Physical mechanisms of low frequency noises in superconducting qubits

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Astafiev, Y. Pashkin, Y. Nakamura (NEC, Tsukuba), R. Simmonds (NIST, Boulder), J.

1 Physical mechanisms of low frequency noises in superconducting qubits Lara Faoro LPTHE and Rutgers University (USA) Lev Ioffe (Rutgers) and Alexei Kitaev (CalTech) Exp. Collaborators: O. Astafiev, Y. Pashkin, Y. Nakamura (NEC, Tsukuba), R. Simmonds (NIST, Boulder), J. Martinis (UCSB) and R. McDermott (UW-Madison) O. Buisson and W. Guichard. (Grenoble) M. Gershenson (Rutgers) 1

2 Outline 1. Superconducting qubits: - Brief introduction on Quantum Computation (QC) and Josephson qubits - Qualitative understanding of different types of noises in superconducting qubits: (charge, critical current, flux and Quasiparticle Poisoning) 2. Novel idea that localized electron states (traps) in the insulator (oxide) surrounding the superconducting island can provide the mechanism for all noises in the Josephson qubits: charge noise, critical current, the flux noise and even the quasiparticle poisoning. New experiments prompted by these novel theoretical ideas 3. This study is relevant to experiments but it addresses fundamental unresolved issues [Level broadening in closed systems - Kondo physics and superconductivity] 2

Elementary quantum information unit: the qubit A qubit is any quantum system with exactly two degrees of freedom: we use them to represent binary 0 and 1 hydrogen

3 Elementary quantum information unit: the qubit A qubit is any quantum system with exactly two degrees of freedom: we use them to represent binary 0 and 1 hydrogen atom Ground state Excited state spin 1/2 electron Spin-down state Spin-up state In general the state of the qubit is a superposition of the basis states and Bloch sphere 3

4 Quantum Computation final state i Parallel evolution providing the quantum speedup. Perturbations from the environment destroy the parallel evolution of the computation each qubit must be prepared in some known state: initial state the qubits can be manipulated through quantum gates the qubits must be protected from decoherence each qubit can be measured in a basis: final state 4

5 What we need to build a quantum computer and why it is so difficult? For quantum computer one needs: 1. A scalable physical system with many ( ) well characterized qubits 2. The ability to initialize the state of the qubits to a simple fiducial state, i.e. 3. Long decoherence times, much longer than the gate operation time, i.e. 4. A universal set of quantum gates 5. A specific measurement capability DiVincenzo Criteria Every real qubit is a quantum open system 5

6 In QC there are two types of errors 1. Single bit flip ( classical error) T 1! Relaxation time 2. Phase error ( quantum error) T 2! Dephasing time Correction of both types of errors is very difficult!! But QEC codes have been invented 6

7 The challenge has started: Which candidates and why superconducting qubits might at the end win? 7

Building qubits with integrated circuits Scalability and flexibility in design are achieved by combining elementary elements Desiderata for quantum circuits: - low

8 Building qubits with integrated circuits Scalability and flexibility in design are achieved by combining elementary elements Desiderata for quantum circuits: - low dissipation - non-linear (non-dissipative elements) - low (thermal) noise Solutions: - use superconductors - operate at low temperatures - use Josephson tunnel junctions 8

9 Different types of superconducting qubits phase size ~10µm 2 flux size ~ 0.1µm 2 Josephson junction UCSB GRENOBLE NEC IBM charge size ~ 0.01µm 2 Superconductors: Nb, Al Tunnel barrier: AlO x charge - flux SACLAY CPB in a cavity A non-linear inductor without dissipation 9

10 Example: from the Cooper pair box to the Josephson charge qubit Electrostatic Josephson energy E N = 0 N = N g The system coherently oscillates between the charge states and and 10

