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).

0.00

0.10

0.20

0.30

0.40

-10 -5 0 5 10

X ( ( ( (aB ))))

ρ (

ρ (

ρ (

ρ (x

)) )) F=0.10F=0.12F=0

(a)

0.00

0.10

0.20

0.30

0.40

-10 -5 0 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

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

0

1 10-5

2 10-5

3 10-5

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

0

0.5

1

0

0.5

1

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

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

0

0.5

1

0

0.5

1

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

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

Re[ρ] Im[ρ]

0

0.5

1

0

0.5

1

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

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

0

0.5

1

0

0.5

1

|H><H|

|H><V|

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

0

0.5

1

0

0.5

1

|H><H|

|H><V|

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

Experiment ρ0

0.5

1

0

0.5

1

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

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

0

0.5

1

0

0.5

1

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

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

0

0.5

1

0

0.5

1

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

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

0

0.5

1

0

0.5

1

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

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

0

0.5

1

0

0.5

1

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

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

State |H> |D> Mixed Partially Mixed

ρ1 00 0

12

1 11 1

12

1 00 1

1 + 36

36 (1 + i)

36 (1 − i) 1 − 3

6

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


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


ρImpreciseDensityMatrix

AutomatedTomography


(Long

1 AB2 AA3 CA

15 CE16 AC

16 NewMeasurements

AB = 0.5AA = 0.3CA = 0.1

CE = 0.2AC = 0.2

16Precise

Probabilities


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

1

2

3

4

1

2

3

4

-0.5

-0.25

0

0.25

0.5

1

2

3

4

-0.5

-0.25

0

0.25

0.5

1

2

3

4

1

23

4

-0.4

-0.2

0

0.2

0.4

1

2

3

4

-0.4

-0.2

0

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

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)

foundations of solid-state quantum information...

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