Solid-State Spin Quantum Computers

Size: px

Start display at page:

Download "Solid-State Spin Quantum Computers"

Martha Nelson
5 years ago
Views:

1 Solid-State Spin Quantum Computers 1 NV-Centers in Diamond P Donors in Silicon

2 Kane s Computer (1998) P- doped silicon with metal gates Silicon host crystal + 31 P donor atoms + Addressing gates + J- coupling gates + Read- out gates A scalable quantum computer? Concept: B.E. Kane, Nature 393 (1998) 133 SiO (5 nm) Si Metal A J A gate oxide 5 nm 0 nm 31 P 31 P matrix back gate Impact: Pros: Cons: very high, feasible concept for a solid- state spin quantum computer ca. 100 researchers in Australia and U.S.A. started investigating this 1999 All- electric, close to silicon technology (industry turnover: US$) Challenging to manufacture (P placement, thin gate metals) Actuality: still new results as ion implantation methods become better e.g., J.J. Pla et al., Nature 496 (013) 334: 1- Qubit Control and Read- Out

3 P donor in silicon 3 P has 5 valence electrons, one more than Si At room temperature, the extra electron is completely delocalised in the conduction band (doping effect) At low temperature (T 1 K), the extra electron is loosely bound to the P nucleus ( hydrogen- like wave function) a Si = ε Si m a = 4πεε 0! * 0 m e 3 Å E Si = k m* ε E 31 mev 0 ( k 3 ) Si ε Si = 11.7, m* = 0.19 a 0 = 0.53 Å, E 0 = 13.6 ev 31 P =

Kane s Concept: Overview 4 silicon can be made spin-free ( 8 Si), acting like a hard spin vacuum each 31 P has nuclear spin I=1/ and associated electron spin S=1/

A-gate + + + J-gate I and S are coupled by the hyperfine interaction A next neighbours are coupled by exchange interaction J Silicon substrate 31 P ~0 nm 31 P Los

4 Kane s Concept: Overview 4 silicon can be made spin-free ( 8 Si), acting like a hard spin vacuum each 31 P has nuclear spin I=1/ and associated electron spin S=1/ nuclear spin I as qubit S is for controlling information: Read-In 1- and -Qubit gates Read-Out SiO barrier V = 0 SET A-gate J-gate + V > 0 A-gate B 0 J-gate A-gate J-gate I and S are coupled by the hyperfine interaction A next neighbours are coupled by exchange interaction J Silicon substrate 31 P ~0 nm 31 P Los Alamos Science 7 (00), 84 A and J can be modified by applying electrical fields (metal gates) S state can be converted to charge and then read out with an SET ~0 nm 31 P

5 The Spin Qubit 5 each 31 P has nuclear spin I and electron spin S H 0 /! = ( γ S S z γ I I z )B 0 + SAI 31 P = γ S = g S µ B /! 8 GHz / T γ I = g I µ n /! 17 MHz / T ( 31 P) ν n ESR at T 0.3 K, B0 = 1.77 T Nature 496 (013) 334 ν e1 ν e ν n1 >99.9% at T 0.3 K, B0 = 1.77 T

Selective 1-Qubit Rotation 6 Use global RF field to turn nuclear spins I, hyperfine interaction A for local addressing

= γ I B 0 + m S A (a) A +++++ q 1 J SiO barrier Electron cloud q A (a ) A-gate, 0 V 0 resonance frequency is

γ S γ I 3 Ψ e ( r = 0) 117 MHz contact hyperfine interaction (overlap of electron and nucleus) controlled by A-gate

6 Selective 1-Qubit Rotation 6 Use global RF field to turn nuclear spins I, hyperfine interaction A for local addressing A resonance frequency for I ΔE /! = γ I B 0 + m S A (a) A q 1 J SiO barrier Electron cloud q A (a ) A-gate, 0 V 0 resonance frequency is individual if A can be locally modified 4π A =!γ S γ I 3 Ψ e ( r = 0) 117 MHz contact hyperfine interaction (overlap of electron and nucleus) controlled by A-gate (b) Nuclear resonance frequency (MHz) Nuclear resonance frequency (MHz) Silicon substrate q q A-gate potential (V) (c) q A-gate potential (V) q 1.0 (b ) (c ) A-gate, +1 V A-gate, 1 V Los Alamos Science 7 (00),

7 Next-Neighbour Interactions (1/) Electron wave function overlap leads to exchange interaction J can be controlled by J-gate Low J: -Qubit Coupling (a) (b) A 1 J A (SWAP, 4 CNOT, ) E/µ µ B B0 SiO barrier 1 + µ B B 0 0 4J 7 H = H 1 + H + 4J S 1 S New basis for coupled electron spins: Silicon substrate No J: Isolated Qubits Los Alamos Science 7 (00), J/µ B B 0 High J: Spin-To-Charge Conversion (Readout) Triplet (S = 1) Singlet (S = 0) T + T 0 = 1 ( + ) T = = 4J S = 1 ( )

