Foundations of Solid-State Quantum Information...
Transcript of Foundations of Solid-State Quantum Information...
Foundations of Solid-State Quantum Information Processing
(ITR/SY #EIA-0121568; Sept. 2001 -- Aug. 2006)
• Robert Averback• James Eckstein• Paul Goldbart• Paul Kwiat• Anthony Leggett• Myron Salamon• John Tucker• Dale VanHarlingen
Studying variously sized spin-based qubits in several condensed-matter systems, to understand and optimize the tradeoff between Coherence and Controllability
Qubit “size”
Coh
eren
ce
Controllability
Who (else) are we? Other Collaborators:• Y.-C. Chang (UIUC)• J. Clarke (U. C., Berkeley)• R.-R. Du (Univ. Utah)• C. P. Flynn (UIUC)• D. James (LANL)• D. Loss (Univ. Basel)• M. Leuenberger (U. Basel)• B. Munro (HP, Bristol)• V. Ryazanov (Inst. Solid
State Physics, Moscow)• T.-C. Shen (Utah State Univ.)• J. Tejada (Univ. Barcelona)• A. White (Univ. Queensland)• F. Wilhelm (Ludwig
Maximilians Univ.)
Graduate Students:• Joseph Altepeter• Trevis Crane• Bruce Davidson• Soren Flexner• Sergey Frolov• Kim Garnier• Evan Jeffrey• Swagatam Mukhopadhyay• Patricio Parada-Salgado• Nicholas Peters• Stephen Robinson• Tzu-Chieh Wei
Post-doc:• Young Sun
Undergraduates:• D. Achilles• M. Rakher
Outline• Introduction to Quantum Computing,
and the problem of decoherence• P-spins in Silicon• Magnetic Nanoclusters• Π-junction SQUIDS• Fabrication technologies -- “quieter”
superconductors• Optical “benchmarking”• Misc.• What next...
Quantum Computing 101• Unlike classical bits, which are either in the state “0” or “1”,
quantum bits (“qubits”) can be in arbitrary superpositions:
• In principle, a qubit can comprise any two-level system.• Basic requirements:
– Qubits must be controllable (high fidelity gate operations, readout, etc.)– Qubits must be well-isolated from their environment (no decoherenceno decoherence!!)– System must eventually be scalable to useful numbers of qubits
• Under these circumstances, a quantum computer can solve certain problems -- e.g., factoring, exact simulation of multi-spin systems -- much faster than any classical computer.
• Solid-state qubits have been proposed as likely candidates to meet the above constraints.
• Our goal is to investigate single- and few-qubit interactions in solid state systems, for several different qubit “sizes”.
ψ = α 0 + β 1
Our Solid-State Qubits
• Phosphorous spin in silicon (n = 1)• Small magnetic nanoparticles (n = 100 - 10,000)• Magnetic moment of current loops in SQUIDS
(n = 1010)
Our “benchmark”Correlated photons from spontaneous
parametric downconversion --> state synthesis, state- and process-tomography;
decoherence and error correction
Our goal is to systematically integrate P-donor qubits with epitaxial device structures capable of detecting individual electrons, determining their quantum states, and observing their movements through qubit arrays under gate control.
Single spin qubit (P in silicon, a la Kane)
G1
output
Simplified electron spin read-out
silicon
D-
J G2+++
Planar SET(all P-donors)target
R=10 aB~300Å
Detecting the motion of individual electrons between donor sites, and characterizing the exchange energy due to wavefunction overlap, will be difficult using relatively large Al-oxide SETs on the surface (telegraph and 1/f noise).
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X ( ( ( (aB ))))
ρ (
ρ (
ρ (
ρ (x
)) )) F=0.10F=0.12F=0
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X ( ( ( (aB) ) ) )
ρ (
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Calculation of charge distribution under parallel uniform electric field (R=10aB) [Y.-C. Chang, UIUC]
There exists a window between two critical electric fields (0.095 <<<< F <<<< 0.120),within which the singlet state transforms to a doubly-occupied configuration,while the triplet state remains in a bound coupled donor state. (E ~ 104 V/cm)
Singlet state Triplet state
Readoutdonor
Qubitdonor
Readoutdonor
Qubitdonor
Atomically Ordered Devices Based on STM LithographyJ. R. Tucker, University of Illinois, and T.-C. Shen, Utah State University
Solid-State Electronic Devices 42, pp. 1061-1067, 1998.
(1) Remove H-atoms from Si dangling bondsby STM lithography in UHV.
T.-C. Shen, et al., Science 268, 1590, 1995.
single dangling bonds
depassivated dimersSi(100)-2x1:H
(2) Selectively adsorb PH3 molecular precursors onto the STM-exposed areas.
