norbert m. linke tiqi group, chris monroe jqi, umd...tiqi group, chris monroe jqi, umd - a...
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Hardware for universal quantum computers
Norbert M. Linke
TIQI group, Chris MonroeJQI, UMD
- a programmable trapped-ion machine -
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Overview
Ion trap quantum computer modulehardware (5-7 qubits)modular gates and compiler
Quantum algorithms and applicationsBernstein Vaziraniarchitecture comparison
Outlook: current and future workquantum machine learningscaling up
Quantum computingwhat is a qubit?requirementswhy ions make good qubits
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Quantum computing
Classical bit Qubit
0
1
0 or 1superposition
n-bit register 2n states superposition of 2n states(entanglement)
bits
000 001 010 100011 101 110 111
0
0 1
1
a + b
000 + 111example:
000 001 010 100011 101 110 111
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Quantum computing
Function evaluation – quantum parallel processing
000 001 010 100011 101 110 111
F(000) F(001) F(010) F(100)F(011) F(101) F(110) F(111)
Quantum Processor
F(x)
2n calculations at once
Quantum logic gates
OutputInput
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Quantum computing
Example operation – the controlled-NOT (CNOT) gate
entangled state
phase kick-back
classical states
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Many possible implementations – systems under investigation- super-conducting circuits- photonic networks- neutral atoms- NMR systems- NV centers- SINGLE IONS- ……
Building a quantum computer – requirements
Why is this so hard? – more requirements
- good qubits (quantum system with 2 levels, preparation, read-out)- universal set of gates (single qubit gate, 2-qubit entangling gate)
- long coherence times- many qubits - low gate errors
overhead for error correction
Quantum computing
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Trapped ions
A good quantum computing candidate – why?
- Isolated quantum system, preparation and read-out with laser light- gate operations (using lasers/microwaves)
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The ion trap quantum computer (vision)
Ion trap Quantum computing – the big pic
quantum register
“accumulator”
segmented electrodes
D. J. Wineland et al. 1998 C. Monroe / J. Kim et al. 2013
Are we there yet…? – challenges
- Higher fidelity operations- Scalability: control over more qubits
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+
+
+- -
Ion traps (reality)
Wolfgang Paul (Nobel Prize 1989)
The linear Paul trap – dynamic confinement in electric RF quadrupole + DC potential
Microfabricated versions – surface traps
MAT (Oxford)
D.P.L. Aude Craik et al., PRA 95 (2017)
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Ion traps: state-of-the-art
Surface trap foundries – chips engineered by pros
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trapped ion Coulomb crystals
Ion traps: hardware in current UMD module
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S. Olmschenk, et al., PRA 76 (2007)
Trapped ion qubits: 171Yb+ level structure
atomic clock qubit -> B-field insensitivelong coherence times: ~1s
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12.6 GHz2S1/2
2P1/2
369 nm
F=0
F=1
F=0
F=1
Trapped ion qubits: State initialization
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12.6 GHz2S1/2
2P1/2
F=0
F=1
F=0
F=1
369 nm
2.1 GHz
Trapped ion qubits: State detection
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drive gates with pair of laser beams at 355nm
2S1/2
2P3/2
100 THz
D=33 THz
|0
|1
355 nm
2P1/2
GHz6.12HF
D=66 THz
171Yb+ as a qubit: coherent manipulation
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Modular architecture
S. Debnath et al. Nature 536 (2016)
Grover, Hidden Shift, EC …
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Hardware
2S1/2
2P3/2
D=33 THz
|0
|1
355 nm
2P1/2
GHz6.12HF
171Yb+
D=66 THz
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Hardware: Read-out
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Modular architecture
S. Debnath et al. Nature 536 (2016)
Grover, Hidden Shift, EC …
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Quantum control: single qubit rotations (R-gates)
Raman beat note
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Beatnote frequency
HFtr
ansi
tio
n p
rob
abili
ty
carrier
redsideband
bluesideband
x +HFx HF
Quantum control: entangling gates (XX-gates)
…
mode1
mode2
1 5 15
entangled state(EPR pair)
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Quantum control: Full connectivity
not limited to local operations
NML et al. PNAS 114, 13 (2017)
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Modular architecture
S. Debnath et al. Nature 536 (2016)
Grover, Hidden Shift, EC …
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0100
1000
0010
0001
Quantum compiler: Modular CNOT gates
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CNOT [1:2] F=96.4(6)%
CNOT [3:4] F=96.6(5)%1
0
0.2
0.4
0.6
0.8
CNOT [1:3] F=97.6(7)% CNOT [1:4] F=95.9(7)% CNOT [1:5] F=97.9(5)%
CNOT [2:3] F=95.6(6)% CNOT [2:4] F=98.4(7)% CNOT [2:5] F=96.8(7)%
CNOT [3:5] F=97.6(6)% CNOT [4:5] F=97.2(5)%
spam reduces this by ~2%
Quantum compiler: Modular CNOT gates
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CNOT [1:2] F=96.4(6)%
CNOT [3:4] F=96.6(5)%1
0
0.2
0.4
0.6
0.8
CNOT [1:3] F=97.6(7)% CNOT [1:4] F=95.9(7)% CNOT [1:5] F=97.9(5)%
CNOT [2:3] F=95.6(6)% CNOT [2:4] F=98.4(7)% CNOT [2:5] F=96.8(7)%
CNOT [3:5] F=97.6(6)% CNOT [4:5] F=97.2(5)%
spam reduces this by ~2%
Quantum compiler: Modular CNOT gates
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Modular architecture
Grover, Hidden Shift, EC …
S. Debnath et al. Nature 536 (2016)
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Quantum algorithms: build it …and they will come!
