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 |
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ASJC Scopus subject areas
- Atomic and Molecular Physics, and Optics
Cite this
Solving strongly correlated electron models on a quantum computer. / Wecker, Dave; Hastings, Matthew B.; Wiebe, Nathan; Clark, Bryan K; Nayak, Chetan; Troyer, Matthias.
In: Physical Review A - Atomic, Molecular, and Optical Physics, Vol. 92, No. 6, 062318, 10.12.2015.Research output: Contribution to journal › Article
}
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.
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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 -