Building schedules

Hamiltonian as a list of coefficients and Observables

Schedule objects are specified using a collection of pairs of time-dependent coefficients and Observable objects. Time dependent coefficients are simply arithmetic expressions (built from Variable), with a possible open parameter representing the time dependence (usually a variable t). This collection of pairs is called a “drive”.

Here is a simple example that constructs a schedule containing the time-dependent Hamiltonian:

\[H(t) = (1 - t) \sigma_z^{(0)} + t \sigma_x^{(0)}\]

from qat.core import Variable, Schedule, Observable, Term

t_variable = Variable("t")
schedule = Schedule(drive=[(1 - t_variable, Observable(1, pauli_terms=[Term(1, 'Z', [0])])),
                           (t_variable, Observable(1, pauli_terms=[Term(1, 'X', [0])]))],
                    tmax=23.0)

print(schedule)

drive:
(1 - t) * 1 * (Z|[0])
t * 1 * (X|[0])
tmax = 23.0

As one can see, the time during which the schedule is defined (the tmax parameter) also needs to be provided.

Note

It often leads to a faster Schedule creation (especially for tens or hundreds of qubits) if the coefficient of a Hamiltonian’s term is fed straight inside the respective Term (instead of leaving a coefficient \(1\)).
Also, if the same Pauli operator will be applied to many terms, list comprehension for the pauli_terms argument of an Observable will lead to a speed-up (compared to having as many tupples in the drive).

Using abstract variables

All scalars (i.e coefficients, tmax, etc) can be abstract arithmetic expressions:

from qat.core import Variable, Schedule, Observable, Term

t_variable = Variable("t")
tmax_expr = 15 * Variable("tmax") - 5
schedule = Schedule(drive=[(1 - t_variable, Observable(1, pauli_terms=[Term(1, 'Z', [0])])),
                           (t_variable, Observable(1, pauli_terms=[Term(1, 'X', [0])]))],
                    tmax=tmax_expr)

print(schedule, "\n")
print(schedule(tmax=10))

drive:
(1 - t) * 1 * (Z|[0])
t * 1 * (X|[0])
tmax = ((15 * tmax) - 5) 

drive:
(1 - t) * 1 * (Z|[0])
t * 1 * (X|[0])
tmax = 145

Hamiltonian as one Observable

Drives can also be declared using an Observable with time-dependent coefficients:

from qat.core import Variable, Schedule, Observable, Term

t_variable = Variable("t")
hamiltonian = (1 - t_variable) * Observable(1, pauli_terms=[Term(1, 'Z', [0])]) + \
              t_variable * Observable(1, pauli_terms=[Term(1, 'X', [0])])
schedule = Schedule(drive=hamiltonian,
                    tmax=23.0)
print(schedule)

drive:
1 * (1 - t) * (Z|[0]) +
t * (X|[0])
tmax = 23.0