8 Next-Neighbour Interactions (/) 8 J- gate mediated coupling between adjacent electron spins + hyperfine coupling A between nuclear spin and its electron spin = indirect coupling between adjacent nuclear spin qubits Lowest spin states at small J: 11 = Φ + = 1 ( + ) Φ = 1 ( ) 00 = (a) A 1 J A SiO barrier Silicon substrate Los Alamos Science 7 (00), 84 (b) E/µ B B µ B B 0 4J J/µ B B 0 Splitting between Φ + and Φ : γ S (B0 = T, 4J / = 1 T, A = 115 MHz) ω J = A γ S B 0 4J A γ S B 0 (π ) 75 khz 75 khz sets the maximum speed of two-qubit gates!

9 Two-Qubit Operations (1/) 9 SWAP Operation: J = 0 J 0 1. independent qubits, J = 0. turn J on fast 3. base change of (10) and (01) to superposition states: ( ) ( ) 10 = Ψ 10 = 1 Φ + Φ 01 = Ψ 01 = 1 Φ + + Φ 4. superposition evolves in time Ψ 10 τ ( ) SWAP ( t) = 1 Φ + Φ e iω Jt 11 = 10 = 01 = 00 = 11 = Φ + = 1 ( + ) Φ = 1 ( ) 00 = ( ) = Ψ 01 1 Φ + + Φ 5. wait until SWAP: 6. turn J off fast τ SWAP = π /ω J 6.7 µs

10 Two-Qubit Operations (/) 10 CNOT Operation: 1. independent qubits, J = 0. apply A- gate voltages so that A 1 (control) > A (target qubit) 3. turn J on slowly (adiabatically) and slowly make A 1 = A 4. net result so far: J = 0 J 0 11 = 10 = 01 = 00 = 11 = Φ + = 1 ( + ) Φ = 1 ( ) 00 = 10 Φ +, 01 Φ 5. apply r.f. field B ac resonant with transition 6. wait until π- pulse is achieved 7. reverse steps Φ 11 Φ Φ Φ + 10, Φ 01 CNOT result: 01 Φ Φ

11 Readout Scheme (1/4) 11 spin-to-charge conversion by spin-dependent tunnelling Goal: read state of target qubit q t Recipe: 1. couple q t to read- out qubit q r so that. q t - electron will tunnel to q r iff q t = 0 3. monitor charge state of q r with an SET 4. reset charge states Result: Single- electron transistor (SET) is off for q t = 1, q r in neutral D 0 state on for q t = 0, q r in charged D state (d) No Tunneling (q t = ) q t = D 0 (c) Tunneling (q t = ) J J A t SiO barrier A t J J E-field A r q r A r SiO barrier D 0 SET SET D 0 state: 1 electron (of q r ) D state: electrons (of q t and q r ) D state exists only for S = 0! must force total electron spin S=0 when q t = 0 D + q t = E-field q r D

12 E/µ B B 0 A t A r >> hω J A t = A r A t = A r Readout Scheme (/4) 1.50 Φ + q t initially in state Φ T Φ + T Φ + T Φ S q t initially in state 1 two S Φ rous Electron States Nuclear States with S = 1 T = (c) Tunneling (q 0 t = ) (d) No Tunneling (q Φ + = 1/ + t = ) J/µ B Figu J A B 0 S = 0 S = 1/ t J A Φ = 1/ r J A t J A r J-ga SET SET (b) States Adiabatically Evolved through the Cross SiO betw S barrier SiO barrier elec 1.49 Φ E-field E-field J/µ B B 0 < 0.5, J Φ T + A t A r >> hω J q t = q r q t = q r Φ T Φ + q t initially in state 1.50 Φ + q Φ t initially in state S Figure 4. Single-Electron Transistor Φ+ (SET) (c) Tunneling Readout (q (d Φ t = ) Scheme sisto (a) The graph shows the eight lowest-energy nuclear-spin J A states t J for the A coupled r 1.51 target and readout qubits q t, q r in the region where the S = 0 and the lowest SET energy S = 1 electron-spin states cross. (b) We can adiabatically evolve the J/µ B B SiO 0 barrier nuclear-electron states by biasing the J- and A-gates, as seen in this (partial) sequence of steps. The electrons are initially in the S = 1 state T E-field. If q J/µ B B 0 < 0.5, J/µ B B 0 < 0.5, J/µ B B 0 > 0.5, t was initially in the A t = Astate, then the r A t A r >> hω J Aelectrons t = A r will remain in T regardless of the state q t = q r of q r. If initially q t =, then at the end of the sequence, the electrons will be in q t initially in state the S = 0 state S. (c) Only the two electrons in the S state can bind to a single T Φ + T Φ + phosphorous atom in silicon. Given a suitable biasing of the gate electrodes, we can try to T induce Φ an electron S to tunnel to a readout qubit q q t initially in state r. If the tunneling is successful, the electrons were S in Φ the S state, and q t =. The tunneling current E/µ B B The thos gate W get atom get A the tron way ates sour fere sour sma from of in acts to fl the

voltage is originally biased at V0, (blue dot), then a change in the local charge distribution effectively modifies it to V0 δ, and the source-drain current will change dramatically (red dot).

