Quantum Computation with Superconducting Quantum Devices T.P. Orlando, S. Lloyd, L. Levitov, J.E. Mooij - MIT M. Tinkham

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Quantum Computation with Superconducting Quantum
Devices T.P. Orlando, S. Lloyd, L. Levitov, J.E.
Mooij - MITM. Tinkham Harvard M. Bocko, M.
Feldman U. of Rochester
orlando_at_mit.edu web.mit.edu/superconduc
tivity
7/28/02

• Objective
• To use superconducting loops and Josephson
  junctions
• To model the measurement process, understand
  decoherence, and to develop scalable algorithms,
• To combine these qubits with classical on-chip,
• high-speed superconducting control electronics,
• To implement the fabrication and testing of the
  superconducting qubits.

Put 30mk data here
(Put collaborative UR/MIT experiment here)

• Status
• Measurements of the two states in a Nb qubit with
  0.45mm junctions an underdamped Nb dc-SQUID
• Energy landscape determined from thermal
  activation measurements for Tgt 300mK
• A Q factor of 106 which agrees with measurements
  of the Rsubgap gt 1 MW.
• Al qubits Measured relaxation time 1 ms
• SFQ components (delay lines, DC/SFQ,
  T-flip-flops) measured at low current density and
  low temperature.
• Modeling the environmental coupling to the qubit
  and the measurement process
• Scalable architecture for adiabatic quantum
  computing

Objective Approach Theory To
understand the measurement and control processes,
develop algorithms and guide the experimental
design and testing. Circuits To design, analyze
and demonstrate superconducting circuitry for the
on-chip input and the required control functions
for qubit manipulation. Implementation To test
and analyze results from each integration step
oversee fabrication and improve junction quality.
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Participants and Collaborators
MIT Seth Lloyd Lin Tian, Bill
Kaminsky Leonid Levitov Terry Orlando Ken
Segall Donald Crankshaw Daniel Nakada,
Janice Lee Bhuwan Singh, David Berns
Harvard University Michael Tinkham Nina
Markovic, Sergio Valenzuela
University of Rochester Mark Bocko Marc
Feldman Jon Habif, Pavel Rott Xingxiang Zhou
Gui-Zhen Zhang, Michael Wulf
MIT Lincoln Laboratory Karl Berggren Jay Sage
TU DELFT Johan Mooij Kees Harmans Alexander
ter Haar
University of Munich Frank Wilhelm Markus Storcz
AFRL Jeff Yepez
This work is supported in part by the AFOSR
grant F49620-01-1-0457 under the DoD University
Research Initiative on Nanotechnology (DURINT)
program and ARDA, and in part by the AFOSR/NM
and also by the NSA and ARDA under ARO grant
number DAAG55-998-1-0369. The Type II computing
is funded by AFOSR/NM.
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Collaborations

• Lincoln Laboratory (fabrication and type-II
  computing)
• Delft (off-chip experiments, Al qubits, tight
  collaboration, theory)
• TRW (fabrication source)
• MIT (MIT/Cambridge Consortium, NSF Center, Type
  II computing)
• Univ. Munich (Frank Wilhelm) Theory
• AFRL (Yepez) Type II computing
• SQUBIT European Project

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Outline

• General Overview (Terry Orlando)
• Introduction
• Highlights of recent results
• Future work
• Implementation Review (Ken Segall)
• Circuits Review (Marc Feldman)
• Experiments from Delft (Kees Harmans)
• Theory Review (Seth Lloyd)

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Persistent Current Qubit
This qubit design uses a superconducting loop
interrupted by three Josephson Junctions. The two
lowest energy states, which serve as the 0gt and
1gt states of the qubit, have circulating
currents in opposite directions, with opposite
magnetic fields of 0.001 ?0.
current
?j3
v
?1
?2
?j2
?j1
ƒ1
Rotating the qubit will require flux oscillations
at the frequency of the energy difference. The
Rabi frequency depends on the magnitude of the
flux oscillations.
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Quantum Computation with Superconducting Quantum
Devices T.P. Orlando, S. Lloyd, L. Levitov, J.E.
Mooij - MITM. Tinkham Harvard M. Bocko, M.
Feldman U. of Rochesterin collaboration with
K. Berggren, MIT Lincoln Laboratory
7/28/02

Fabrication modeling, and measurements

• Persistent current qubit fabricated in Nb with
  submicron junctions
• Two states seen in measurement (thermal
  activations and energy levels)

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Thermal Activation Theory
Condition for ltIswgt 0
Thermal rate with damping (Energy diffusion
regime)
Energy barrier linear in flux

• EJ indicates junctions are small (0.55 mm)
• Q suggests long relaxation times (T1 Q/w0 4
  ms)

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Lincoln Lab Rsubgap measurement
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Macroscopic quantum superposition in a Josephson
junction loop
Delft University of Technology DIMES The
Netherlands MIT Cambridge Caspar van der
Wal, A. Ter Haar, Kees Harmans, Hans Mooij
T. Orlando, L. Levitov, S. Lloyd