Y. Wang, M. J. Bronikowski, and R. J. Hamers, J. Phys. Chem. 98, 5966, 1994.
Epitaxial single-electron transistor: donor pattern on a pre-implanted STM template
GS D
B
pre-implanted contacts
P-donor SET
undoped Si substrate
Studies of low-T Si overgrowth and unpatterned P-delta layers are nearly complete. Ion implanted STM templates are now ready.Low-temperature surface preparation is nearly optimized.Low-T (~4K) system installed for measurements on implants and SET devices.
Magnetic nanoparticlesThe Basic Idea
•Create single-domain ferromagnetic particles—size depends on the material.
~10 nm --> S = 104 or so.
•Locate them on or in a suitable material
•Arrange to have the magnetization easily rotatable in some plane (--> anisotropric cluster)
•Control the tunnel barrier between two equivalent orientations of the total spin.
•Confirm tunneling via tunnel splitting and/or Rabi oscillations by kicking with rf fields.
•Link spins (in a controlled manner) using SQUID loops
M
d
E
θ
Image of moment insuperconductor
First step—try to measure loss of magnetization due to onset of tunneling
oxide
Nb
Deposit permalloy particles on Nb overlain with an oxide wedge. Maybe backed by a magnet to align easy axis up.
Measure magnetization escape rate (of an aggregate of clusters) as a function of oxide thickness above and below Tc. We expect a crossover between thermal excitation over the barrier and tunneling as the temperature is reduced.
Test ideas of the reduction of the barrier height with the inverse cube of the wedge thickness.
SiO2 , SiNx
Al2 O3
~20 nm
Aluminum (superconductor)
magnetic material (e.g. permalloy)
~6 nm
~3 nmsuperconducting
wire
Josephson junction
Quantum circuit: two nanoparticle qubits “connected” by superconducting loop
Permalloy clusters
Average size: small clusters 4-6 nmlarge clusters 15 nm
Ave. density: small clusters ~ 7E10 cm-2
large clusters ~ 4E9 cm-2
Drilling holes with STEM
30nm thick silicon nitride membraneJEOL 2010F STEM “drill”32 pulses (950 pA) of 10 seconds eachEELS spectrum --> D ~ 2.5 nm
Next step is to fill the hole with ferromagnetic material
Superconducting flux qubits for Quantum Computing
Josephson junctionI = Ic sinφ
Superconducting loop
Magnetic flux Φ
Circulating current J
E
J
Qubit states correspond to clockwiseand counterclockwise currents
Basic Qubit = rf SQUID
Φ = 1/2 Φ0
Our approach: utilize π-Josephson junctions in superconducting flux qubit
πJ
Spontaneous circulating current in rf SQUID
ππππ-junctionNegative Ic ! minimum energy at π
I
φ
E
φπ 2π0π 2π0
• Provides natural and precisely-degenerate two-level system
Advantages of an intrinsic ππππ-phase shift
• Decouple qubit from environment since no external drive needed
π-phase shift induced by magnetic moment in weak ferromagnetic barrier
SNb
SNb
FCuNi
SC-FM-SC junctions
(Chernogolovka)
Quasiparticle injection junctions
(Groningen)
π-phase shift from nonequilibriumquasiparticle distribution inside barrier
Schemes for generating ππππ-Josephson junctions
Trombone experiment: measure spontaneous flux for phase shift of π
Nb flux transformer
moveable Nb ground plane
Josephson junction
Ongoing research projects/plans
1. Verify π-junction behavior via phase-sensitive tests
2. Observe coherent quantum oscillation in a flux qubit incorporating π-junctions.
Current phase-relation experiment: map out I(φ) by SQUID interferometry
x
Junction barrierJunction barrierJunction barrierJunction barrierX = F, N, …X = F, N, …X = F, N, …X = F, N, …
transformer couplingqubit
= π-junction
dc SQUID detector
epitaxial Nb
epi PdNi alloy Tc 15K
epitaxial Nb
epitaxial π-junction
heteroepitaxialinterfaces
Single crystal Josephsonjunctions for qubits
Each superconducting Qubit has 2 quantum states, but from 106 to 1018 atoms. Compare polycrystalline and single crystal devices.Decoherence results from excitation of low energy degrees of freedom and from mesoscopic fluctuations – 1/f noise effects.
π-junctions are irreproducible due to material inhomogeneity.
Needs epitaxial single crystal superconductive devices.
Use epitaxial Nb-film growth developed by Flynn at UIUC.
Goal: reduce quantum state decoherence due to material defects and noise
R-plane A-plane
A-plane
LEEM image
1400 C anneal
Epitaxial growth of Nb films with large atomically flat terraces proceeds via 3D nucleation followed by consolidation. RHEED shows specular reflection from smooth regions. Thicker (>100 nm) films fill in. High temperature anneal leads to larger terraces and unit cell step bunching. Use such surfaces for interfaces in epitaxial Josephson junction structures.
