A method of reducing quantum leakage in a qubit device is disclosed. The method comprises receiving a set of energy level values for a multi-level system which includes first and second working levels |0>, |1> which provide a qubit and at least one other level |2> and performing an iteration at least once. the iteration comprising determining quantum leakage from at least one of the first and second working levels to the at least one non-working level for a quantum operation A comprising at least one pulse wherein each pulse has a respective pulse duration, determining whether the quantum leakage is greater than or equal to a threshold value; and, in dependence on the quantum leakage being greater than or equal to the threshold value, changing the duration of at least one of the at least one pulse.
Please help me write a proper abstract based on the patent claims. CLAIM: 1. A method comprising: receiving a set of energy level values for a multi-level system which includes first and second working levels |0>, |1> which provide a qubit and at least one other level |2>; and performing an iteration at least once comprising: determining quantum leakage from at least one of the first and second working levels to the at least one non-working level for a quantum operation A comprising a set of one or more pulses including a pulse having a given pulse duration; determining whether the quantum leakage is greater than or equal to a threshold value; and based on the quantum leakage being greater than or equal to the threshold value, changing the duration of at least one said pulse. 2. A method according to claim 1 comprising repeating the iteration for a different given pulse duration. 3. A method according to claim 1, wherein determining quantum leakage comprises determining: αi=ΣjN|Cij|2 where αi is quantum leakage for a working level i, where i=i1 or i2 is zero or a positive integer, and j is a non-working level, where j is zero or a positive integer and not equal to i1 or i2, and N is a positive integer greater than or equal to 2. 4. A method according to claim 3, wherein i=(0, 1) and j≠(0, 1)≧2. 5. A method according to claim 3, wherein N≧10, N≧50 or N≧100. 6. A method according to claim 1, further comprising measuring the set of energy level values. 7. A method according to claim 6, wherein measuring the set of energy level values comprises measuring a test multi-level system. 8. A method according to claim 1, wherein the threshold value is less than or equal to 1×10−5. 9. A method according to claim 1, wherein the threshold value is less than or equal to 1×10−6. 10. A method according to claim 1, wherein changing the duration of the at least one of the at least one pulse comprises increasing or decreasing the duration of the pulse by a predetermined amount.