Let's build a quantum computer!

Andreas Dewes
Acknowledgements 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

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 simulated
efficiently with a classical computer.1)
A computer that makes use of quantum
mechanics can do it.
It can also be faster for some other
mathematical problems.
1) http://www.cs.berkeley.edu/~christos/classics/Feynman.pdf

Classical Computing
http://commons.wikimedia.org/wiki/File:Abacus_1_(PSF).png

Bit Registers
InA
0 … 00, 0 … 01, … , 1 … 11
...
InB
In..
n bits
𝑁 = 2 𝑛 states

Logic Gates
InA
InB
Out
f
InA 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 ≠ 𝑗
1 𝑖 = 𝑗
𝑖, 𝑗 ∈ 00 … 000,00 … 001, … , 11 … 111
In..
...
𝑁=2𝑛possibilities

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
numberofevaluationsoff

Quantum Bit / Qubit
|0>
Qubit  Two-Level Atom
|1>

Quantum Superposition
|0>
|1>

|𝜓 = 𝑎|0 + 1 − 𝑎 ∙ 𝑒 𝑖𝜑 |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 ∙ 𝑒 𝑖𝜑
|1
0 1

0 1
|0>
|𝜓 =|0 ; probability = a

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
0.5 𝑛/2
|0 + |1 … |0 + |1
n times

...
0.51/2 |0 + |1
0.51/2
|0 + |1
0.51/2
|0 + |1
𝑁 = 2 𝑛
states in superposition
0.5 𝑛/2
|00 … 0 + ⋯ + |11 … 1

omitting 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 and
project the qubit into the respective state
Can become entangled with other qubits

Back to business...
************ Launch Missile
Wrong password!

Quantum Searching our
Password
|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
fj
Grover
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 iterations
required

Time Complexity Revisited
search space size – N
numberofevaluationsoff
quantum
speed-up

Number Factorization: Shor Alg.
problem size – n (number of bits)
Runtime
𝑟 = 𝑞 ∙ 𝑠; q,s prime numbers

How to Build a
Quantum 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 Processor
Using superconducting qubits (Transmons - Wallraff et al., Nature 431 (2004) )
1m
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
putindilutioncryostat

|0>
|0>
Y/2
Y/2
iSWAP
Z-/2
Z-/2
iSWAP
X/2
X/2
Readout
0 1
0 1
Y(/2)
readout
50 100 150 200 ns
f01[f(t)],a(t)
0
iSWAP iSWAP
Z(/2)
X(/2)
Running Grover-Search for 2 Qubits
Calculate fj Apply Grover operator
40
Prepare superposition

Dewes et. al., PRB Rapid Comm 85 (2012)
|0>
|0>
Y/2
Y/2
iSWAP
Z±/2
Z±/2
iSWAP
X/2
X/2
0 1
0 1
67 %
55 %
62 %
52 %
f00 f01 f10 f11
Single-Run Success Probability
41
classical benchmark
(with "I'm feeling lucky"
bonus)
ReadoutCalculate fj Apply Grover operatorPrepare superposition

Challenges
Decoherence
Environment measures and manipulates the qubit
and destroys its quantum state.
Gate Fidelity & Qubit-Qubit Coupling
Difficult to reliably switch on & off qubit-qubit
coupling with high precision for many qubits
And some more:
High-Fidelity state measurement, qubit reset, ...

Recent Trends in
Superconducting
Quantum 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
coherencetime-ns
year
Superconducting Qubits:
Reported Coherence Time (T)
Cooper pair box
Quantronium
Circuit QED
3D Cavities

Summary
Quantum computers are coming!
...but still there are many engineering
challenges to overcome...
Bad News
Likely that governments and big corporations
will 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:
ich@andreas-dewes.de // @japh44

Let's build a quantum computer!