Variable Balanced Transformer for Gradiometer Flux Qubits

1
Variable Balanced Transformer for Gradiometer
Flux Qubits
Luigi Longobardi, Vijay Patel, Timur V. Filippov,
and James E. Lukens State University of New York
at Stony Brook
2
ABSTRACT Accurate measurements of the flux
states of a flux qubit require a controllable
coupling between the qubit and a readout
circuit. We have developed a design for a
transformer for flux qubits. The transformer has
a gradiometer configuration in which each arm is
broken by a small loop containing two Josephson
junctions. When the inductances of the two arms
are equal, ideally the coupling is zero. In order
to unbalance the transformer and provide tunable
coupling, the control flux through one of the dc
SQUIDs is changed. This changes the Josephson
inductance of that arm and unbalances the
transformer.
3
Motivation

• Provide a controllable (ON/OFF) coupling between
  qubits
• Minimize flux back action of magnetometer in OFF
  state

4
QubitTransformerMagnetometer
Gradiometer design
5
Tunable Transformer
6
Gains
Sample-to-Magnetometer Gain
Magnetometer-to-Sample Gain
1st Order Solution
At balance
7
2nd Order Solution
SIGNAL
NOISE
8
2nd Order Solution
OFF and ON States
OFF
ON
Ideal Case
Noise-free magnetometer
9
2nd Order Solution
Non-Ideal Case
P
L
if
then inductance prefactor
10
Design Parameters

• L0 1.6 pH
• Lj 8 pH
• PL ? 104

11
Mm1 12 pH M1s 5 pH
M1s
Mm1
m
1
s
35 ?m
Design
12
Qubit-to-Qubit Coupling
13
Conclusion

• Transformer ON and OFF states were analyzed
• Maximal gain ratio for but multiple states are
  possible
• Prototype of transformer was designed
• We are in the process of fabricating and testing
  this prototype

This work was supported in part through AFOSR
by a DURINT program founded by ARDA and DoD.