Foundations of Solid-State Quantum Information Processing (ITR/SY - - PowerPoint PPT Presentation

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” Coherence 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 decoherence no 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

• utput

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-

• xide SETs on the surface (telegraph

and 1/f noise).

0 .0 0 0 .1 0 0 .2 0 0 .3 0 0 .4 0

• 1 0
• 5

5 1 0

X ( ( ( (aB) ) ) ) ρ ( ρ ( ρ ( ρ (x) ) ) )

F=0.10 F=0.12 F=0

(a) 0.00 0.10 0.20 0.30 0.40

• 10
• 5

5 10 X ( ( ( (aB) ) ) ) ρ ( ρ ( ρ ( ρ ( x) ) ) ) (b)

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

Readout donor Qubit donor Readout donor Qubit donor

Atomically Ordered Devices Based on STM Lithography

• J. 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 bonds by STM lithography in UHV.

T.-C. Shen, et al., Science 268, 1590, 1995. single dangling bonds depassivated dimers Si(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

G S 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 nanoparticles

The 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 in superconductor

First step—try to measure loss of magnetization due to onset of tunneling

• xide

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 nm

superconducting wire Josephson junction

Quantum circuit: two nanoparticle qubits “connected” by superconducting loop

Permalloy clusters

Average size: small clusters 4-6 nm large clusters 15 nm

• Ave. density: small clusters ~ 7E10 cm-2

large clusters ~ 4E9 cm-2

Drilling holes with STEM

30nm thick silicon nitride membrane JEOL 2010F STEM “drill” 32 pulses (950 pA) of 10 seconds each EELS spectrum --> D ~ 2.5 nm Next step is to fill the hole with ferromagnetic material

Superconducting f lux qubits f or Quantum Computing

J osephson j unct ion I = I c sinφ Super conduct ing loop Magnet ic f lux Φ Cir culat ing cur rent J

E J

Qubit st at es correspond t o clockwise and count erclockwise current s

Basic Qubit = rf SQUI D

Φ = 1/ 2 Φ0

Our approach: ut ilize π-J osephson j unct ions in superconduct ing f lux qubit

π J

Spont aneous circulat ing current in rf SQUI D π π π π- junction

Negat ive I c ! minimum energy at π

I φ E φ

π 2π π 2π

• Provides nat ural and precisely-degenerat e t wo-level syst em

Advantages of an intrinsic π π π π- phase shif t

• Decouple qubit f rom environment since no ext ernal drive needed

π-phase shift induced by magnetic moment in weak ferromagnetic barrier S

Nb

S

Nb

F

CuNi

SC- FM- SC junctions (Chernogolovka) Quasiparticle injection junctions (Groningen) π-phase shift from nonequilibrium quasiparticle distribution inside barrier

Schemes f or generating π π π π- Josephson junctions

Trombone experiment: measure spontaneous flux for phase shift of π

Nb f lux t r ansf or mer moveable Nb gr ound plane J osephson j unct ion

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 barrier Junction barrier Junction barrier Junction barrier X = F, N, … X = F, N, … X = F, N, … X = F, N, …

transformer coupling qubit = π- junction dc SQUID detector

epit axial Nb

epi PdNi alloy Tc 15K

epit axial Nb

epit axial π-j unct ion het eroepit axial int erf aces

Single cryst al J osephson j unct ions f or qubit s

Each superconduct ing Qubit has 2 quant um st at es, but f rom 106 t o 1018 at oms. Compare polycryst alline and single cryst al devices. Decoherence result s f rom excit at ion of low energy degrees of f reedom and f rom mesoscopic f luct uat ions – 1/ f noise ef f ect s. π-j unct ions are irreproducible due t o mat erial inhomogeneit y. Needs epit axial single cryst al superconduct ive devices. Use epit axial Nb-f ilm growt h developed by Flynn at UI UC. Goal: reduce quantum state decoherence due to material def ects and noise

R-plane A-plane A-plane

LEEM image

1400 C anneal

Epit axial growt h of Nb f ilms wit h large at omically f lat t erraces proceeds via 3D nucleat ion f ollowed by consolidat ion. RHEED shows specular ref lect ion f rom smoot h

• regions. Thicker (>

100 nm) f ilms f ill in. High t emperat ure anneal leads t o larger t erraces and unit cell st ep bunching. Use such surf aces f or int erf aces in epit axial J osephson j unct ion st ruct ures.