State of the art of superconducting qubits Charge NEC/Chalmers Charge/Phase

Charging versus Josephson energy # of Cooper pairs History 1 st qubit

Several experiments with two degrees of freedom C-NOT gate (2003 NEC, 2006

11 State of the art of superconducting qubits Charge NEC/Chalmers Charge/Phase Saclay/Yale Flux TU Delft/SUNY Phase NIST/UCSB Junction size E J = E C Charging versus Josephson energy # of Cooper pairs History 1 st qubit demonstrated in 1998 (NEC Labs, Japan) Long coherence shown 2002 (Saclay/Yale) Several experiments with two degrees of freedom C-NOT gate (2003 NEC, 2006 Delft and UCSB ) Bell inequality tests being attempted (2006, UCSB) [failure due to low readout visibility!] 1 st time domain tunable coupling of two flux qubits (2007, NEC Labs, Japan) Coupling superconducting qubits via a cavity bus (2007 Yale and NIST) 11

12 Relaxation and dephasing times T1! Relaxation time T 2! Dephasing time Design Group T 2 T 1 Visibility Phase qubit UCSB ~ 85 nsec 110 nsec > 90% Operation time Logical quality factor Flux qubit NEC ~ 0.8 µsec 1 µsec ~ 20/30% ~ 0.02 µsec * Transmon (CPB in a cavity) Yale ~ 2 µsec ~ 1.5 µsec > 95 % ~ 0.05 µsec * * Projected values 12

13 How far are we from Fault-Tolerance QEC? Log 10 (Program length) A. Steane (PRA, 2003) -Log 10 Q Logical -Log 10 R R=N/K - redundancy Q Logical < Need Q Logical >> 104 for many qubit system 13

14 What is responsible for the short coherence times? external circuit (gaussian noise from impedance wires) motion of charges in associated dielectrics and oxides (charge noise) motion of charges in the barrier (critical current noise) motion of trapped vortices in superconductor (flux noise) relaxations of paramagnetic spins located at the Superconductor Insulator interfaces (flux noise) tunneling of a single quasiparticle in and out of the superconducting island (quasiparticle poisoning) 14

Topological QC Kitaev (1997) Theory superconducting arrays: Ioffe, Doucot

15 Two strategies 1. Trying to understand the origin of the noise so to improve the current devices Interesting new physics? The rest of this talk 2. Design novel qubits that are protected from errors (hardware QEC) - Topological QC Kitaev (1997) Theory superconducting arrays: Ioffe, Doucot Experiments: Rutgers and Grenoble Double degenerate ground states! M. Gershenson s Lab. at Physics Dep, Rutgers Global encoded states of the JJ array 15

16 Charge noise: spectrum Josephson charge qubit size ~ 0.01 µm 2 Quantronium size ~ 0.01µm 2 O. Astafiev et al. (2004, 2006) 16

17 Critical current fluctuations: noise spectrum Flux qubit size ~ 0.1µm 2 Phase qubit size ~10µm 2 F. Wellstood, D. J. Van Harlingen et al. (late 80s) J. Eroms et al. (2006) S. Pottorf et al. (2007) 17

18 Low frequency flux noise below 1 K: noise spectrum Universal value: Flux qubit size ~ 0.1µm 2 Phase qubit size ~10µm 2 F. Wellstood (late 80s) J. Martinis et al. (2007) 18

19 Coherence times (ns)! Dephasing and 1/f noise Spin echo Free decay Noise spectrum !/2" N g -1/2 G. Ithier et al. PRB 05 Saclay, quantronium 3.0x10 7! 2.5x ) 1/T 2 (s 2.0x x x x x10-2.0x x x10-4!" qb [" 0 ] K. Kakuyanagi et al NTT, Flux Qubit Y. Nakamura et al NEC, Flux Qubit 19

Charge noise: problems with conventional TLSs A common belief: charged impurities are TLSs in the surrounding insulators Faoro & Ioffe, 2006 Quantum coherent TLS P. Anderson et al. (1972) J. L.

