Optically-controlled controlled quantum dot spins for quantum computers David Press Yamamoto Group Applied Physics Department Ph.D. Oral Examination April 28, 2010 1
What could a Quantum Computer do? Simulating Hard to simulate quantum mechanics with normal computer.... so simulate physics on a quantum computer. Richard Feynman, Int. J. Theor. Phys. 21, 467 (1982) Factoring Shor s Algorithm: Fast factoring of large integers. Peter Shor, Proc. 35 th Annual Symposium on Foundations of Computer Science, (1994) Classically, to factor an n-bit number into its prime products takes ~O(exp[n]) time. Shor s Algorithm, a quantum computer could factor an n-bit number in ~O(n 3 ) time 2
Qubits Classical Bit Quantum Bit (qubit) 0 or 1 a 0 b 1 P(0) a P(1) b 2 2 a 2 b 2 1 Classical Register Quantum Register 10010111 a 0 00000000... a 255 a 1 11111111 00000001 3
Qubits on the Bloch Sphere z 1 Quantum Bit (qubit) a 0 b 1 sin 0 2 cos e 2 i 1 y x 0 Decoherence time: T 2 maintain Memory time 4
Single-bit Operations Classical Single-Bit Gate Quantum Single Qubit Gate 0 or 1 a 0 b 1 NOT Gate Arbitrary Rotation [SU(2)] in out in R out z 1 y x 0 5
2-bit Operations Classical 2-Bit Gate AND Gate Quantum 2-Qubit Gate C-NOT Gate x x A B a 0 b 1 y y' A B Output 0 0 0 0 1 0 1 0 0 1 1 1 Inputs Outputs x y x x + y 0 0 0 0 0 1 0 1 1 0 1 1 1 1 1 0 6
2-bit Operations Classical 2-Bit Gate AND Gate Quantum 2-Qubit Gate C-NOT Gate x x A B a 0 b 1 y y' The C-NOT and single-qubit gates are universal for quantum computation 1 1 Barenco et al., PRA 52, 3457 (1995) 7
What do we need? Topological Surface Code Architecture 1-2-D array of qubits - 1 logical qubit topologically encoded in many physical qubits - built-in error resistance R 1 CNOT 0 or 1? 1 0 o0 1 Ingredients - initialization - arbitrary 1-qubit gates - nearest-neighbor 2-qubit gates - measurement 1 Raussendorf & Harrington, PRL, 2007 8
What do we need? Topological Surface Code Architecture 1-2-D array of qubits - 1 logical qubit topologically encoded in many physical qubits - built-in error resistance Estimation 2-1000 physical qubits per logical qubit - Gate error rate ~ 0.1% - T 2 / T gate ~ 10 4 - Shor s algorithm on 1024 bit number ~ 10 8 physical qubits 1 Raussendorf & Harrington, PRL 98, 190504 (2007) 2 Van Meter et at., Arxiv:0906.2686 9
What will Qubits be made of? Hardware of Qubits Trapped ions? Atoms in an optical lattice? Superconducting circuits? Diamond NV centers? Quantum dots? Review: T. D. Ladd et al., Nature 464, 45 (2010) 10
Qubit Comparison System Gate error rate (%) 1-qubit 2-qubit T 2 /Gate time 1-qubit 2-qubit Coherence time (T 2 ) Trapped ion 0.5 0.7 >10 6 >10 5 15 s Trapped neutral atom 1 3 s Superconducting circuit 0.7 10 10 3 10 2 4 s Diamond NV center 2 10 3 2 ms e - spin in QD electrical control 5 10 3 3 s e - spin in QD optical control 2 10 5 3 s T. D. Ladd et al., Nature 464, 45 (2010) and references therein 11
Quantum Computing Checklist 1. Scalable physical system 2. Qubit state must be initialized 3. Qubit state must be measured 4. Single-qubit gates must be demonstrated 5. Two-qubit gates must be demonstrated 6. Qubit must have long decoherence (memory) time 12
Outline Implementation of a single qubit operations in a quantum dot spin Initialization (optical pumping) Measurement (single photon counting) Rotation gate (ultrafast optical pulses) Spin echo Extends decoherence time from ns s 13
Optical Quantum Dot Qubits 14
Quantum Dots 100 nm SEM Image of uncapped QDs x z 100nm Al mask 10 m windows InGaAs QDs, ~ 10 9 cm -2 10 nm -Doping 2 x QD- Density GaAs AlAs AlAs GaAs AlAs GaAs substrate 15 x 5 x 24
Quantum Dots objective 100 nm SEM Image of uncapped QDs x z 100nm Al mask 10 m windows InGaAs QDs, ~ 10 9 cm -2 10 nm -Doping 2 x QD- Density GaAs AlAs AlAs GaAs AlAs GaAs substrate 16 x 5 x 24
Quantum Dot Energy Levels No applied magnetic field Trion X - GaAs InGaAs C. B. GaAs Electron V. B. 1.3 ev Hole Spin projections along z-axis Electron e - 17
Quantum Dot Energy Levels Magnetic field in Voigt geometry Trion X - B ext h Electron Larmor Frequency Electron e - e e = g e B B ext ~ 26 GHz @ B ext ~ 7 T 18