Het eroepit axial growt h of smoot h Nb f ilms

1 10-5 2 10

• 5

3 10-5 50 100 150 200 250 300

single crystal epitaxial niobium film on A-plane sapphire Temperature (K) T

c=9.2K

resistivity (Ohm-cm)

Optical “benchmarking”: Single Qubit Generation

|V> |H> 2 θ1 4 θ1 |V> |H> 4 θ1 |H> 2 θ3 4 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 = 1 4 ArcTan 2B Cos[δ] 2A −1

    + ArcTan

2B Sin[δ] 2A −1

( )

2 + 4B2 Cos2 δ

( )

           

θ1 = 1 4 ArcCos 2A −1

( )2 + 4B2

[ ]

θ3 = 1 2 ArcTan 2B Cos[δ] 2A −1    

Fidelity 1.000 0.998 0.999 0.999

Theory ρ

0.5 1 0.5 1

|H><H| |H><V| |V><H| |V><V|

0.5 1 0.5 1

|H><H| |H><V| |V><H| |V><V|

Re[ρ] Im[ρ]

0.5 1 0.5 1

|H><H| |H><V| |V><H| |V><V|

0.5 1 0.5 1

|H><H | |H><V| |V><H| |V><V|

0.5 1 0.5 1

|H><H | |H><V| |V><H| |V><V|

Experiment ρ

0.5 1 0.5 1

|H><H| |H><V| |V><H| |V><V|

0.5 1 0.5 1

|H><H| |H><V| |V><H| |V><V|

0.5 1 0.5 1

|H><H| |H><V| |V><H| |V><V|

0.5 1 0.5 1

|H><H| |H><V| |V><H| |V><V|

0.5 1 0.5 1

|H><H| |H><V| |V><H| |V><V|

State |H> |D> Mixed Partially Mixed ρ

1      

1 2 1 1 1 1      

1 2 1 1      

1+

3 6 3 6 (1+ i) 3 6 (1− i)

1−

3 6

     

Experiment vs. Theory

Two-crystal Source

ψ = 1 2 H 1 H 2 + e

iϕ 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:

Automated Tomography System (30 Minute Run)

(Long

List of 16 Measurements

1 HH 2 HV 3 VH 15 RD 16 DH

16 Measurements

HH = 0.507 HV = 0.345 VH = 0.110 RD = 0.234 DH = 0.189

16 Precise Probabilities

Maximum Likelihood Technique

ρ

Precise Density Matrix

Automated Tomography System (3 Minute Run)

List of 16 Measurement s

1 HH 2 HV 3 VH 15 RD 16 DH

16 Measurements

HH = 0.5 HV = 0.3 VH = 0.1 RD = 0.2 DH = 0.2

16 Imprecise Probabilities

Maximum Likelihood Technique

ρ

Imprecise Density Matrix

Automated Tomography System (30 Minute Run)

(Long

1 AB 2 AA 3 CA 15 CE 16 AC

16 New Measurements

AB = 0.5 AA = 0.3 CA = 0.1 CE = 0.2 AC = 0.2

16 Precise Probabilities

Maximum Likelihood Technique

ρ ρ ρ ρ

Ultra- Precise Density Matrix

Find a rough estimate of the state

Use this rough estimate to find the ideal set of 16 measurements to use.

2

F = 0.983

Im Re

1 2 3 4 1 2 3 4

• 0.5
• 0.25

0.25 0.5 1 2 3 4

• 0.5
• 0.25

0.25 0.5 1 2 3 4 1 2 3 4

• 0.4
• 0.2

0.2 0.4 1 2 3 4

• 0.4
• 0.2

0.2 0.4

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

Summary

By studying qubits encoded in magnetic moments of systems

• f 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 Functionality

Superconducting phase dynamics Photon entanglement Magnetic nanoparticles Quantum spins in Silicon

S y s t e m s i z e

Physical realization of system of coupled qubits for performing quantum logic Scalable quantum computer

The I NSQUI D = I Nductive SQUI D

scheme f or quiet ent anglement / readout of Qubit f lux st at e Qubit det ect or SQUI D readout SQUI D

ΦSQ ΦQ

coupling induct ance I NSQUI D operat es as a f ast , quiet swit ch: OFF st at e Qubit isolat ed t o allow quant um evolut ion ON st at e Qubit st rongly coupled t o readout SQUI D

• r t o ot her Qubit s

(I n collabor at ion wit h J ohn Clar ke, UC Berkeley)