group", CEA Saclay.
R. Lauro, Y. Kubo, F. Ong, A. Palacios-Laloy, V. Schmitt
PhD Advisors: Denis Vion, Patrice Bertet, Daniel Esteve
Let's Build a Quantum Computer!31C3
29/12/2014
Motivation
Outline
Quantum Computing
What is it & why do we want it
Quantum Algorithms
Cracking passwords with quantum computers
Building A Simple Quantum Processor
Superconductors, Resonators, Microwaves
Recent Progress in Quantum Computing
Architectures, Error Correction, Hybrid Systems
Why Quantum Computing?
Quantum physics cannot be simulatedefficiently with a classical computer.1)
A computer that makes use of quantummechanics can do it.
It can also be faster for some othermathematical problems.
1) http://www.cs.berkeley.edu/~christos/classics/Feynman.pdf
Classical Computing
http://commons.wikimedia.org/wiki/File:Abacus_1_(PSF).png
Bits
0 1
Bit Registers
InA
0…00, 0…01,… , 1…11
...
InB
In..
n bits
𝑁 = 2𝑛 states
Logic Gates
InA
InB
Out
f
Logic Gates
InA
InB
Out
fInA InB Out
0 0 1
0 1 1
1 0 1
1 1 0
NAND-Gate
A problem: Password cracking
************ Launch Missile
Forgot your pasword?
A Password Checking Function
InA
InB
Out
fj
𝑓 = 0 𝑖 ≠ 𝑗1 𝑖 = 𝑗
𝑖, 𝑗 ∈ 00…000,00…001,… , 11…111
In..
...
𝑁=
2𝑛
po
ssib
iliti
es
A Cracking Algorithm
1. Set register state to i = 00000...0
2. Calculate f(i)
3. If f(i)= 1, return i as solution
4. If not, increment i by 1 and go to (2)
Time Complexity of our Algorithm
search space size - N
num
ber
ofevalu
ations
off
Quantum Computing
Quantum Bit / Qubit
|0>
Qubit Two-Level Atom
|1>
Quantum Superposition
|0>
|1>
|𝜓 = 𝑎|0 + 1 − 𝑎 ∙ 𝑒𝑖𝜑 |1
How to imagine superposition
http://en.wikipedia.org/wiki/Double-slit_experiment#mediaviewer/File:Doubleslit3Dspectrum.gif
Quantum Measurements
|0>|1>
|𝜓 = 𝑎|0 + 1 − 𝑎 ∙ 𝑒𝑖𝜑 |1
0 1
Quantum Measurements
0 1
|0>
|𝜓 = |0 ; probability = a
Quantum Measurements
0 1
|1>
|𝜓 = |1 ; probability = 1-a
QuBit Registers
...
|𝐴
|𝐵
|𝑍
|𝐴 |𝐵 … |𝑍
QuBit Registers
...
|𝐴
|𝐵
|𝑍
|𝐴𝐵…𝑍
Multi-Qubit Superpositions
...
0.51/2 |0 + |1
0.51/2 |0 + |1
0.51/2 |0 + |1
0.5𝑛/2 |0 + |1 … |0 + |1
n times
Multi-Qubit Superpositions
...
0.51/2 |0 + |1
0.51/2 |0 + |1
0.51/2 |0 + |1
𝑁 = 2𝑛 states in superposition
0.5𝑛/2 |00…0 +⋯+ |11…1
Multi-Qubit Superpositionsomitting normalizations
...
|0 + |1
|0 + |1
|0 + |1
|00…0 +⋯+ |11…1
Quantum Gates
𝑓
...
|0…00 ∙ 𝑓(0…00) + |0…01 ∙ 𝑓(0…01) + …+ |1…11 ∙ 𝑓(1…11)
|0 + |1
|0 + |1
|0 + |1
Quantum Entanglement
0 1
|0
|01 + |10
𝑓
𝑓(|01 ) = |01 + |10
|1
|0 |1
Summary: Qubits
Quantum-mechanical two-level system
Can be in a superposition state |𝟎 + |𝟏
A measurement will yield either 0 or 1 andproject the qubit into the respective state
Can become entangled with other qubits
Back to business...
************ Launch Missile
Wrong password!
Quantum Searching ourPassword
|0…000 + |0…010 + |01…10𝟏 + |1…110
𝑓𝑗
...
|0 + |1
|0 + |1
|0 + |1
But how we get the solution?
