### Abstract

One of the main applications of future quantum computers will be the simulation of quantum models. While the evolution of a quantum state under a Hamiltonian is straightforward (if sometimes expensive), using quantum computers to determine the ground-state phase diagram of a quantum model and the properties of its phases is more involved. Using the Hubbard model as a prototypical example, we here show all the steps necessary to determine its phase diagram and ground-state properties on a quantum computer. In particular, we discuss strategies for efficiently determining and preparing the ground state of the Hubbard model starting from various mean-field states with broken symmetry. We present an efficient procedure to prepare arbitrary Slater determinants as initial states and present the complete set of quantum circuits needed to evolve from these to the ground state of the Hubbard model. We show that, using efficient nesting of the various terms, each time step in the evolution can be performed with just O(N) gates and O(logN) circuit depth. We give explicit circuits to measure arbitrary local observables and static and dynamic correlation functions, in both the time and the frequency domains. We further present efficient nondestructive approaches to measurement that avoid the need to reprepare the ground state after each measurement and that quadratically reduce the measurement error.

Original language | English (US) |
---|---|

Article number | 062318 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 92 |

Issue number | 6 |

DOIs | |

State | Published - Dec 10 2015 |

### Fingerprint

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A - Atomic, Molecular, and Optical Physics*,

*92*(6), [062318]. https://doi.org/10.1103/PhysRevA.92.062318

**Solving strongly correlated electron models on a quantum computer.** / Wecker, Dave; Hastings, Matthew B.; Wiebe, Nathan; Clark, Bryan K; Nayak, Chetan; Troyer, Matthias.

Research output: Contribution to journal › Article

*Physical Review A - Atomic, Molecular, and Optical Physics*, vol. 92, no. 6, 062318. https://doi.org/10.1103/PhysRevA.92.062318

}

TY - JOUR

T1 - Solving strongly correlated electron models on a quantum computer

AU - Wecker, Dave

AU - Hastings, Matthew B.

AU - Wiebe, Nathan

AU - Clark, Bryan K

AU - Nayak, Chetan

AU - Troyer, Matthias

PY - 2015/12/10

Y1 - 2015/12/10

N2 - One of the main applications of future quantum computers will be the simulation of quantum models. While the evolution of a quantum state under a Hamiltonian is straightforward (if sometimes expensive), using quantum computers to determine the ground-state phase diagram of a quantum model and the properties of its phases is more involved. Using the Hubbard model as a prototypical example, we here show all the steps necessary to determine its phase diagram and ground-state properties on a quantum computer. In particular, we discuss strategies for efficiently determining and preparing the ground state of the Hubbard model starting from various mean-field states with broken symmetry. We present an efficient procedure to prepare arbitrary Slater determinants as initial states and present the complete set of quantum circuits needed to evolve from these to the ground state of the Hubbard model. We show that, using efficient nesting of the various terms, each time step in the evolution can be performed with just O(N) gates and O(logN) circuit depth. We give explicit circuits to measure arbitrary local observables and static and dynamic correlation functions, in both the time and the frequency domains. We further present efficient nondestructive approaches to measurement that avoid the need to reprepare the ground state after each measurement and that quadratically reduce the measurement error.

AB - One of the main applications of future quantum computers will be the simulation of quantum models. While the evolution of a quantum state under a Hamiltonian is straightforward (if sometimes expensive), using quantum computers to determine the ground-state phase diagram of a quantum model and the properties of its phases is more involved. Using the Hubbard model as a prototypical example, we here show all the steps necessary to determine its phase diagram and ground-state properties on a quantum computer. In particular, we discuss strategies for efficiently determining and preparing the ground state of the Hubbard model starting from various mean-field states with broken symmetry. We present an efficient procedure to prepare arbitrary Slater determinants as initial states and present the complete set of quantum circuits needed to evolve from these to the ground state of the Hubbard model. We show that, using efficient nesting of the various terms, each time step in the evolution can be performed with just O(N) gates and O(logN) circuit depth. We give explicit circuits to measure arbitrary local observables and static and dynamic correlation functions, in both the time and the frequency domains. We further present efficient nondestructive approaches to measurement that avoid the need to reprepare the ground state after each measurement and that quadratically reduce the measurement error.

UR - http://www.scopus.com/inward/record.url?scp=84950141895&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84950141895&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.92.062318

DO - 10.1103/PhysRevA.92.062318

M3 - Article

AN - SCOPUS:84950141895

VL - 92

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 6

M1 - 062318

ER -