High-Fidelity Josephson qubit gates – winning a battle against decoherence “Quantum Integrated Circuit” – scalable New breakthroughs: Improved fidelity Universal gates, with tomography 50  qubit – easy to couple Nadav Katz Work done while at UCSB with Prof. John Martinis and group. Contact: Ext: Racah Institute of Physics Colloquium, Nov. 2007

Experimental Quantum Information Processing (QIP) a perplexing explosion of different systems

Experimental QIP – a guide for the perplexed Smaller Ions Neutral Atoms NMR Semiconductor Spins Quantum Dots Superconducting Circuits Easier to isolateEasier to couple & construct Bigger NMR: 2 to 7 qubits; scalability? Ions: up to 8 qubits & scalable Dots: LONG T 1 (T 2 ?) Coherent Oscillations No dissipation Pretty good coherence times Coupled qubits Decoherence?? Goal - reach the fault tolerant threshold – F > 99.95%

The Josephson Junction SC ~1nm barrier Silicon or sapphire substrate Al top electrode Al bottom electrode AlOx tunnel barrier Josephson junction “Josephson Phase” Electrical notation I dc

The Qubit (phase) I dc IRC I dc + C V + V / R = I. Kirchoff’s Laws: V equation of motion Controllable “kinetic” energypotential energy damping Transform to Hamiltonian rep. Quantize (  is an operator)…

Superconducting Qubits PhaseFluxCharge Area ( µ m 2 ): (1) Potential & wavefunction Engineering Z J =1/  10 C 30  10 3  10 5  Yale, Saclay, NEC, Chalmers Delft, IBM, Berkeley UCSB, NIST, Maryland, Wisconsin, Jerusalem

Our Qubit microwave drive Junction Flux bias SQUID ~ 100 microns I dc Qubit Flux bias V SQ SQUID IµwIµw inductor

Operation of the Phase Qubit Qubit basis states |0 , |1  Tune qubit state energies E 10 with dc current I dc Control qubit states with microwave current I µw at  10 Measure state occupation by selective tunneling Minimize fluctuations and dissipation for qubit coherence I dc Qubit Flux bias V SQ SQUID IµwIµw  10 |0  |1 

(1) State Preparation Wait t > 1/  10 for decay to |0> Josephson-junction qubit |0> |1> I = I dc + d I p (t) + I m wc (t)cos w 10 t + I m ws (t)sin w 10 t phase potential pulse height of d I p Prob. Tunnel |0> : no tunnel |1> : tunnel |0> |1> 3 ns Gaussian pulse 96% m wc I m ws I d I p (t) (2) Qubit logic with current bias (3) State Measurement:  U(I dc + d I p ) Fast single shot – high fidelity UU

Experimental Apparatus V source 20dB 4K 20mK 300K 30dB I-Q switch Sequencer & Timer m waves IsIs IfIf VsVs fiber optics rf filters m w filters ~10ppm noise V source ~10ppm noise 20dB Z, measure X, Y IpIp ImwImw IsIs IfIf time Reset Compute Meas. Readout IpIp ImwImw VsVs 0 1 XY Z Repeat 1000x Probability 0,1 10ns 3ns ~5 ns pulses

GHz DAC Electronics Old analog system: time (ns) m wave amplitude IQ mwmw 14 bits, 2x Gs/s FPGA memory, ~2k$ measured waveform

Spectroscopy Bias current I (au) saturate IpIp ImwImw meas.  10 (I) 26 P 1 = grayscale

Qubit Characterization T 2 ~350ns Meas. time T 1 ~450ns time [ns] T  ~100ns Rabi time x  /2 time x  /2 yy Ramsey Echo time xx lifetime P1P

Standard State Tomography (Z, Y, X meas.) time (ns) P1P1 I,X,Y I X Y Z Y  /2 State prep.