1 S. Debnath et al. Nature 536 (2016) 2 NML et al., PNAS 114, 13 (2017)3 NML et al., Sci Adv. 3, 10 (2017) 4 C. Figgatt et al., Nat. Communs. 8, 1918 (2017)5 N. Solmeyer et al., accepted QST (2018) 6 NML et al., arxiv 1712.08581 (2017)7 K. A. Landsman et al., arxiv 1806.02807 8 M. Benedetti et al., arxiv 1801.07686 (2018)9 A. Seif et al., arxiv 1804.07718(2018) 10 in preparation
Fault-tolerant quantum error detection3 – K. Brown (Georgia Tech.)
Renyi entropy measurement of a Fermi-Hubbard model system6 – S. Johri (Intel)
Quantum game theory and Nash equilibria5 – N. Solmeyer (Army Research Lab)
Quantum machine learning8 – A. Ortiz (NASA)
Quantum scrambling and out-of-time-order correlators7 – N. Yao (UC Berkeley)
Hidden Shift algorithm2 – M. Roetteler (Microsoft)
Quantum Fourier Transform, Bernstein-Vazirani algorithm, Deutsch-Josza algorithm1
Grover’s algorithm4 – D. Maslov (NSF)
…
Bacon-Shor quantum error correction codes10 – T. Yoder (Harvard)
Deuteron VQE – R. Pooser (Oak Ridge)
Quantum machine learning8,10 – A. Ortiz (NASA)
Neural-network-based qubit readout9 – A. Seif (QuiCS/UMD)
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Example algorithms 1
Bernstein-Vazirani algorithm: oracle implements
f(x)
oracle
E. Bernstein and U. Vazirani, SIAM J. Comput. 26 (1997)
INPUT
OUTPUT f(x)0
use all states
carries information
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Example algorithms 1
Bernstein-Vazirani algorithm: oracle implements
information about the oracle- single shot
CNOT imprints a phase flip on the qubits
oracle
E. Bernstein and U. Vazirani, SIAM J. Comput. 26 (1997)
f(x)
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Example algorithms 2
Hidden shift algorithm: oracle implements
example “known” function
circuit
e.g.
information about the oracle- single shot
oracle
A. M. Childs et al., in Proceedings of TQC 8 (2013)M. Roetteler, in Proceedings of 21st SODA (2010)
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star-shaped (superconductor) fully connected (ion trap)
Bernstein-Vazirani algorithm
Hidden shift algorithm
NML et al. PNAS 114, 13 (2017)
Connectivity matters: architecture comparison (2016)
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star-shaped (superconductor) fully connected (ion trap)
Bernstein-Vazirani algorithm
Hidden shift algorithm
≤4 ≤4
2-qubit gate count
NML et al. PNAS 114, 13 (2017)
Connectivity matters: architecture comparison
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star-shaped (superconductor) fully connected (ion trap)
Bernstein-Vazirani algorithm
Hidden shift algorithm
4
≤4 ≤4
2-qubit gate count
10
NML et al. PNAS 114, 13 (2017)
QC architecture comparison: experimental results
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star-shaped (superconductor) fully connected (ion trap)
Bernstein-Vazirani algorithm
Hidden shift algorithm
4
≤4 ≤4
2-qubit gate count
10
NML et al. PNAS 114, 13 (2017)
QC architecture comparison: experimental results
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Quantum machine learning: Bars and Stripes
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Quantum machine learning: Bars and Stripes
Benedetti, M. et al. arxiv 1801.07686 (2018)
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Quantum machine learning: Bars and Stripes
2-Layer star connectivity
2-Layer all-to-all connectivity
Benedetti, M. et al. arxiv 1801.07686 (2018)
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Quantum machine learning: Bars and Stripes
Benedetti, M. et al. arxiv 1801.07686 (2018)
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Quantum machine learning: Bars and Stripes
Animation from Wikipedia by Ephramac
Use Particle Swarm Optimization (PSO)
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Quantum machine learning: Bars and Stripes
Best particle out of 21
2-Layer star connectivity
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no system will be fully connected for large N
the compilation challenge
D. Kielpinski et al., Nature 417 (2002)
C. Monroe et al., Phys. Rev. A 89 (2014)
Outlook 1: the future - scaling up
D. Hucul, et al., Nature Phys. 11 (2015)
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Michael Goldman
Marko Cetina
Kristin Beck
Outlook 2: control over ~20 qubits
Laird Egan
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Chris Monroe ShantanuDebnath
KevinLandsman
NML CarolineFiggatt
DaiweiZhu
Dmitri Maslov(NSF)
Martin Roetteler(Microsoft)
Ken Brown(Georgia Tech)
Sonika Johri(Intel)
Norman Yao(UC Berkeley)