Methods and apparatuses for rapid measurement of the motional mode phase in trapped ion chains

1 . A method of measuring motional mode phase of a plurality of ions in a single ion chain, comprising:

selecting a first ion of the plurality of ions in the single ion chain;

selecting a second ion of the plurality of ions in the single ion chain, the second ion being different than the first ion;

applying a first carrier π/2 pulse to the first ion;

applying a first red sideband π pulse to the first ion after the first carrier π/2 pulse is applied;

applying a second red sideband π pulse to the second ion, wherein the second ion is entangled with the first ion through a motional mode shared by the first ion and the second ion;

applying a second carrier π/2 pulse to the second ion after the second red sideband π pulse is applied; and

scanning a phase of the second carrier π/2 pulse.

2 . The method of claim 1 , further comprising:

applying each of a plurality of red sideband π pulses to each of remaining ions of the plurality of ions;

applying each of a plurality of carrier π/2 pulses to each of the remaining ions of the plurality of ions; and

scanning a plurality of phases of the plurality of carrier π/2 pulses to determine a relative phase associated with a motional mode.

3 . The method of claim 2 , wherein scanning the plurality of phases comprises applying a fixed phase to a last π/2 pulse of the plurality of carrier π/2 pulses.

4 . A non-transitory computer readable medium having instructions stored therein that, when executed by one or more processors of a quantum information processing (QIP) system, cause the one or more processors to:

select a first ion of a plurality of ions in a single ion chain;

select a second ion of the plurality of ions in the single ion chain, the second ion being different than the first ion;

control a light source to:

apply a first carrier π/2 pulse to the first ion;

apply a first red sideband π pulse to the first ion after the first carrier π/2 pulse is applied;

apply a second red sideband π pulse to the second ion, wherein the second ion is entangled with the first ion through a motional mode shared by the first ion and the second ion; and

apply a second carrier π/2 pulse to the second ion after the second red sideband π pulse is applied; and

scan a phase of the second carrier π/2 pulse.

5 . The non-transitory computer readable medium of claim 4 , further comprising instruction to:

control the light source to:

apply each of a plurality of red sideband π pulses to each of remaining ions of the plurality of ions; and

apply each of a plurality of carrier π/2 pulses to each of the remaining ions of the plurality of ions; and

scan a plurality of phases of the plurality of carrier π/2 pulses to determine a relative phase associated with a motional mode.

6 . The non-transitory computer readable medium of claim 5 , wherein the instructions for scanning the plurality of phases comprises instruction for applying a fixed phase to a last π/2 pulse of the plurality of carrier π/2 pulses.

7 . A quantum information processing (QIP) system, comprising:

a controller configured to:

select a first ion of a plurality of ions in a single ion chain; and

select a second ion of the plurality of ions in the single ion chain, the second ion being different than the first ion;

a light source configured to:

apply a first carrier π/2 pulse to the first ion;

apply a first red sideband π pulse to the first ion after the first carrier π/2 pulse is applied;

apply a second red sideband π pulse to the second ion, wherein the second ion is entangled with the first ion through a motional mode shared by the first ion and the second ion; and

apply a second carrier π/2 pulse to the second ion after the second red sideband π pulse is applied; and

scan a phase of the second carrier π/2 pulse.

8 . The QIP system of claim 7 , wherein:

the light source is further configured to:

apply each of a plurality of red sideband π pulses to each of remaining ions of the plurality of ions;

apply each of a plurality of carrier π/2 pulses to each of the remaining ions of the plurality of ions; and

the controller is further configured to scan a plurality of phases of the plurality of carrier π/2 pulses to determine a relative phase associated with a motional mode.

9 . The QIP system of claim 8 , wherein scanning the plurality of phases comprises applying a fixed phase to a last π/2 pulse of the plurality of carrier π/2 pulses.

10 . The method of claim 1 , further comprising identifying the single ion chain having the plurality of ions.

11 . The non-transitory computer readable medium of claim 4 , further comprising instruction to identify the single ion chain having the plurality of ions.

12 . The QIP system of claim 7 , wherein the controller is further configured to identify the single ion chain having the plurality of ions.