Quantum Dot Energy Levels Magnetic field in Voigt geometry Photoluminescence H V V H h H V V H Polarization angle (deg) e Wavelength (nm) 19
Spin Rotation Ground state transition in the presence of a lossy excited state Detuned Raman transition 1 (t) e 0 (t) [Aside] Stimulated Raman Adiabatic Passage (STIRAP) e Ultrafast Detuned Raman transition (t) e (t) 1 e 0 1 (t) 0 (t) 1 e 0 eff 1 e 0 1 0 20
Spin Rotation Circularly-polarized 4 ps Rotation Pulse e = 26 GHz BW = 110 GHz = 270 GHz = 925 nm Pulse duration << Larmor period 21
Spin Initialization and Measurement Narrowband CW optical pump - initializes into in ~ ns - measures population in - emits single photon, detected by photon counter Single Photon Detection 22
Experimental Setup T = 1.5 K, B ext ~ 2-10 T 23
Experimental Setup 24
Spin Initialization Fixed rotation pulse of = Population in Initialization fidelity: F 0 = 92±7% D. Press et al., Nature 456, 218 (2008) 25
1-pulse: Rabi Oscillations Reduced detuning Population in Vary Rotation Pulse energy to observe Rabi Oscillations between e-spin states D. Press et al., Nature 456, 218 (2008) 26
2-pulses: Ramsey Interference Two /2 pulses separated by variably time delay High-contrast Ramsey Fringes /2-pulse fidelity: F /2 ~ 98% 27
Arbitrary Single-Qubit Gate Vary pulse rotation angle and time delay Explores entire surface of Bloch sphere Total time for arbitrary gate < 40 ps D. Press et al., Nature 456, 218 (2008) 28
Decoherence Time Nuclear spins in QD lead to slowly-fluctuating background B field e - spin envelope function s-like Bloch wavefunction Lattice nuclei e = e 0 ± [100 1000] MHz T 2* ~ 1-10 ns due to shot-to-shot B variations Spin echo refocuses inhomogeneously broadened spins, measure T 2 /2 T T /2 29
Decoherence Time: T 2 * start T switch! T 30 finish
Decoherence Time: T 2 start T switch! T 31 finish
Spin Echo and T 2 * Hahn Spin Echo (and T 2 * ) /2 T T 2T 2 * /2 2T = 264 ns T 2* = 1.71 ± 0.08 ns D. Press, et al., Nature Photonics (in press) 32
Spin Echo and T 2 D. Press, et al., Nature Photonics (in press) 33
Summary: Quantum Computing Checklist 1. Scalable physical system e - spin in semiconductor quantum dot 2. Qubit state must be initialized Optical pumping F 0 ~ 92% 3. Qubit state must be measured Photon counting 4. Single-qubit gates must be demonstrated Ultrafast optical pulses F /2 ~ 98% 5. Two-qubit gates must be demonstrated 6. Qubit must have long decoherence (memory) time Spin echo: 2 ns 3 s 34
Future Work Scalability Position- and wavelength-controlled QDs Schneider et al., APL 92, 183101 (2008) Measurement Photon counting measurement: multi-shot (F ~ 10-4 ) Single-shot non-demolition spin measurement 35
Future Work 2-qubit gates Neighboring qubits driven by common optical mode, pick up non-linear phase shift Yamamoto, et al., Phys. Scr. T137, 014010 (2009) Decoherence time Extend T 2 beyond 3 s with Dynamical Decoupling Carr & Purcell, Phys. Rev. 94, 630 (1954) Meiboom & Gill, Rev. Sci. Inst. 29, 688 (1958) 36
Limits of Technology It would appear that we have reached the limits of what it is possible to achieve with computer technology, although one should be careful with such statements, as they tend to sound pretty silly in 5 years. (Said in 1949) John von Neumann 37
Acknowledgements 38
Advisor Prof. Yoshi Yamamoto 39
Committee Prof. Hideo Mabuchi * Prof. David Miller * Prof. Stephen Harris Chair: Prof. Aaron Lindenberg * Thanks for reading, too! 40
Stanford Yamamoto group past and present: Kristiaan, Peter, Thaddeus, Stephan Yurika Peterman, Rieko Sasaki Ginzton: Larry Randall, Paula Perron, Claire Nicholas Würzburg/Samples: Christian Schneider, Sven Höfling, Andreas Löffler, Benedikt Friess, Stephan Reitzenstein, Alfred Forchel 41
Friends & Family AP/EE: Ilya Fushman, Andrei Faraon, Dirk Englund, Mike Wiemer, Rafael Aldaz All my Stanford & Tahoe friends! Family Murray, Heather, Roberta, me 42
Anika! 43
Thank you! Questions? 44
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