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Quantum Computing: Concept and Realization K. W. Kim, A. A. Kiselev, V. M. Lashkin, W. C. Holton, and V. Misra North Carolina State University NC STATE UNIVERSITY Outline - Classical vs. Quantum - Performance vs. number of elements - Gedanken quantum computer - Implementations and comparison - Our current proposal - Physics - Design - Future projections NC STATE UNIVERSITY Classical Bit vs. Quantum Qubit V1 Quantum Bit 1= |1〉 = is any two-level quantum system, 0= V0 |0〉 = for example, Electron Spin =? = C1|1〉 + C0|0〉 It’s an error! It’s a superposition! NC STATE UNIVERSITY Two spins: Four states in superposition: 22 = C00|00〉 + C01|01〉 + C10|10〉+C11|11〉 Entanglement of spins 1 and 2 N spins: 2N states in superposition ... 0...00 + 0…01 + … + 1…11 NC STATE UNIVERSITY Problem Solving: tractable vs. intractable Universal Exponential NP complete NP P - A classical computer solves problems of type P - An N-bit quantum computer solves exponential problems NC STATE UNIVERSITY Moore’s Law as a potential limitation Number of chip components ~ performance 1018 Classical Age Quantum Age 1014 2010 10 2000 10 1990 106 Quantum Device 1970 CMOS 102 101 100 10-1 10-2 10-3 Feature Size (microns) Another side --- cryptography Security enabled by the Uncertainty Principle and by the No-Cloning Theorem NC STATE UNIVERSITY Basic ideas of QC |1〉 = |0〉 = - Information stored in spin 1/2 quantum systems (qubits) - Quantum computation scheme Initialization Processing Measurement ψ i → U M KU 2U1 ψ i → ψ ˆ ˆ ˆ f 0 1 NC STATE UNIVERSITY Fundamental gates: only two required for all operations π 1. 2 single bit rotation input output R 2. Controlled NOT A A B A XOR B NC STATE UNIVERSITY Quantum computer * Hamiltonian (coupled) Hˆ = 1 ω 1σˆ 1 + 1 ω 2σˆ 2 + 1 J σˆ 1 • σˆ 2 2 2 4 11 ω2 ω2 + J ω1 + J 2 2 10 ω1 01 ω1 − J 2 ω2 ω2 − J 00 2 NC STATE UNIVERSITY Information processing via coherent pulses - use superpositions (ω ) π 00 → 1 2 ( 00 + 01 2− J 2 ) 2 - use entangled states ( ) 1 ( 00 + 11 π ω1 + J 2 00 → ) 2 Parallel computation and speed up! NC STATE UNIVERSITY QC Requirements • Possibility to address qubits individually • Initialize qubits • Perform one- and two-qubit operations • Read-out final result • Small decoherence rate compared to ops rate • Scalability (the more qubits - the better) NC STATE UNIVERSITY Implementations Implementations - Not solid state QC * Trapped ions * NMR on molecules * Electrons trapped on liquid He - Solid state QC - Orbital degree of freedom - Spin degree of freedom - Macroscopic wavefunction in superconductor NC STATE UNIVERSITY Asymmetric III-V Quantum Dot Quantum Computer Asymmetric III-V Quantum Dot Quantum Computer Drain Gate Insulator Top Contact p+ Electrode Asymmetric n Surrounding AlGaAs/GaAs Pillar Quantum Dots p n+ Oxide Source Source Silicon .2 s GaAs Substrate 0 aA Silicon pillar 5 x= 0.4 , G x = As x Electric dipole qubit transitions with , a 1- Qubits unique by As G Al x x dipole-dipole coupling G a 1- fabrication Al x Sanders, Kim and Holton Phys. Rev. A 60 #5 4146 Nov 99 Electrons trapped in quantum dots coupled to Electrons trapped in quantum dots coupled to terahertz cavity photons terahertz cavity photons III-V Quantum dots distinguishable electrically with each quantum dot containing one electron. Dot array in micro-cavity. Coupling via terahertz cavity modes. Electric dipole qubit transitions. Sherwin, Imamoglu, and Montroy Phys. Rev. A 60 #5 3508 Nov 99 Quantum dot spins and cavity QED Quantum dot spins and cavity QED III-V quantum dot electron spins coupled Qubit coupling mediated by through microcavity mode microcavity mode Qubits individually addressed by tapered fiber tips Imamoglu, Awschalom, Burkard, DiVincenzo et al PRL 83 #20 4204 15 Nov 99 Coupled Nuclear Spins Arrayed in Silicon Coupled Nuclear