Foundations of Solid-State Quantum Information Processing (ITR/SY #EIA-0121568; Sept. 2001 -- Aug. 2006) Studying variously sized spin-based qubits in several condensed-matter systems, to understand and optimize the tradeoff between Coherence and Controllability • Robert Averback • James Eckstein Controllability • Paul Goldbart Coherence • Paul Kwiat • Anthony Leggett • Myron Salamon Qubit “size” • John Tucker • Dale VanHarlingen
Who (else) are we? Other Collaborators: • Y.-C. Chang (UIUC) Post-doc: Graduate Students: • J. Clarke (U. C., Berkeley) • Young Sun • Joseph Altepeter • R.-R. Du (Univ. Utah) • Trevis Crane • C. P. Flynn (UIUC) Undergraduates: • Bruce Davidson • D. James (LANL) • D. Achilles • Soren Flexner • D. Loss (Univ. Basel) • M. Rakher • Sergey Frolov • M. Leuenberger (U. Basel) • Kim Garnier • B. Munro (HP, Bristol) • Evan Jeffrey • V. Ryazanov (Inst. Solid • Swagatam Mukhopadhyay State Physics, Moscow) • Patricio Parada-Salgado • T.-C. Shen (Utah State Univ.) • Nicholas Peters • J. Tejada (Univ. Barcelona) • Stephen Robinson • A. White (Univ. Queensland) • Tzu-Chieh Wei • F. Wilhelm (Ludwig Maximilians Univ.)
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: ψ = α 0 + β 1 • 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”.
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 = 10 10 ) Our “benchmark” Correlated photons from spontaneous parametric downconversion --> state synthesis, state- and process-tomography; decoherence and error correction
Single spin qubit (P in silicon, a la Kane) 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. Detecting the motion of individual Simplified electron spin read-out electrons between donor sites, and characterizing the exchange energy G1 J G2 due to wavefunction overlap, will be + ++ difficult using relatively large Al- oxide SETs on the surface (telegraph and 1/ f noise). silicon D - Planar SET R=10 a B ~300Å output target (all P-donors)
Calculation of charge distribution under parallel uniform electric field (R=10a B ) [Y.-C. Chang, UIUC] Singlet state Triplet state 0 .4 0 0.40 (b) (a) 0 .3 0 0.30 F=0.10 ) ρ ( x ) ) ) ) ) ) ρ ( x ) 0.20 0 .2 0 F=0.12 ρ ( ρ ( ρ ( ρ ( ρ ( ρ ( F=0 0.10 0 .1 0 0.00 0 .0 0 -1 0 -5 0 5 1 0 -10 -5 0 5 10 X ( ( ( a B ) ( ) ) ) Readout Qubit Readout Qubit X ( ( a B ) ) ( ( ) ) donor donor donor donor 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 ~ 10 4 V/cm)
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 (2) Selectively adsorb PH 3 molecular by STM lithography in UHV . precursors onto the STM-exposed areas . Si(100)-2x1:H depassivated dimers single dangling bonds Y. Wang, M. J. Bronikowski, and R. J. Hamers, T.-C. Shen, et al., Science 268, 1590, 1995. J. Phys. Chem . 98, 5966, 1994.
Epitaxial single-electron transistor: donor pattern on a pre-implanted STM template G S D P-donor SET pre-implanted contacts undoped Si substrate B 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 M •Create single-domain ferromagnetic particles—size depends on the material. ~10 nm --> S = 10 4 or so. d •Locate them on or in a suitable material •Arrange to have the magnetization easily rotatable in some plane (--> anisotropric cluster) Image of moment in •Control the tunnel barrier between two superconductor equivalent orientations of the total spin. E •Confirm tunneling via tunnel splitting and/or Rabi oscillations by kicking with rf fields. •Link spins (in a controlled manner) using SQUID loops θ
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 T c. 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.
Quantum circuit: two nanoparticle qubits “connected” by superconducting loop magnetic material (e.g. permalloy) Josephson junction superconducting ~3 nm wire ~6 nm SiO 2 , SiN x ~20 nm Al 2 O 3 Aluminum ( superconductor )
Permalloy clusters Drilling holes with STEM Average size: small clusters 4-6 nm 30nm thick silicon nitride membrane large clusters 15 nm JEOL 2010F STEM “drill” Ave. density: small clusters ~ 7E10 cm -2 32 pulses (950 pA) of 10 seconds each large clusters ~ 4E9 cm -2 EELS spectrum --> D ~ 2.5 nm Next step is to fill the hole with ferromagnetic material
Superconducting f lux qubits f or Quantum Computing Qubit st at es correspond t o clockwise Basic Qubit = rf SQUI D and count erclockwise current s Super conduct ing Magnet ic f lux Φ E loop Cir culat ing cur rent J J osephson j unct ion J I = I c sin φ Φ = 1/ 2 Φ 0 Our approach: ut ilize π -J osephson j unct ions in superconduct ing f lux qubit π - junction π π π Negat ive I c ! minimum energy at π π J I E φ Spont aneous circulat ing φ current in rf SQUI D π 2 π π 2 π 0 0
Advantages of an intrinsic π π π π - phase shif t • Provides nat ural and precisely-degenerat e t wo-level syst em • Decouple qubit f rom environment since no ext ernal drive needed Schemes f or generating π π π π - Josephson junctions SC- FM- SC junctions Quasiparticle injection junctions π -phase shift induced by magnetic π -phase shift from nonequilibrium moment in weak ferromagnetic barrier quasiparticle distribution inside barrier F S S CuNi Nb Nb (Chernogolovka) (Groningen)
Ongoing research projects/ plans 1. Verify π -junction behavior via phase-sensitive tests Trombone experiment: measure Current phase-relation experiment: spontaneous flux for phase shift of π map out I( φ ) by SQUID interferometry J osephson j unct ion x Nb f lux t r ansf or mer moveable Nb gr ound Junction barrier Junction barrier Junction barrier Junction barrier plane X = F, N, … X = F, N, … X = F, N, … X = F, N, … 2. Observe coherent quantum oscillation in a flux qubit incorporating π -junctions. transformer dc SQUID detector qubit coupling = π - junction
Single cryst al J osephson j unct ions f or qubit s Goal: reduce quantum state decoherence due to material def ects and noise Each superconduct ing Qubit has 2 quant um st at es, but f rom 10 6 t o 10 18 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. epit axial π -j unct ion Needs epit axial single cryst al superconduct ive devices. het eroepit axial epit axial Nb int erf aces Use epit axial Nb-f ilm growt h epi PdNi alloy T c 15K developed by Flynn at UI UC. epit axial Nb
Recommend
More recommend