20 Charge noise: problems with conventional TLSs A common belief: charged impurities are TLSs in the surrounding insulators Faoro & Ioffe, 2006 Quantum coherent TLS P. Anderson et al. (1972) J. L. Black and B. I. Halperin, (1977) L. Levitov (1991) A. L. Burin (1995) In the barrier, having a typical volume, there is a very low density of TLS Astafiev et al Relaxation in phase qubits, NIST UCSB, MD, Grenoble 20

21 Results of TLSs analysis Theory of TLS NEC Experiments S q (!) S q (!) 2 T "! "!!! For substrate volume Qualitative disagreement between theory and experiments!! 21

22 A novel idea Faoro, Ioffe Faoro, Kitaev and Ioffe 2008 Localized electron states (traps) in the insulator (oxide) surrounding the superconducting island on all sides can provide mechanism for all noises in Josephson qubits: charge noise critical current noise flux noise quasiparticle poisoning - Common feature of the traps: they a large Coulomb interaction that prevents a double occupation and this provide a source of unpaired spins. - But there are two energy scales: Kondo Temperature (depends exponentially on the hybridization with the conducting electron in the bulk superconductor). Superconducting gap In the theory traps with: Charge noise, critical current and quasiparticle poisoning Flux noise 22

23 Brief review of Kondo effect The goal of our theory: superconductor insulator Let us forget superconductivity for a moment 1. Kondo problem: magnetic impurity coupled to an electron gas Electrons scatter off the Impurity in inelastic spin spin processes Kondo Temperature: Elastic scatterings as the impurity is screened by electrons forming a bound state singlet with the impurity. 2. Magnetic impurity in a metal: the impurity is modeled as a localized state with on site repulsion U Hybridization : in the limit S-W transformation 23

24 A simple toy model Faoro, Kitaev and Ioffe 2008 Although simple, the model allows us to capture the relevant physics! superconductor insulator Notation: Low-energy eigenvalues Factorized states Odd number of electrons Entangled state ( bound state ) Even number of electrons 24

25 Doublets and singlet carry different charge superconductor insulator Low energy states Doublets (non entangled) Singlet Bound-entangled Charged!! No - Charge!! Screening [ Unpaired spins On the SI interface] Dangerous for: Flux noise Harmless! Dangerous for: Charge noise, critical current and quasiparticle poisoning [ States very close in energy (that can be activated at low T) and that are respectively charged and uncharged, so they are some special charged flucutators ] 25

26 Important remarks There are different microscopic mechanisms that are responsible for the charge noise and the critical current fluctuations: - conventional random motion of charges (glassy TLSs) T dependence - 1/f low frequency noise - white noise and quantum resonances at high frequency - complicate physics at the SI interface between localized electron states (traps) and the conducting electrons in the bulk superconductor T 2 dependence - 1/f low frequency noise - ohmic noise at high frequency CONSEGUENCES We need to improve (clean as much as we can) the quality of SI interface Because this theoretical analysis shows that SUPERCONDUCTIVITY carries additional sources of noise! 26

Tracking down the two microscopic mechanisms: a novel plan of experiments on suspended SETs held in normal and superconducting state at NEC, Tsukuba In collaboration with Y. Pashkin et al.

27 Tracking down the two microscopic mechanisms: a novel plan of experiments on suspended SETs held in normal and superconducting state at NEC, Tsukuba In collaboration with Y. Pashkin et al., 2007 Measurement of current of superconducting SET biased to JQP peak (2 Δ) or quasiparticle current at 4 Δ. Charge noise appears as peak position fluctuations. Substrate/Island SiO/Al SiO/Pd SiN/Al --/Al Large Small Super Normal Super Normal T?? e 2 /Hz?? T 2?? e 2 /Hz?? T?? e 2 /Hz???? T e 2 /Hz?? T 2 T e 2 /Hz?? 1. Substrate matters! SiO better than SiN 2. In SET on SiN we get the correct temperature dependence 3. Unfortunately the analysis was done randomly 4. Contrary to Zorin data (2000) the noise in suspended SET is comparable with 27 the noise in non suspended SET

Charge noise spectra Large island: 530 nm Small island: 180 nm Junctions size: 30 nm x 30 nm Suspended SET (530 nm) in superconducting state Noise spectra Data Timetraces at 4Δ peak, dt=20s, tm ~ 16

