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QUANTUM SIMULATION AND COMPUTINGA NEW WAY OF COMPUTING BEYOND SUPERCOMPUTERS
JENS EISERT, FU BERLIN HARDWARE HACKING, BIG TECH DAY 11
MOORE’S LAW
▸ Gordon Moore (Intel, 1965): Number of transistors in integrated circuits doubles approximately every two years
Zuse Z3 (1941)
▸ Gordon Moore (Intel, 1965): Number of transistors in integrated circuits doubles approximately every two years
MOORE’S LAW
ENIAC, EDVAC, ORDVAC, BRLESC-I (1945-62)
Zuse Z3 (1941)
▸ Gordon Moore (Intel, 1965): Number of transistors in integrated circuits doubles approximately every two years
Zuse Z3 (1941)
Tran
sist
or c
ount
MOORE’S LAW
ENIAC, EDVAC, ORDVAC, BRLESC-I (1945-62)
Zuse Z3 (1941)
▸ Gordon Moore (Intel, 1965): Number of transistors in integrated circuits doubles approximately every two years
Zuse Z3 (1941)
Tran
sist
or c
ount
▸ Minimum feature size down to that of single atoms
MOORE’S LAW
▸ Gordon Moore (Intel, 1965): Number of transistors in integrated circuits doubles approximately every two years
Tran
sist
or c
ount
▸ Minimum feature size down to that of single atoms
▸ Different physical laws matter
MOORE’S LAW
QUANTUM MECHANICS
QUANTUM MECHANICS
▸ Quantum mechanics is a physical theory
QUANTUM MECHANICS
▸ Quantum mechanics is a physical theory
▸ Theory of atoms, molecules, and light quanta
QUANTUM MECHANICS
▸ Developed 1925-1928
QUANTUM MECHANICS
▸ Developed 1925-1928
▸ Basis of semi-conductors, materials science, lasers
QUANTUM MECHANICS
▸ Developed 1925-1928
▸ Basis of semi-conductors, materials science, lasers
▸ Fine structure constant: 7,297.352.566.4(17) x 10-3
QUANTUM MECHANICS
▸ Developed 1925-1928
▸ Basis of semi-conductors, materials science, lasers
▸ Radically different from classical mechanics▸ Fine structure constant: 7,297.352.566.4(17) x 10-3
RANDOMNESS
RANDOMNESS IN QUANTUM MECHANICS
▸ Measurement outcomes are random
Präparation
0 1 1 0 1 0
RANDOMNESS IN QUANTUM MECHANICS
▸ Measurement outcomes are random
Präparation
0 1 1 0 1 0
▸ We are used to randomness…
▸ … but this has an explanation
RANDOMNESS IN QUANTUM MECHANICS
▸ Measurement outcomes are random
Präparation
RANDOMNESS IN QUANTUM MECHANICS
▸ The randomness of quantum mechanics is absolute
Präparation
RANDOMNESS IN QUANTUM MECHANICS
▸ The randomness of quantum mechanics is absolute
Präparation
▸ Bell inequality violated under assumption of local hidden variables
P (a, b|A,B) =
�d�p(�)⇥A(a,�)⇥B(b,�)
UNCERTAINTY
UNCERTAINTY PRINCIPLE
UNCERTAINTY PRINCIPLE
▸ No measurement without disturbance
SUPERPOSITION
SUPERPOSITION PRINCIPLE
0
1
|1i
|0i
SUPERPOSITION PRINCIPLE
|0i+ |1i
|1i
|0i
SUPERPOSITION PRINCIPLE
|0i+ |1i
▸ Systems can be in “many states at once”
|1i
|0i
SUPERPOSITION PRINCIPLE
|0i+ |1i
▸ State space over complex vector space
▸ For spins
{⇢ : ⇢ � 0, tr(⇢) = 1} HH = C⌦n
2n
QUANTUM TECHNOLOGIES
QUANTUM TECHNOLOGIES
▸ Make use of quantum effects on the single quantum system level to think of new technologies in communication, sensing, computation, simulation
SECURE COMMUNICATION
▸ Classical key distribution
010101 010101
Need to share key
SECURE COMMUNICATION
▸ Classical key distribution
010101 010101
Need to share key
▸ Classical key distribution
010101 010101
Need to share key
SECURE COMMUNICATION
010101 010101
▸ Quantum key distribution for secure communication
SECURE COMMUNICATION
010101 010101No information gain without disturbance
▸ Quantum key distribution for secure communication
SECURE COMMUNICATION
010101 010101No information gain without disturbance
▸ Quantum key distribution for secure communication
SECURE COMMUNICATION
+ + ⇥ + ⇥ ⇥ ⇥ +" ! & " & % % !+ ⇥ ⇥ ⇥ + ⇥ + +" % & % ! % !!