• Superposition of states observed
• Relaxation time 5 msec,
• Dephasing time 0.1 msec

MIT
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Relaxation time
Measured relaxation time 1 ms
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New Slide(s) from Delft
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SFQ Results on QC2

• Inductance measurement - its exactly right
• Tested (4.2 K) analog and digital devices on LL
  fabricated chips (500 A/cm2 nominal)
• dc-SQUID coupled to large inductive loop
• Small junction I-Vs 0.4 x 0.4 µm
• RSFQ test circuit
• dc-sfq, JTLs, confluence buffer, splitter,
  JTL clock ring, sfq-dc

Add UR logos, reference here
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Test Results
Operation of the circuit on the previous page.
Each cycle of the input waveform introduces one
SFQ pulse to the circuit. The output flips its
voltage state at each arriving pulse.
350 bits/sec.
3.5 kbits/sec.
Add UR logos, reference here
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On-chip Control for an RF-SQUID M.J. Feldman,
M.F. Bocko, Univ. of Rochester
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Sources of Error in Superconducting Qubits
Decoherence from the environment (use error
correction)

• Offset charge fluctuations
• Quasiparticles
  Q gt 104
• Bias current fluctuations

Dephasing sources (use spin echo techniques)

• Coupling to nuclear spins
• Diople-dipole coupling

Coherent error sources (use dynamic pulse
control)

• Coupling to higher levels
• Two-bit gate coupling

Lin Tian, L. Levitov, et al., General Theory of
Dephasing for the Qubit, Quantum Mesoscopic
Phenomena (2000)
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Model of Measurement Induced Decoherence
Spin-Boson Model gives
Lin Tian, Seth Lloyd, T. Orlando PRB (2001)
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More theory slide

• Adiabatic QC

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Type II Quantum Computing1-D Algorithm
where P is occupancy probability
  ?1,a ?2,a ?3,a ?4,a ?5,a
?6,a
?1,b ?2,b ?3,b ?4,b
?5,b ?6,b
Initialize
F1 F2 F3 F4
F5 F6

Collide
P1a P2a P3a P4a P5a
P6a
P1b P2b P3b
P4b P5b P6b
Measure

P1a ? P2a?P3a? P4a ? P5a? P6a
? ? ? ? ?
? P1b ? P2b ?P3b? P4b
?P5b ?P6b
Stream
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Measurement
Iqubit bias
Imeas bias
f1
f2
Vosc bias
fosc
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Quantum Computation with Superconducting Quantum
Devices T.P. Orlando, S. Lloyd, L. Levitov, J.E.
Mooij - MITM. Tinkham Harvard M. Bocko, M.
Feldman U. of Rochester
orlando_at_mit.edu web.mit.edu/superconduc
tivity
7/28/02

• Progress on last years objectives
• Measurements of the two states in a Nb qubit with
  0.45mm junctions and underdamped Nb dc-SQUID
  Energy landscape determined from thermal
  activation measurements for Tgt 300mK, and a Q
  factor of 106 and Rsubgap gt 1MW.
• SFQ devices at 300 mK and for current densities lt
  200 Amps/cm2
• Al qubits Measured relaxation time 1 ms
• Scalable architecture for adiabatic quantum
  computing with superconductors
• Research plan for the next 12 months
• Measurement of on-chip spectroscopy of a single
  qubit
• On-chip timed oscillator control of a single
  qubit
• Spectroscopy of two-coupled qubits
• Resonance method of measurement of the state of
  the qubit (with Delft)
• Set up Dilution Refrigerators
• Theory here
• Long term objectives (demonstrations)
• - Combine 3 to 5 superconducting qubits with
  on-chip control electronics
• - Measure decoherence in multiple-qubit systems
• - Develop algorithms adapted to superconducting
  electronics
• - Explore quantum control to correct qubit
  dynamics

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Summary Slides of Results, Circuits, and
Publications
Not to be presented
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Results to Date

• Implementation
• Subgap resistance of submicron Nb junctions gt 1
  MW at low temperatures
• LL Resistors remain at 30 mK
• Measurements of the two states in a Nb qubit with
  0.45mm junctions an underdamped Nb dc-SQUID
• Energy landscape determined from thermal
  activation measurements for Tgt 300mK
• A Q factor of 106 which agrees with measurements
  of the Rgap gt 1 MW.
• Delft Experiments Spectroscopy of superposition
  states
• Developing of gradiometer qubits to lessen flux
  noise
• Experiments on decoherence times and noise
  (Delft)
• Installation of Dilution Refrigerators underway
  at MIT and UR

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• Circuits
• SFQ T-Flip-Flop demonstrated at 300 mK and for
  current densities lt 200 Amps/cm2
• Demonstration of Flip-Chip inductive coupling
• On-chip coupling of JJ Oscillator
• Design of MQC experiments on-chip
• Developing resonant measurement scheme
• Other results here