Spins Arrayed in Silicon Quantum Computer Quantum Computer P – impurities with spin = ½ interact through trapped electron to form coupled system SET used to measure spin-state of final state Kane Nature 393 133 14 May 1999 Electron Spin Transistor (Transpinor) for Quantum Electron Spin Transistor (Transpinor) for Quantum Computing Computing Qubits distinguishable by addressing. Coupling by exchange interaction. in Silicon-Germanium Heterostructures in Silicon Quantum Dots Potential pad Si Oxide Doped Si Si Wang et al Kim and Holton Quant-ph/9905096 11 June 1999 Solid State Quantum Computers Solid State Quantum Computers Parameter Comparison Parameter Comparison OrbitalDegree of Freedom Orbital Degree of Freedom Sanders, Kim and Sherwin, Imamoglu & Platzman & Dykman Author Holton Montroy Electrons trapped in III- Electrons trapped in III- Electrons on liquid He Structure V quantum dots V quantum dots in cavity Surface Electronic states of Electronic states of Electronic states of Storage Mechanism trapped electrons trapped electrons trapped electrons Controlled size of Externally applied Qubit Distinguishability Voltage pulse quantum dots voltage Single bit Ops Rate 1013 Hz 109 Hz 109 Hz Two bit Compute Rate 1010 Hz 108 Hz 107 Hz Decoherence Time 10-6 s 10-4 s 10-4 s Ops to Decoherence 104 ops 104 ops 103 ops Initialization Process 77K Temperature Low Temperature 0.1K Temperature Optical emisson from TACIT photon detector Electron extraction via Readout Process ensemble within cavity tunneling Scalability 50 qubits > 100 qubits 109 qubits Solid State Quantum Computers Solid State Quantum Computers Parameter Comparison Parameter Comparison JJ JJ Spin Degree of Freedom Spin Degree of Freedom Makhlin, Schon & Buckard, Loss & Imamoglu, Awschalom, Author Shnirman DiVincenzo Divincenzo et al Cooper pair with Electrons trapped in Electrons trapped in III-V Structure superconducting box III-V quantum dots Quantum Dots Magnetic states of Magnetic states of Storage Mechanism Josephson junctions trapped electrons trapped electrons Physical location Magnetic field Qubit Distinguishability Physical location gradient 10 10 11 Single bit Ops Rate 10 Hz 10 Hz 10 Hz Two bit Compute Rate 11 10 10 10 Hz 10 Hz 10 Hz Decoherence Time 10-7 s 10-9 s 10-4 s Ops to Decoherence 104 ops 10 ops 106 ops Initialization Process Low Temperature 77K Temperature Not described Coupling to normal Interaction w. laser field Readout Process Photon Scattering state transistor & photon emission Scalability 20 qubits Not discussed > 100 qubits Solid State Quantum Computers Solid State Quantum Computers Parameter Comparison Parameter Comparison Spin Degree of Freedom Spin Degree of Freedom Vrijin, Yablonovitch, Sanders, Kim and Author Kane Wang et al. Holton Electrons trapped at Electrons trapped in Structure P-impurities in Si P-impurities in Si/Ge quantum dots in Si Nuclear magnetic Magnetic states of Magnetic states of Storage Mechanism states of P impurity trapped electrons trapped electrons Voltage applied Voltage applied Variable local Qubit Distinguishability locally to P-gate locally to P-gate magnetic field Single bit Ops Rate 104 Hz 1010 Hz 1010 Hz Two bit Compute Rate 104 Hz 108 Hz 108 Hz Decoherence Time 106 s 10-3 s 10-3 s Ops to Decoherence 1010 ops 105 ops 105 ops Initialization Process 0.8K Temperature Low Temperature Low Temperature Charge transfer to Charge transfer to Charge transfer to Readout Process singlet/triplet singlet/triplet singlet/triplet Scalability 6 6 6 10 qubits 10 qubits 10 qubits Electron Spins Trapped Beneath Coupled Quantum Dots B ψ1 ψ2 ! Hamiltonian for a single quantum dot pair. H = µ B gB 1 S 1 + µ B gB 2 S 2 + JS 1 • S 2 ! Exchange coupling between adjacent quantum dots. r r r * r r * r 2 J = ∫ u (r1 − r2 ) 1 (r1 ) 1 (r2 ) 2 (r2 ) 2 (r1 )dV ψ ψ ψ ψ V NC STATE UNIVERSITY Typical Design