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Hardware for universal quantum computers
Norbert M. Linke
TIQI group, Chris MonroeJQI, UMD
- a programmable trapped-ion machine -
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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0〉|
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
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
Quantum computing
Example operation – the controlled-NOT (CNOT) gate
entangled state
phase kick-back
classical states
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
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
+
+
+- -
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)
Ion traps: state-of-the-art
Surface trap foundries – chips engineered by pros
trapped ion Coulomb crystals
Ion traps: hardware in current UMD module
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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|
+
1〉
0〉
12.6 GHz2S1/2
2P1/2
369 nm
F=0
F=1
F=0
F=1
Trapped ion qubits: State initialization
12.6 GHz2S1/2
2P1/2
F=0
F=1
F=0
F=1
369 nm
2.1 GHz
Trapped ion qubits: State detection
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
Modular architecture
S. Debnath et al. Nature 536 (2016)
Grover, Hidden Shift, EC …
Hardware
2S1/2
2P3/2
D=33 THz
|0
|1
355 nm
2P1/2
GHz6.12HF
171Yb+
D=66 THz
Hardware: Read-out
Modular architecture
S. Debnath et al. Nature 536 (2016)
Grover, Hidden Shift, EC …
Quantum control: single qubit rotations (R-gates)
Raman beat note
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)
Quantum control: Full connectivity
not limited to local operations
NML et al. PNAS 114, 13 (2017)
Modular architecture
S. Debnath et al. Nature 536 (2016)
Grover, Hidden Shift, EC …
0100
1000
0010
0001
Quantum compiler: Modular CNOT gates
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
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
Modular architecture
Grover, Hidden Shift, EC …
S. Debnath et al. Nature 536 (2016)
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)
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
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)
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)
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)
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
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
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
Quantum machine learning: Bars and Stripes
Quantum machine learning: Bars and Stripes
Benedetti, M. et al. arxiv 1801.07686 (2018)
Quantum machine learning: Bars and Stripes
2-Layer star connectivity
2-Layer all-to-all connectivity
Benedetti, M. et al. arxiv 1801.07686 (2018)
Quantum machine learning: Bars and Stripes
Benedetti, M. et al. arxiv 1801.07686 (2018)
Quantum machine learning: Bars and Stripes
Animation from Wikipedia by Ephramac
Use Particle Swarm Optimization (PSO)
Quantum machine learning: Bars and Stripes
Best particle out of 21
2-Layer star connectivity
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)
Michael Goldman
Marko Cetina
Kristin Beck
Outlook 2: control over ~20 qubits
Laird Egan
Chris Monroe ShantanuDebnath
KevinLandsman
NML CarolineFiggatt
DaiweiZhu
Dmitri Maslov(NSF)
Martin Roetteler(Microsoft)
Ken Brown(Georgia Tech)
Sonika Johri(Intel)
Norman Yao(UC Berkeley)
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