0 1 1 0 1 0 0 1
0 1 0 1
Alice’s bitAlice’s basis
Bob’s basis
Bob’s result
Public partKey
State
! Basis +
⇥! Basis
"= |1i, != |0i
&= |0i+ |1i, %= |0i � |1i
010101 010101No information gain without disturbance
▸ Quantum key distribution for secure communication
▸ Security can be proven
SECURE COMMUNICATION
QUANTUM COMPUTERS
QUANTUM COMPUTING
▸ Computational devices with single quantum systems
QUANTUM COMPUTING
▸ Computational devices with single quantum systems
‣ E.g., 01010011 (bits) replaced by (qubits) ↵|0, 1, 0, 1, 0, 0, 1, 1i + �|1, 1, 0, 0, 1, 1, 1, 0i + �|0, 0, 1, 0, 0, 1, 1, 1i + . . .
QUANTUM COMPUTING
▸ Could solve some problems supercomputers cannot
BQP
Classical probabilistic algorithms
Poly time quantum algorithms
BPP
QUANTUM ALGORITHMS
▸ E.g., factoring of large products of prime numbers
‣ A factor of a large number can be found if the period of
can be identified
N p
f(x) = a
x
modN
‣ Periods can be found using the quantum Fourier transformn�1X
i=0
xi|iin�1X
i=0
yi|ii yk =1pn
n�1X
j=0
xje2⇡ijk/n7! with
Shor, SIAM J Comp 26, 148 (1997)
QUANTUM ALGORITHMS
▸ E.g., factoring of large products of prime numbers
‣ A factor of a large number can be found if the period of
can be identified
N p
f(x) = a
x
modN
‣ Periods can be found using the quantum Fourier transformn�1X
i=0
xi|iin�1X
i=0
yi|ii yk =1pn
n�1X
j=0
xje2⇡ijk/n7! with
‣ Solves NP problem in poly time: Runtime
Shor, SIAM J Comp 26, 148 (1997)
‣ Best known classical algorithm
‣ Generalised to hidden subgroup problem
▸ E.g., factoring of large products of prime numbers
QUANTUM ALGORITHMS
▸ E.g., factoring of large products of prime numbers
▸ Solving linear systemsHarrow, Hassidim, Lloyd, Phys Rev Lett 15, 150502 (2009)
Shor, SIAM J Comp 26, 148 (1997)
▸ E.g., factoring of large products of prime numbers
▸ Solving linear systems
▸ Spectral analysis
▸ Semi-definite programming
QUANTUM ALGORITHMS
Harrow, Hassidim, Lloyd, Phys Rev Lett 15, 150502 (2009)
Steffens, Rebenstrost, Marvian, Eisert, Lloyd, New J Phys 19, 033005 (2017)
Brandão, Kalev, Li, Lin, Svore, Wu, arXiv:1710.02581
Shor, SIAM J Comp 26, 148 (1997)
▸ Can tolerate small errors in all steps (at high cost)
FAULT TOLERANT QUANTUM COMPUTING
E.g., Litinski, Kesselring, Eisert, von Oppen, arXiv:1704.01589
▸ The race for building quantum computers
FAULT TOLERANT QUANTUM COMPUTING
▸ Not there, but with 50 superconducting qubits taking shape
(IBM)
(Google)
(Rigetti)(D-wave)
QUANTUM SIMULATORS
QUANTUM SIMULATION
▸ Quantum simulators: Not all strongly correlated quantum systems/materials can be classically simulated
QUANTUM SIMULATION
▸ Quantum simulators: Not all strongly correlated quantum systems/materials can be classically simulated
▸ Idea: Simulate quantum systems with quantum systems
Richard Feynman
QUANTUM SIMULATION
Cold atoms in optical lattices
▸ Quantum simulators: Not all strongly correlated quantum systems/materials can be classically simulated
▸ Idea: Simulate quantum systems with quantum systems
QUANTUM SIMULATION
▸ Simulate interesting physical situations