Measurement in detail I dc ImwImw  pulse What is the quantum state after a partial measurement (p<1) ? Question: Full measurement (p=1) projects to either or p~1 p=0.5

Partial measurement evolution Theory: A. Korotkov, UCR Following Dalibard et al. PRL 68, 580 (1992). Prob. = p/2 tunnel out Prob. = 1-p/2 Apply state tomography to test theory Answer:

Partial measurement - results But can the effect of such a partial measurement be undone? High fidelity z rotations

Quantum erasure Partial measure Erasure (0.9  ) tomography & final measure state preparation 7 ns partial measure p IwIw IzIz p t 10 ns partial measure p p 10 ns7 ns xx Probablistic recovery of quantum state even with strong measurement Nontrivial sequence – Very good control Process tomography of the erasure (~85% fidelity)

Coupled Qubits CcCc C On Resonance: Straightforward to implement: simple coupling tunable fast readout simultaneous measurement eg. UMaryland CcCc

Simultaneous Measure of Coupled Qubits: i-SWAP gate p S i-SWAP gate p PABPAB A B t osc  z-gate  /2 z-gate P 10 P 01 P 11 Eigenstate, Bell singlet

Tomography: Direct Proof of Entanglement p A B p/2 state tomography I,X,Y fidelity = 0.86 expect = 0.87

Process Tomography 4 initial states / qubit p A B i-swap state tomography I,X,Y Samples Bloch sphere enough to describe gate for ANY initial state (i-swap) 1/2 is a universal gate

16 Density Matrices: Data (3 min.) Process Tomography

DATA T 1 = 450ns C M = 8% C uW = 5% vis = 85% π g/π = 20MHz Re [  ]Im [  ] Preliminary Data SIM Fidelity: Tr(  thy  exp ) = 0.427

Qubit Coherence: Where’s the Problem? Energy D. of States Inductors & Junctions Capacitors Superconductors: Gap protects from dissipation X-tal or amorphous metal Protected from magnetic defects 2D~4 T c eV Circuits Good circuit design (uwave eng.) resonator (X-tal)(amorphous) Many low-E states Only see at low T

Qubit Improvements (dielectric loss) P 1 (probability) 1 st gen. T 1 = 500 ns t Rabi (ns) 2 nd gen. 3 rd gen. T 1 = 40 ns T 1 = 110 ns 40% 60% 90% No Si wafer SiO 2 -> SiN x Small junction + shunting C (loss of SiN x limits T 1 ) 60  m SiN x capacitor

New Qubit Data P 1 (probability) t Rabi (ns) 4 th gen. T 1 = 470 ns 90% Interdigitated C – (topologically protected) sapphire dielectric (radiation from large size?) T  ~ 300 ns Optimistic for further dramatic improvements We know crystals are “superinsulators” How to fabricate? 5 th gen. a-Si:H dielectric (Q ~ 40000) T 1 = 450 ns

time 16 ns XX 12 ns swap hold time 16 ns TLS XX interact with TLS time [  s] T 1,TLS ~ 1.2  s time [ns] T swap ~ 12ns Strong interaction with TLS (S = 40MHz) Long-lived TLS is quantum memory P1P1 P1P1 excite qubit off-resonance z-pulse into resonance “on” “off” measure off on TLS off on Bias Frequency TLS Resonance – not a bug, a feature… On-Off coupling with change in bias 8%

Quantum Memory with Process Tomography 16ns TLS init 12 ns storeloadmem – Initialize Create states over the entire Bloch sphere. 2 – Store Swap state into TLS. Qubit now in ground state. 3 – Load After holding for 16ns, swap again to retrieve state from TLS. Process tomography: identity operation dominates process Fidelity: Tr(  th  meas ) = 79%

New Frontier: 50  atoms “Atom” with 50 W impedance |Z qubit | =1/w 10 C Z qubit (  ) 11K1M phase qubit Q F atoms 377  50  Z mismatch makes coherence easier Z match makes coupling easier Error threshold Unlimited range10 -3 – D lattice nearest-neighbor D lattice nearest-neighbor10 -8 Architecture 50  enables long distance coupling Much better error threshold !

Future Prospects Demonstrated basic qubit operations Initialize, gate operations, controlled measurement 10 to 100 logic operations Tomography conclusively demonstrates entanglement Decoherence mechanism understood Optimize dielectrics, expect future improvements Problem is NOT (only) T 1 !! Future: tunable coupling, CNOT gate with process tomography New designs and regimes (cavity QED and microbridges) Scale-up infrastructure designed (“brute force” to ~40 qubits) Very optimistic about qubit quantum computer