Table 1 Circuit depth comparison of the different TDS algorithms investigated and shown in Fig. 1 for the 1D transverse-field Ising model

From: Efficient and practical Hamiltonian simulation from time-dependent product formulas

Algorithm

2-qubit gate depth

CNOT depth

# steps in Fig. 1

Trotter 1

2N

4N

15

Trotter 2

2N + 1

4N + 2

15

Trotter 4

10N + 1

20N + 2

3

optimised Trotter 8

30N + 1

60N + 2

1

THRIFT 1

2N

4N + 2

15

THRIFT 2

2N + 1

4N + 2

15

THRIFT 4

10N + 1

20N + 2

3

optimised THRIFT 8

30N + 1

60N + 2

1

Magnus-THRIFT 1

2N

4N

15

Magnus-THRIFT 2

12N + 3

36N + 9

2

optimised small A 4

12N

24N

2

  1. The first column shows the 2-qubit depth of the circuit corresponding to N Trotter steps in terms of arbitrary 2-qubit gates. The second column shows the corresponding cost in terms of CNOT gates. Finally, the third column gives the number of Trotter steps used in Fig. 1, which correspond to a fixed budget of arbitrary 2-qubit gates of 31.
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