Trotzky, Chen, Flesch, McCulloch, Schollwöck, Eisert, Bloch, Nature Physics 8, 325 (2012)
Gring, Kuhnert, Langen, Kitagawa,Rauer, Schreitl, Mazets, Smith, Demler, Schmiedmayer, ,Science 337, 1318 (2012)
Kaufman, Tai, Lukin, Rispoli, Schittko, Preiss, Greiner, Science 353, 794 (2016)
Choi, Hild, Zeiher, Schauß,Rubio-Abadal, Yefsah, Khemani, Huse, Gross, Science 352, 1547 (2016)
Equilibration Pre-thermalization Thermalization
Many-body localization
QUANTUM SIMULATION
▸ Some properties can be obtained beyond supercomputers
QUANTUM SIMULATION
▸ Some properties can be obtained beyond supercomputers
‣ Imbalance as function of time for under Bose-Hubbard Hamiltonian
Trotzky, Chen, Flesch, McCulloch, Schollwoeck, Eisert, Bloch, Nature Phys 8, 325 (2012)
nodd
| (0)i = |0, 1, . . . , 0, 1i
QUANTUM SIMULATION
▸ Some properties can be obtained beyond supercomputers
‣ Imbalance as function of time for under Bose-Hubbard Hamiltonian
Trotzky, Chen, Flesch, McCulloch, Schollwoeck, Eisert, Bloch, Nature Phys 8, 325 (2012)
nodd
Best available classical matrix-product state simulation, bond dimension 5000
| (0)i = |0, 1, . . . , 0, 1i
QUANTUM SIMULATION
▸ Some properties can be obtained beyond supercomputers
‣ Imbalance as function of time for under Bose-Hubbard Hamiltonian
Trotzky, Chen, Flesch, McCulloch, Schollwoeck, Eisert, Bloch, Nature Phys 8, 325 (2012)
nodd
Best available classical matrix-product state simulation, bond dimension 5000
‣ The approximation of dynamics with matrix-product states requires exponential resources in time
| (0)i = |0, 1, . . . , 0, 1i
QUANTUM SIMULATION
▸ Some properties can be obtained beyond supercomputers
Random Periodic Translationally invariant
Bermejo-Vega, Hangleiter, Schwarz, Raussendorf, Eisert, Phys Rev X 8, 021010 (2018)
▸ Simple Ising nearest-neighbor architectures
QUANTUM SIMULATION
▸ Some properties can be obtained beyond supercomputers
Random Periodic Translationally invariant
Relate to logical circuits
Bermejo-Vega, Hangleiter, Schwarz, Raussendorf, Eisert, Phys Rev X 8, 021010 (2018)
▸ Simple Ising nearest-neighbor architectures
BPP
BQP
U U 0Additive error✏
A
x Stockmeyer
Multiplicative
error
sU 0(x)
1/poly(n)
Use complexity theory tools
QUANTUM SIMULATION
▸ Some properties can be obtained beyond supercomputers
Random Periodic Translationally invariant
Relate to logical circuits
Bermejo-Vega, Hangleiter, Schwarz, Raussendorf, Eisert, Phys Rev X 8, 021010 (2018)
▸ Simple Ising nearest-neighbor architectures
BPP
BQP
U U 0Additive error✏
A
x Stockmeyer
Multiplicative
error
sU 0(x)
1/poly(n)
Use complexity theory tools
‣ Present technology (basic) quantum simulators already outperform supercomputers on some tasks (and can be verified)
GETTING GOING…
FLAGSHIP PROGRAM FOR QUANTUM TECHNOLOGIES
▸ 1G€ Euros-Flagship for quantum technologies
OUTLOOK
▸ “Quantum computing is exciting even if you restrict yourself to saying things that are true.”
OUTLOOK
▸ “Quantum computing is exciting even if you restrict yourself to saying things that are true.”
THANKS FOR YOUR ATTENTION
