Minimum Trotterization Formulas for a Time-Dependent Hamiltonian
When a time propagator e δ t A for duration δ t consists of two noncommuting parts A = X + Y , Trotterization approximately decomposes the propagator into a product of exponentials of X and Y . Various Trotterization formulas have been utilized in quantum and classical computers, but much less is kn...
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| Published in | Quantum (Vienna, Austria) Vol. 7; p. 1168 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
06.11.2023
|
| Online Access | Get full text |
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| Summary: | When a time propagator
e
δ
t
A
for duration
δ
t
consists of two noncommuting parts
A
=
X
+
Y
, Trotterization approximately decomposes the propagator into a product of exponentials of
X
and
Y
. Various Trotterization formulas have been utilized in quantum and classical computers, but much less is known for the Trotterization with the time-dependent generator
A
(
t
)
. Here, for
A
(
t
)
given by the sum of two operators
X
and
Y
with time-dependent coefficients
A
(
t
)
=
x
(
t
)
X
+
y
(
t
)
Y
, we develop a systematic approach to derive high-order Trotterization formulas with minimum possible exponentials. In particular, we obtain fourth-order and sixth-order Trotterization formulas involving seven and fifteen exponentials, respectively, which are no more than those for time-independent generators. We also construct another fourth-order formula consisting of nine exponentials having a smaller error coefficient. Finally, we numerically benchmark the fourth-order formulas in a Hamiltonian simulation for a quantum Ising chain, showing that the 9-exponential formula accompanies smaller errors per local quantum gate than the well-known Suzuki formula. |
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| ISSN: | 2521-327X 2521-327X |
| DOI: | 10.22331/q-2023-11-06-1168 |