The twin-set device is fabricated by a double-angle evaporation process, which replicates each of the features. Unequal voltage on A1 and A causes an electron to tunnel from one bar to the next.

The two signals r can be correlated to discriminate the charge transfer signal from reproducible charge noise or from random noise events.

) Typical SET signal as a function of gate voltage, Right SET which mimics the extra electron tunnelling onto 0.005 the readout qubit q.

distinguish The readout protocol consists of three rem 13 in Fig. 1b. s(i) A Load phase, during spin phases, shownfrom intended ignals.

05 Their correlation igh signal- to- noise Gate voltage (V) the SET island to the donor, since µ SET SET > µ#, µ". The electron loading is signalled by ISET dropping to zero.

Those events cause and the island. This means that for Problem with sing particular voltage biases on the gate, ties of our SETs built in house.

13 voltage is originally biased at V0, (blue dot), then a change in the local charge distribution effectively modifies it to V0 δ, and the source-drain current will change dramatically (red dot). (c) This is an image of the twin-set test device obtained with a scanning electron microscope. The image to the right is a magnified version of the central region. The twin-set device is fabricated by a double-angle evaporation process, which replicates each of the features. Unequal voltage on A1 and A causes an electron to tunnel from one bar to the next. (d) The movement of charge is detected as a change in the source/drain conductance in both SETs simultaneously. The two signals r can be correlated to discriminate the charge transfer signal from reproducible charge noise or from random noise events. Read-Out Scheme (3/4) Conductance, G (e/h) (d) Left SET Charge noise 13 left SET right SET SET Vpulse ISET Correlation (a. u.) Typical SET signal as a function of gate voltage, Right SET which mimics the extra electron tunnelling onto the readout qubit q. G G SETs awhile re used side- by- side in o rder to (ii) electron resides Here, on thetwo donor, ISET 6= 0 when the random charge fluctuations ( noise ) donor is ionized.distinguish The readout protocol consists of three rem 13 in Fig. 1b. s(i) A Load phase, during spin phases, shownfrom intended ignals. which an electron in an unknowngives spinhstate tunnels from ratio.iset Their correlation igh signal- to- noise Gate voltage (V) the SET island to the donor, since µ SET SET > µ#, µ". The electron loading is signalled by ISET dropping to zero. the We have developed several readout due to the discrete, single-electron capacitive coupling between the gate simulation devices to testkane the proper-readout: tunneling events. Those events cause and the island. This means that for Problem with sing particular voltage biases on the gate, ties of our SETs built in house. In the the output of both SETs to change state very near conduction band abruptly. edge, likely todue ionise. (iii) source, Dand drain, currentis flow device seen in Figure 5, two thin In contrast, signals to through the SET becomes exquisitely metal bars, isolated from each other unwanted charge noise (reproducible to e sensitive to minute changes in the by a tunnel junction, substitute for the fluctuations in the conductance versus Load Read Empty voltage curve) tend notbto affect both charge distribution of the local enviphosphorous atoms.acontrol gates are load μ SETs simultaneously. By correlating ronment. The presence of a single used to electrostatically push single Source μ electrons from one bar to the next. the outputs of the two SETs,μwe are additional electron is readily M detectable as amodern change in the SET s The two SETs are then used to detect able to clearly identify the singlereadout μ charge transfer events and reject source/drain conductance. the change in the charge distribution SET SET t uses tunnelling of qt ISET island Fig. onto SET island in chan 93 out Number 7 00 Los Alamos Science Single electron peak Drain t V D

Readout Scheme (4/4) Nature 467 (010) 687; 489 (01) 541; 496 (013) 334 14 All experiments at 300 mk.

14 Readout Scheme (4/4) Nature 467 (010) 687; 489 (01) 541; 496 (013) All experiments at 300 mk. Very high- fidelity readout moderately fast ESR pulses (pi = 75 ns) e- spin T e = 00 µs, with XYXY: 400 µs can also use nuclear spin T n = 3.5 ms (D 0 state) T n = 60 ms (D + state) but (pi = 66 µs)

15 Kane s Silicon QC - a Summary 15 Clear concept for DiVincenzo-compatible scalability Rather slow hardware due to indirect coupling Very hard to fabricate, but break-throughs in read-out (010) and manipulation (013) new ion implantation techniques (from ion traps) silicon industry advances as well (smaller feature sizes) Some revival of interest after too many silent years don t count it out yet!

Electron spin qubits in P donors in Silicon

Electron spin qubits in P donors in Silicon IDEA League lectures on Quantum Information Processing 7 September 2015 Lieven Vandersypen http://vandersypenlab.tudelft.nl Slides with black background courtesy