Parameters 30nm • Pillar radius ~50 nm Gate 15nm SiO2 • Gate radius~15 nm • Pillar height~100 nm Undoped 65nm • SiO2 region~15 nm Si • Doping region~20 nm • Donor concentration ~3.e18 Doped Si 20nm cm-3 • Temperature~1.6 K NC STATE UNIVERSITY Confining in the radial direction • Strong electrostatic confinement in the radial and z-directions along with the SiO2/Si interface potential barrier serves to confine a single electron in the quantum dot NC STATE UNIVERSITY Single electron occupancy • Single electron occupancy in the quantum dot holds over a finite range of the gate voltage: • 0.23<V<0.31 (Volts) NC STATE UNIVERSITY Exchange energy control • A single electron trapped beneath each dot gate provides the magnetic spin utilized in the quantum computer. A gate intermediate to the gate that performs the electron trapping can serve to vary the coupling between a given pair of electrons. NC STATE UNIVERSITY Reconfigurable Quantum Computer Showing Reconfigurable Quantum Computer Showing Transpinor Output Sensors Transpinor Output Sensors Current conductors to generate time dependent magnetic field bias, enabling single qubit addressing Potential pads enabling single electron trapping Transpinor output Wave function distortion pads detectors on periphery Charge transfer pad Magnetic Field Unique current addressing. Controllable coupling. Uniform µ- wave field. Transpinor output. Address Array provides unique magnetic field at addressed qubit Interconnect array Pulsed current to generate Y-axis local magnetic field Pulsed Magnetic field into paper from blue & red currents Quantum Dot Electrode Pulsed Magnetic field out of paper from blue & red currents Addressed qubit Interconnect array X-axis Qubit Addressing !For an external magnetic field = 3.0 Tesla !The resonant microwave frequency = ω = 94 GHz !And with a line width ~ 0.3 gauss or 1 MHz !And requiring a magnetic field address on 30x line width = 9 gauss !A current in the addressing wire = 1.12 10-4 amp !And with a wire dimension of 100x100 angstrom !The current density = 5 107 amp/cm2 !This is just at the threshold for electro migration for dc current at RT, but is OK for our application of pulses at low temperature. NC STATE UNIVERSITY Pulsed Microwave Field Generated Using a Microstrip Resonator Permanent Magnet Static Magnetic Field * From Permanent Magnet Quantum Dot Quantum Strong microwave H fields Computer Silicon Chip Critical coupling Microwave Pin diode Pin diode Input Ceramic Substrate Pin diode bias for rapidly turning on and off the H field * Interconnect wires on chip to generate pulsed magnetic field at each qubit and chip pin-out not shown in this figure. NC STATE UNIVERSITY Fabrication of Silicon Q-Dot Array Q-Dot Q-Computer Q-Computer " Manufacturable using Integrated Circuit technology specified for the 70- nm technology node. (International Technology Roadmap for Semiconductors, 1999 edition). " Layout and addressing for dynamic Quantum Computer control analogous to DRAM design and manufacture. (number of metal/dielectric layers considerably less than for 1Mbit DRAM). " Resulting Quantum Computer chip coupled to microwave radiation field at ~ 94 GHz by placement in stripline cavity. " External magnetic field ~ 3.0 Tesla provided by permanent magnet outside the microwave cavity. " Readout achieved by charge transfer via SETs on periphery (not shown) dependent on spin orientation (similar to readout for other proposed Quantum Computer designs based on spin). NC STATE UNIVERSITY Distinct Advantage of Design # Scalable using mainstream silicon technology. # 1,000,000 qubits. # Hi-speed single bit ops rate and compute rate. #Both readily tunable. # Randomly and individually addressable qubits. # Large number of ops before loss of coherence. # 100,000 ops to coherence loss. # Dynamically Reconfigurable. NC STATE UNIVERSITY