Heteroepitaxial growth of smooth Nb films
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2 10-5
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0 50 100 150 200 250 300
single crystal epitaxial niobium film on A-plane sapphire
Temperature (K)
Tc=9.2K
resi
stiv
ity(O
hm-c
m)
Optical “benchmarking”: Single Qubit Generation
|V>|H>2 θ1 4 θ1
|V>|H>
4 θ1
|H>
2 θ34 θ2
|V>ρ
|V>|H>2 θ2 4 θ2
Decoherer
HWP@ θ2
QWP@ θ3
HWP@ θ1
ρ|H> V
An arbitrary state:
ρ =A B e−i δ
B ei δ 1 − A
θ2 =14
ArcTan2B Cos[δ]
2A −1
+ ArcTan
2B Sin[δ]
2A −1( )2 + 4B2 Cos2 δ( )
θ1 = 14
ArcCos 2A −1( )2 + 4B2[ ]
θ3 = 12
ArcTan 2B Cos[δ]2A −1
Fidelity 1.000 0.998 0.999 0.999
Theory ρ
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|H><H| |H><V|
|V><H| |V><V|
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|H><H| |H><V|
|V><H| |V><V|
Re[ρ] Im[ρ]
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|V><H| |V><V|
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Experiment ρ0
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|V><H| |V><V|
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State |H> |D> Mixed Partially Mixed
ρ1 00 0
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1 11 1
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1 00 1
1 + 36
36 (1 + i)
36 (1 − i) 1 − 3
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Experiment vs. Theory
Two-crystal Source
ψ =12
H 1 H 2 + eiϕ V 1 V 2( )
#1
H-polarized�(from #1)
Type-I �phase-matching
#2
V-polarized�(from #2)
#1
H-polarized�(from #1)
Type-I �phase-matching
Maximally-entangled state
Quantum State Tomography
Measuring the density matrix for the 2-photon quantum system (c.f., measuring the Stokes parameters for a single photon)
Example: HH + VV
AUTOMATED TOMOGRAPHY:
ADAPTIVE TOMOGRAPHY:
AutomatedTomography
System(30 Minute Run)
(Long
List of 16Measurements
1 HH2 HV3 VH
15 RD16 DH
16Measurements
HH = 0.507HV = 0.345VH = 0.110
RD = 0.234DH = 0.189
16Precise
Probabilities
MaximumLikelihoodTechnique
ρPreciseDensityMatrix
AutomatedTomography
System(3 Minute Run)
List of 16Measurement
s
1 HH2 HV3 VH
15 RD16 DH
16Measurements
HH = 0.5HV = 0.3VH = 0.1
RD = 0.2DH = 0.2
16Imprecise
Probabilities
MaximumLikelihoodTechnique
ρImpreciseDensityMatrix
AutomatedTomography
System(30 Minute Run)
(Long
1 AB2 AA3 CA
15 CE16 AC
16 NewMeasurements
AB = 0.5AA = 0.3CA = 0.1
CE = 0.2AC = 0.2
16Precise
Probabilities
MaximumLikelihoodTechnique
ρρρρUltra-
PreciseDensityMatrix
Find a roughestimate of
the state
1
Use this rough estimateto find the ideal set of 16
measurements to use. 2
F = 0.983
ImRe
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Miscellaneous activities• Theoretical studies of state-synthesis, entanglement, and tradeoff
between entanglement and mixture.• Experimental studies of geometrical phase on partially-
decohered states (relevant for fault-tolerant computation) [REU]
• Quantum Information Science Seminar– 24 talks, 14 external speakers– 30-70 attendees; physics, math, chem., ECE
• Quantum Information Open House (12/5/01)– ~demonstrations of fundamental quantum-info. primitives– ~400 visitors, 120 high school students
The next steps...• P in Silicon
– First electrical measurements on lines and planar tunnel junctions; simulations of self-ordered P-delta layer, tunnel junctions and SETs
– Assemble new UHV-STM measurement system• Magnetic nanoparticle
– Characterize demagnetization of nanoparticles; create “filled” holes• Superconducting qubits
– Construct, verify and characterize π-junction qubits• Low noise “connections”
– Fabricate single-crystal Nb superconductors, overlain with Pd-Ni• Theory
– Determine optimal readout schemes to minimize quantum back-action• Optical “benchmark”
– Arbitrary qubit synthesis and adaptive process tomography
SummaryBy studying qubits encoded in magnetic moments of systems of widely varying sizes, we hope to understand the tradeoff between a qubit’s resistance to decoherence and our ability to control/readout the quantum state.
Quantum Coherence
Func
tiona
lity
Superconducting �phase dynamics
Photon entanglement
Magnetic nanoparticles
Quantum spins �in Silicon
System size
Physical realization of system of coupled qubits for performing quantum logic
Scalablequantum computer
The INSQUID = INductive SQUIDscheme for quiet entanglement/readout of Qubit flux state
Qubit
detector SQUID readout SQUID
ΦSQΦQ
coupling inductance
INSQUID operates as a fast, quiet switch:
OFF state Qubit isolated to allow quantum evolution
ON state Qubit strongly coupled to readout SQUIDor to other Qubits
(In collaboration with John Clarke, UC Berkeley)