# Higher-order methods for simulations on quantum computers

## Abstract

To implement many-qubit gates for use in quantum simulations on quantum computers efficiently, we develop and present methods reexpressing exp[[minus]i(H[sub 1]+H[sub 2]+[center dot][center dot][center dot])[Delta]t] as a product of factors exp[[minus]iH[sub 1][Delta]t], exp[[minus]iH[sub 2][Delta]t],[hor ellipsis], which is accurate to third or fourth order in [Delta]t. The methods we derive are an extended form of the symplectic method, and can also be used for an integration of classical Hamiltonians on classical computers. We derive both integral and irrational methods, and find the most efficient methods in both cases. [copyright] [ital 1999] [ital The American Physical Society]

- Authors:

- (NASA/Fermilab Astrophysics Group, Fermi National Accelerator Laboratory, Box 500, Batavia, Illinois 60510-0500 (United States))

- Publication Date:

- OSTI Identifier:
- 6466476

- Alternate Identifier(s):
- OSTI ID: 6466476

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review A

- Additional Journal Information:
- Journal Volume: 60:3; Journal ID: ISSN 1050-2947

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EFFICIENCY; HAMILTONIANS; QUANTUM MECHANICS; SIMULATION; MATHEMATICAL OPERATORS; MECHANICS; QUANTUM OPERATORS 661100* -- Classical & Quantum Mechanics-- (1992-)

### Citation Formats

```
Sornborger, A.T., and Stewart, E.D.
```*Higher-order methods for simulations on quantum computers*. United States: N. p., 1999.
Web. doi:10.1103/PhysRevA.60.1956.

```
Sornborger, A.T., & Stewart, E.D.
```*Higher-order methods for simulations on quantum computers*. United States. doi:10.1103/PhysRevA.60.1956.

```
Sornborger, A.T., and Stewart, E.D. Wed .
"Higher-order methods for simulations on quantum computers". United States. doi:10.1103/PhysRevA.60.1956.
```

```
@article{osti_6466476,
```

title = {Higher-order methods for simulations on quantum computers},

author = {Sornborger, A.T. and Stewart, E.D.},

abstractNote = {To implement many-qubit gates for use in quantum simulations on quantum computers efficiently, we develop and present methods reexpressing exp[[minus]i(H[sub 1]+H[sub 2]+[center dot][center dot][center dot])[Delta]t] as a product of factors exp[[minus]iH[sub 1][Delta]t], exp[[minus]iH[sub 2][Delta]t],[hor ellipsis], which is accurate to third or fourth order in [Delta]t. The methods we derive are an extended form of the symplectic method, and can also be used for an integration of classical Hamiltonians on classical computers. We derive both integral and irrational methods, and find the most efficient methods in both cases. [copyright] [ital 1999] [ital The American Physical Society]},

doi = {10.1103/PhysRevA.60.1956},

journal = {Physical Review A},

issn = {1050-2947},

number = ,

volume = 60:3,

place = {United States},

year = {1999},

month = {9}

}

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