𝑟𝑒𝑠𝑢𝑙𝑡 =01…10𝟏 𝑝 =
1
𝑁
∗∗ ⋯∗∗ 𝟎 𝑝 = 1 −1
𝑁
fj
...
|0 + |1
|0 + |1
|0 + |1
0 1
0 1
0 1
0 1
|0 + |1
|0 + |1
|0 + |1
Solution: Grover Algorithm
fjGrover
Operator
...
0 1
0 1
0 1
0 1
repeat 𝑁 times
𝑟𝑒𝑠𝑢𝑙𝑡 = 01…10𝟏 𝑝 ≈ 1∗∗ ⋯∗∗ 𝟎 𝑝 ≈ 0
Grover L.K.: A fast quantum mechanical algorithm for database search, Proceedings, 28th Annual ACM Symposium on the Theory of Computing, 1996
Efficiency of Grover Search(for 10 qubits)
N = 1024
25 iterationsrequired
Time Complexity Revisited
search space size – N
num
ber
ofevalu
ations
off
quantumspeed-up
Number Factorization: Shor Alg.
problem size – n (number of bits)
Ru
ntim
e
𝑟 = 𝑞 ∙ 𝑠; q,s prime numbers
How to Build aQuantum Processor?
photo not CC-licensed photo not CC-licensed
University of Innsbruck (http://www.quantumoptics.at/) University of Santa Barbara (http://web.physics.ucsb.edu/~martinisgroup/)
...and many more technologies:
Nuclar magnetic resonance,
photonic qubits, quantum dots,
electrons on superfluid helium,
Bose-Einstein condensates...
Ion Trap Quantum Processors Superconducting Quantum Processors
a)
100 m
1 mm
A Simple Two-Qubit ProcessorUsing superconducting qubits (Transmons - Wallraff et al., Nature 431 (2004) )
1m
38
Dewes et al. Phys. Rev. Lett. 108, 057002 (2012)
thermally anchor and
shield from EM fields
mount on microwave
PCB and wirebond
39
*20 mK
pu
tin
dilu
tion
cry
osta
t
|0>
|0>
Y/2
Y/2
iSW
AP Z-/2
Z-/2
iSW
AP X/2
X/2
Readout
0 1
0 1
Y(
/2)
readout
50 100 150 200 ns
f 01[f(t)]
,a(t
)
0
iSWAP iSWAPZ(
/2)
X(
/2)
Running Grover-Search for 2 QubitsCalculate fj Apply Grover operator
40
Prepare superposition
Dewes et. al., PRB Rapid Comm 85 (2012)
|0>
|0>
Y/2
Y/2
iSW
AP Z±/2
Z±/2
iSW
AP X/2
X/2
0 1
0 1
67 %55 %
62 %52 %
f00 f01 f10 f11
Single-Run Success Probability41
classical benchmark(with "I'm feeling lucky"
bonus)
ReadoutCalculate fj Apply Grover operatorPrepare superposition
Challenges
Decoherence
Environment measures and manipulates the qubitand destroys its quantum state.
Gate Fidelity & Qubit-Qubit Coupling
Difficult to reliably switch on & off qubit-qubitcoupling with high precision for many qubits
And some more:
High-Fidelity state measurement, qubit reset, ...
Recent Trends in SuperconductingQuantum Computing
Better Qubit Architectures
Better Qubits and Resonators
Quantum Error Correction
Hybrid Quantum Systems
(photos not included since not CC-BY licensed)
Moore's Law: Quantum Edition(for superconducting qubits)
1
10
100
1000
10000
100000
1000000
1998 2000 2002 2004 2006 2008 2010 2012 2014
coh
eren
ceti
me
-n
s
year
Superconducting Qubits:
Reported Coherence Time (T)
Cooper pair box
QuantroniumCircuit QED
3D Cavities
Summary
Quantum computers are coming!
...but still there are many engineeringchallenges to overcome...
Bad News
Likely that governments and big corporationswill be in control of QC in the short term.
Thanks!
More "quantum information":
Diamonds are a quantum computer’s best friend –
Tomorrow, 30.12 at 12:45h in Hall 6 by Nicolas Wöhrl
Get in touch with me:
[email protected] // @japh44