Scaling up a Josephson JunctionQuantum Computer
• Basic elements of quantum computer
have been demonstrated
• 4-5 qubit algorithms within reach
• 8-10 likely
• With improvement in coherence,
further scaling up
John Martinis, UCSB
Quantized Voltages and Currentsof Microfabricated Circuit
100m
Qubit
(old NIST design)
control port
controlport
readoutport
Josephson Junction forms non-linear LC resonator
(1) State Preparation Wait t > 1/ for decay to |0>
Josephson-Junction Qubit
I = Idc + Idc(t) + Iwc(t)cos10t + Iws(t)sin10t
|0> : no tunnel
|1> : tunnel
3 ns pulse
wcI
wsI
Idc(t)
(2) Qubit logic with current bias
(3) State Measurement: U(Idc+Ip) Fast single shot – high fidelity
GHz) 6 ; ;mK (20 10kT
U()
E0
E1
E2
|0>
|1>
ExperimentalApparatus
V source
20dB 4K
20mK
300K
30dB
I-Q switch
Sequencer & Timer
waves
IsIVs
fiber optics rf filters
w filters
~10ppm noise
V source~10ppm noise
20dB
20dB
Z, measure
X, Y
Ip
Iw
Is
Itime
Reset Compute Meas. Readout
Ip
Iw
Vs
0 1
X Y
Z
Repeat 1000xProbability 0,1
10ns
3ns
~5 ns pulses
Qubit Characterization
~350ns
Meas.time
T1 ~400ns
0 100 200 300 400 500 600
time [ns]
T~100ns
Rabi
time
x/2
time
x/2
x/2 x/2y
Ramsey
Echo
time
xlifetime
P1
0
1
0
1
Single Qubit Gate Errors: Measurement Errors
1610 1614 1618 1622
6.8
7
7.2
Flux Bias [mV]
Fre
qu
en
cy [G
Hz]
3 ns
Iw
Iz
8 ns
nothing or -pulse
measure
measurement
TLS leakage
Spectroscopy
|1> (misidentified as |0>)• 4.5% splitting at 7GHz• 3-5% other splittings• 1% T1 during measurement
0 0.5 1
0
0.5
1
7.22 GHz
0 0.5 1
0
0.5
1
6.75 GHz
Imeas / Ic
thy: 96.6%exp: 85.0%
thy: 96.6%exp: 89.5%
|0> (misidentified as |1>)• 3.4% stray tunneling
Error Budget
|0>|1>
Tun
nelin
g P
rob.
Single-Qubit Gate Errors: Limited by T1
measureIw
Iz
8 ns 8 ns
X X
0 20 400
10
20
P1 [%]
separation
3.4%stray tunneling
pulse separation [ns]
4% error at separation 11 ns
T1 decaypulsenon-linearity
double - error:
4%single-qubit gate fidelity:
98%
Vary the time between pi pulses to separate gate fidelity from decoherence due to T1 decay.
(limited by T1)
Direct measure of probabilityChecks on measurement & -gates
Coupled Qubits
Cc
C
011010012/ 10 C
CS c
0 0
1 0 0 1
1 1
On Resonance:
Straightforward to implement: simple coupling tunable fast readout simultaneous measurement
Cc
Entangling 2-Qubit Gate (Universal)
0 50025050 100 150 200 300 350 400 4500
20
40
60
80
100
t [ns]
Pro
bab
ilit
y o
f |0
1>,
|10>
, o
r |1
1> [
%]
|00>
Entanglement of Formation
0.2635 ebit
real imag
t
0 0
1 0 0 1
1 1S
DATA
T1 = 450nsCM = 8% CuW= 5%vis = 85%g/ππ = 20MHz
Re [] Im [] Process Tomography of 2-Qubit Gate
SIM
Fidelity:Tr(thyexp) = 0.427
time16 ns
X
12 ns 12 ns
swap swaphold
time16 ns
TLS
X interact with TLS
1610 1614 1618 1622
6.8
7
7.2
Flux Bias [mV]
Fre
qu
en
cy [G
Hz]
0 1 2 3 4 0
0.5
1
time [s]
0 0.5 10
0.5
1
time [s]
T1,TLS ~ 1.2s
0 50 1000
1
time [ns]
Tswap ~ 12ns
• Strong interaction with TLS (S = 40MHz)• Long-lived TLS is quantum memory
P1
P1
excite qubit off-resonancez-pulse into resonance
“on”
“off”
measure
offon
TLSoffon
Bias
Fre
qu
en
cyOn-Off Coupling to TLS Memory
• On-Off coupling with change in bias
8%
Quantum Memory with Process Tomography
)Im()Re(
16ns16 ns
TLS
init
12 ns 12 ns
store loadmem
1 2 3
1 – InitializeCreate states over the entire Bloch sphere.
2 – StoreSwap state into TLS. Qubit now in ground state.
3 – LoadAfter holding for 16ns, swap again to retrieve state from TLS.
Process tomography:identity operation dominates process
Fidelity:Tr(thymeas)
= 79%
Summary and Future Prospects
•Demonstrated basic qubit operations with fidelity
Initialize, gate operations, simultaneous measurement
10 to 50 logic operations
Tomography conclusively demonstrates entanglement
•Decoherence mechanism understood
Optimize dielectrics, expect future improvements
•Working on Bell violation, advanced CNOT gates (+ tunable)
•Simulating 4-5 qubit algorithms
•Scale-up infrastructure designed (“brute force” to ~100 qubits)
Very optimistic about 4 -10 qubit quantum computer
Single-Qubit Gate Errors: Tomography Check
detu
ning
[M
Hz]
measureIw
Iz
8 ns 8 ns
X
detuning (both pulses)
phase [/]theory
experimentGoal:Measure fidelity of pi-pulse (longest single-qubit gate) separately from measurement errors.
Idea: Two pi-pulses bring state back to |0>, where the only measurement error is stray tunneling. Remaining error is due to pi-pulses only.
Tomography Check: On resonance, phase of second pulse has no effect, as expected for pi-pulses.
0
1
P1
P1
|2> Errors from Fast Pulses
Zoom in on 2-state errors for many pulse lengths
0.4 0.8 1.2 1.60
50
100
Measure Pulse Amplitude [V]
P o
f T
unne
ling
[%]
|0>
4ns
5ns
6ns
8ns
Two State Errors
Measure
(FWHM)
X
Gaussian pulses:Minimum width in time and frequency
frequency
pu
lse
po
wer
1021
4ns
8ns
10
21
6.05 6.15 6.250
60
Microwave Frequency [GHz]
P |1
> [%
]
25 30 35 40 450.2
0.4
0.6
0.8
1
Delay between 01 pulses [ns]
P |2
> [
%]
- Pulses Give Low Background & Error Filtering
Measure |2> State
5 ns
|2> Error Two Photon Qubit
200MHz
delay
Ramsey Fringe Filtering of |2> state
4P2-error
X X
Delay timedelay [ns]
High Power Spectroscopy
Error vs. Gaussian Pulse Width
0 1 2 3 4 5 6 7 810
-6
10-5
10-4
10-3
10-2
10-1
100
[ns]
|2
erro
r
0 1 2 3 4 5 6 7 810
-6
10-5
10-4
10-3
10-2
10-1
100
[ns]
|2
erro
r
10-4S-curve-
FT theorySpectrum analyzerQuantum simulation
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