Estimating the ground-state probability of a quantum simulation with product-state measurements
.One of the goals in quantum simulation is to adiabatically generate the ground state of a complicated Hamiltonian by starting with the ground state of a simple Hamiltonian and slowly evolving the system to the complicated one. If the evolution is adiabatic and the initial and final ground states ar...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2015-10-01
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| Series: | Frontiers in Physics |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fphy.2015.00085/full |
| _version_ | 1811228323245719552 |
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| author | Bryce eYoshimura James eFreericks |
| author_facet | Bryce eYoshimura James eFreericks |
| author_sort | Bryce eYoshimura |
| collection | DOAJ |
| description | .One of the goals in quantum simulation is to adiabatically generate the ground state of a complicated Hamiltonian by starting with the ground state of a simple Hamiltonian and slowly evolving the system to the complicated one. If the evolution is adiabatic and the initial and final ground states are connected due to having the same symmetry, then the simulation will be successful. But in most experiments, adiabatic simulation is not possible because it would take too long, and the system has some level of diabatic excitation. In this work, we quantify the extent of the diabatic excitation even if we do not know {it a priori} what the complicated ground state is. Since many quantum simulator platforms, like trapped ions, can measure the probabilities to be in a product state, we describe techniques that can employ these simple measurements to estimate the probability of being in the ground state of the system after the diabatic evolution. These techniques do not require one to know any properties about the Hamiltonian itself, nor to calculate its eigenstate properties. All the information is derived by analyzing the product-state measurements as functions of time. |
| first_indexed | 2024-04-12T09:56:05Z |
| format | Article |
| id | doaj.art-1b58d924f4e5451f86acfd0cf85505e6 |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-04-12T09:56:05Z |
| publishDate | 2015-10-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-1b58d924f4e5451f86acfd0cf85505e62022-12-22T03:37:41ZengFrontiers Media S.A.Frontiers in Physics2296-424X2015-10-01310.3389/fphy.2015.00085166025Estimating the ground-state probability of a quantum simulation with product-state measurementsBryce eYoshimura0James eFreericks1Deparment of Physics, Georgetown UniverisityDeparment of Physics, Georgetown Univerisity.One of the goals in quantum simulation is to adiabatically generate the ground state of a complicated Hamiltonian by starting with the ground state of a simple Hamiltonian and slowly evolving the system to the complicated one. If the evolution is adiabatic and the initial and final ground states are connected due to having the same symmetry, then the simulation will be successful. But in most experiments, adiabatic simulation is not possible because it would take too long, and the system has some level of diabatic excitation. In this work, we quantify the extent of the diabatic excitation even if we do not know {it a priori} what the complicated ground state is. Since many quantum simulator platforms, like trapped ions, can measure the probabilities to be in a product state, we describe techniques that can employ these simple measurements to estimate the probability of being in the ground state of the system after the diabatic evolution. These techniques do not require one to know any properties about the Hamiltonian itself, nor to calculate its eigenstate properties. All the information is derived by analyzing the product-state measurements as functions of time.http://journal.frontiersin.org/Journal/10.3389/fphy.2015.00085/fullquantum simulationion trapTransverse field Ising modeladiabatic state preparationground state probability |
| spellingShingle | Bryce eYoshimura James eFreericks Estimating the ground-state probability of a quantum simulation with product-state measurements Frontiers in Physics quantum simulation ion trap Transverse field Ising model adiabatic state preparation ground state probability |
| title | Estimating the ground-state probability of a quantum simulation with product-state measurements |
| title_full | Estimating the ground-state probability of a quantum simulation with product-state measurements |
| title_fullStr | Estimating the ground-state probability of a quantum simulation with product-state measurements |
| title_full_unstemmed | Estimating the ground-state probability of a quantum simulation with product-state measurements |
| title_short | Estimating the ground-state probability of a quantum simulation with product-state measurements |
| title_sort | estimating the ground state probability of a quantum simulation with product state measurements |
| topic | quantum simulation ion trap Transverse field Ising model adiabatic state preparation ground state probability |
| url | http://journal.frontiersin.org/Journal/10.3389/fphy.2015.00085/full |
| work_keys_str_mv | AT bryceeyoshimura estimatingthegroundstateprobabilityofaquantumsimulationwithproductstatemeasurements AT jamesefreericks estimatingthegroundstateprobabilityofaquantumsimulationwithproductstatemeasurements |