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• Theory
• Theory of persistent current qubit
• Calculation of intrinsic decoherence mechanisms
  and sources of errors
• Method to overcome off-resonant excitations
• Modeling of decoherence of coupling and measuring
  circuits- circuit model formulation
• Modeling of measurement process with DC SQUID
• Exploration of coupling schemes for qubits
• Scalable architecture for adiabatic quantum
  computing with superconducting

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I. Circuits and Components That Have Already
Been TestedA. Simple Control Circuits1.
On-chip DC-SQUID oscillators have been tested and
sufficient inductive coupling to another circuits
has been demonstrated. These oscillators however
only operated around 3 GHz, so oscillators with
variable frequency are now being fabricated.
(MIT)2. Demonstration of inductive coupling
between separate chips for use in coupling qubits
with control circuits fabricated on different
chips (Lincoln).3. Theoretical modeling of the
effect of these simple control circuits on the
decoherence of the qubit was included in the
designs of the oscillators and measuring
system.(MIT/Delft/Rochester)4. Test at 4.2K of
an RF SQUID coupled to a superconductive
comparator with readout to room temperature
(Lincoln).5. Fixed-current superconducting
loops, for magnetic flux biasing (Rochester)B.
Complex Circuit and components1. The following
components have been designed, fabricated,and
tested at 4.2 K. a. DC/SFQ and
SFQ/DC converters (Rochester) b. DRO
memory cells (Rochester) c.
T-Flip-flops (Rochester) d. Chains
of up to 16 T-Flip-flops as counters.
(Rochester) e. SFQ clocks (pulse
oscillators) of fixed frequencies designed
from 5 to 40 GHz. (Rochester)
f. Pulse splitters and combining buffers
(Rochester)
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II. Types of Circuits and components that are
being fabricated on QC3 (scheduled for
completion in later this year.)A. Simple
Circuits1. On-chip DC-SQUID oscillators to
work in the 5-15 GHz regime (some connected to
detectors and some to qubits to do on-chip
spectroscopy) (MIT)2. On-chip SFQ microwave
oscillator to work at 8 GHZ regime. (some
connected to detectors and some to qubits to do
on-chip spectroscopy) (Rochester/MIT)3. A qubit
coupled inductively to a coplanar waveguide.
Using an external microwave generator, operating
at 1-20GHz, it is possible to map the energy
separation between the lowest two energy levels.
(Lincoln and MIT)B. Complex ExperimentsList
experiments on QC3 and explain briefly whose
circuit and why the circuit is important.1. An
NDRO memory cell, similar to a DRO cell but with
a non-destructive read-out, is being fabricated.
Asuccessful test will allow the timed oscillator
experiment (Rochester)2. Timed oscillator
experiment -- by using two out-of-phase counter
and an NDRO memory cell, we can make a variable
duty cycle oscillator to drive a qubit with a
SQUID detector controlled off-chip.
(Rochester)3. Qubit readout experiments a.
QFP Comparators coupled with varying strengths to
RF SQUID qubits (Lincoln) b. QFP Comparators
coupled to persistent-current qubits
(Lincoln) c. SFQ Comparators coupled to rf
SQUID qubits and to testlines (Rochester)
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C. Full Quantum Experiments Circuits
(more-than-complex circuits) 1.
Superposition-state time evolution experiment
using rf SQUID qubit. This design has all-SFQ
inputs and outputs, all on-chip but off-chip
timing. (Rochester) 2. Superposition-state time
evolution experiment using single-Josephson-juncti
on qubit (inspired by Martinis and Han
experiments), with on-chip SFQ control circuits.
Specifically designed to be portable to TRW
fabrication. (Rochester)
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Publications
1. Design of Persistent Current Qubit J. E.
Mooij, et al., Science, 285, 1036, (1999) T.
P. Orlando, et al., PRB 60, 15398 (1999) 2.
General Theory of Dephasing for the Qubit
Lin Tian, L. Levitov, et al., in Quantum
Mesoscopic Phenomena (2000) 3. Pulse Scheme to
Decouple Higher Levels Lin Tian and S.
Lloyd, PRA 62, 50301 (2000) 4. Measurements of
the Qubit Energy Levels C. van der Wal, C.
Harmans, J. E. Mooij, et al. Science 290, 773,
(2000) 5. Inductance Effects on the Qubits
D. Crankshaw, E. Trias, et al. IEEE Trans.
Applied Supercond. 11, 1223, (2001) 6.
Fabrication of Nb Qubits and Circuits K.
Berggren, D. Nakada, et al. Proceedings of the
International Conference on Experimental Methods
in Quantum Computation, 2001. Rinton
Press. 7. Modeling of the Measurement Process
C. van der Wal, F. Wilhelm, et al., to be
published Lin Tian, S. Lloyd, and T.
Orlando, et al., to be published D.
Crankshaw, et al., to be published