28 Charge noise spectra Large island: 530 nm Small island: 180 nm Junctions size: 30 nm x 30 nm Suspended SET (530 nm) in superconducting state Noise spectra Data Timetraces at 4Δ peak, dt=20s, tm ~ 16 hours Suspended SET (530 nm) in normal state (B=1T) Frequency Amplitude Amplitude Data Timetraces at 4Δ peak, dt=20s, tm ~ 16 hours Frequency The suspended SET in normal state is tenfold quieter! 28

29 Flux noise Generally, low frequency 1/f noise in dc-squids can be generated from: - fluctuating paramagnetic spins on the surface of the superconducting loops - fluctuating spins in the substrate - the junctions (as critical current) Until few months ago, the only measurement of flux noise spectra were the ones performed by F. Wellstood: A - B -C -E -G D - J K 29

30 Wellstood s results Two different regimes for the flux noise: above 1 K : T 2 -dependence -> thermally activated below 1K: saturation T<500 mk -> an other small energy scale is governing the noise. The slope of the noise is not!! It is extremely hard thinking of some microscopic mechanism leading to this weird slope 30

31 Let us try to argue 1. Noise saturation below 1K Some very low energy scales are involved. This would naturally point towards the nuclear spins or spin-spin dipolar interaction but 1/f dependence persists up to 1 MHz. This implies that energy scales are larger that the ones associated to nuclear spins (~1 KHz) and it is even to high for the dipolar interaction at conventional densities. [echo analysis Y. Nakamura at NEC] 2. Rough universality of the noise, i.e. area independence This points that the source of the noise in likely to be spins on the surface (each spin contributes roughly to 1/d, where d is the width of the SQUID loop, to the flux) but how spins create the dynamics of the magnetic field? ESR experiments [Schenkel et al. 2006, Edwards, 1987 ] done on Si/SiO 2 have show that: (i) the surface density of paramagnetic spins [Pb centers] varies between This value is barely sufficient to match the experimental universal value but this implies that all these spins remain active at low temperature! (ii) the g factor of the Pb centers is isotropic and it has value of This means that the spin orbit coupling is very weak. 31

32 A possible solution: Paramagnetic spins at the SI boundary whose dynamics is due to RKKY interaction 1. Spin spin interaction Faoro & Ioffe, Spin diffusion 3. Spatial dependence of the probe magnetic field in the SQUID loop 1/f flux noise in good agreement with experiments 32

33 New flux noise measurements from UCSB and UMW SQUID made of Al on a sapphire substrate Spin glass? Larkin, Khmel'nitskii JETP 31, 958 (1970) 33

34 Theoretical challenge I What is the dynamics of collections of spins or TLSs weakly interacting Quantum? Classical? Generation of noise by closed quantum systems (TLSs dynamics at very low temperature, dilute electron spins with dipole dipole interaction) Set of problems equivalent to level broadening in closed systems 34

35 Theoretical challenge II Full theoretical treatment of the interplay between Kondo and superconductivity and its consequences Effects of the other modes in the superconductor? Quasiparticle poisoning related to localization of Kondo cloud: problem of charge dynamics? 35

36 Microscopic origin of noise and Noise phenomenological model NEC, Tsukuba Charge noise in charge qubits UCSB - UWM- NIST- Grenoble Critical current fluctuations Novel idea that localized electron states (traps) in the insulator (oxide) surrounding the superconducting island can provide the mechanism for all noises in Josephson qubits: charge noise, critical current, the flux noise and even the quasiparticle poisoning. UCSB - UWM Low frequency excess flux noise (Faoro, Ioffe and Kitaev) NEC, Tsukuba Study of non gaussian nature of charge noise in suspended SET Design of the circuit to test Common origin of charge and critical current noise Theoretical study of non ideal bangbang as diagnostic tool for spectroscopy of classical fluctuators Asymmetric quantum error correcting codes (dominant dephasing)??? Quasiparticle poisoning: origin from island? Completed, submitted, or Published In progress 36 Future Program

Topologicaly protected abelian Josephson qubits: theory and experiment.

Topologicaly protected abelian Josephson qubits: theory and experiment. B. Doucot (Jussieu) M.V. Feigelman (Landau) L. Ioffe (Rutgers) M. Gershenson (Rutgers) Plan Honest (pessimistic) review of the state