Currently, laser cooling schemes are fundamentally based on the weak coupling regime. This requirement sets the trap frequency as an upper bound to the cooling rate. In this work we present a numerical study that shows the feasibility of cooling in the strong-coupling regime which then allows cooling rates that are faster than the trap frequency with experimentally feasible parameters. The scheme presented here can be applied to trapped atoms or ions as well as to mechanical oscillators. It can also cool medium sized ion chains close to the ground state.Currently, laser cooling schemes are fundamentally based on the weak coupling regime. This requirement sets the trap frequency as an upper bound to the cooling rate. In this work we present a numerical study that shows the feasibility of cooling in the strong-coupling regime which then allows cooling rates that are faster than the trap frequency with experimentally feasible parameters. The scheme presented here can be applied to trapped atoms or ions as well as to mechanical oscillators. It can also cool medium sized ion chains close to the ground state.

arXiv:1001.2714Physical Review LettersMay 6, 201034 citations

LASER COOLING

WORLD SCIENTIFIC eBooksJul 1, 19980 citations

Bravyi-Kitaev Superfast simulation of electronic structure on a quantum computer

Kanav Setia, James D. Whitfield

Present quantum computers often work with distinguishable qubits as their computational units. In order to simulate indistinguishable fermionic particles, it is first required to map the fermionic state to the state of the qubits. The Bravyi-Kitaev Superfast (BKSF) algorithm can be used to accomplish this mapping. The BKSF mapping has connections to quantum error correction and opens the door to new ways of understanding fermionic simulation in a topological context. Here, we present the first detailed exposition of the BKSF algorithm for molecular simulation. We provide the BKSF transformed qubit operators and report on our implementation of the BKSF fermion-to-qubits transform in OpenFermion. In this initial study of a hydrogen molecule we have compared BKSF, Jordan-Wigner, and Bravyi-Kitaev transforms under the Trotter approximation. The gate count to implement BKSF is lower than Jordan-Wigner but higher than Bravyi-Kitaev. We considered different orderings of the exponentiated terms and found lower Trotter errors than the previously reported for Jordan-Wigner and Bravyi-Kitaev algorithms. These results open the door to the further study of the BKSF algorithm for quantum simulation.Present quantum computers often work with distinguishable qubits as their computational units. In order to simulate indistinguishable fermionic particles, it is first required to map the fermionic state to the state of the qubits. The Bravyi-Kitaev Superfast (BKSF) algorithm can be used to accomplish this mapping. The BKSF mapping has connections to quantum error correction and opens the door to new ways of understanding fermionic simulation in a topological context. Here, we present the first detailed exposition of the BKSF algorithm for molecular simulation. We provide the BKSF transformed qubit operators and report on our implementation of the BKSF fermion-to-qubits transform in OpenFermion. In this initial study of a hydrogen molecule we have compared BKSF, Jordan-Wigner, and Bravyi-Kitaev transforms under the Trotter approximation. The gate count to implement BKSF is lower than Jordan-Wigner but higher than Bravyi-Kitaev. We considered different orderings of the exponentiated terms and found lower Trotter errors than the previously reported for Jordan-Wigner and Bravyi-Kitaev algorithms. These results open the door to the further study of the BKSF algorithm for quantum simulation.

arXiv:1712.00446The Journal of Chemical PhysicsApr 25, 2018110 citations

Analysis of superfast encoding performance for electronic structure simulations

Riley W. Chien, Sha Xue, Tarini Hardikar +2 more

In our recent work, we examined various fermion-to-qubit mappings in the context of quantum simulation including the original Bravyi-Kitaev superfast encoding (OSE) as well as a generalized version (GSE). We return to OSE and compare it against the Jordan-Wigner (JW) transform for quantum chemistry considering the number of qubits required, the Pauli weight of terms in the transformed Hamiltonians, and the ${L}_{1}$ norm of the Hamiltonian. We considered a test set of molecular systems known as the Atomization Energy 6 (AE6) as well as hydrogen lattices. Our results showed that the resource efficiency of OSE is strongly affected by the spatial locality of the underlying single-particle basis. We find that OSE is outperformed by JW when the orbitals in the underlying single-particle basis are highly overlapping, which limits its applicability to near-term quantum chemistry simulations utilizing standard basis sets. In contrast, when orbitals are overlapping with only few others, as is the case of hydrogen lattices with very tight orbitals, OSE fares comparatively better. Our results illustrate the importance of choosing the right combination of basis sets and fermion-to-qubit mapping to get the most out of a quantum device when simulating physical systems.In our recent work, we examined various fermion-to-qubit mappings in the context of quantum simulation including the original Bravyi-Kitaev superfast encoding (OSE) as well as a generalized version (GSE). We return to OSE and compare it against the Jordan-Wigner (JW) transform for quantum chemistry considering the number of qubits required, the Pauli weight of terms in the transformed Hamiltonians, and the ${L}_{1}$ norm of the Hamiltonian. We considered a test set of molecular systems known as the Atomization Energy 6 (AE6) as well as hydrogen lattices. Our results showed that the resource efficiency of OSE is strongly affected by the spatial locality of the underlying single-particle basis. We find that OSE is outperformed by JW when the orbitals in the underlying single-particle basis are highly overlapping, which limits its applicability to near-term quantum chemistry simulations utilizing standard basis sets. In contrast, when orbitals are overlapping with only few others, as is the case of hydrogen lattices with very tight orbitals, OSE fares comparatively better. Our results illustrate the importance of choosing the right combination of basis sets and fermion-to-qubit mapping to get the most out of a quantum device when simulating physical systems.

arXiv:1907.02976Physical Review ASep 30, 201910 citations

Laser Cooling

Springer eBooksNov 9, 20050 citations

{L}_{1}

norm of the Hamiltonian. We considered a test set of molecular systems known as the Atomization Energy 6 (AE6) as well as hydrogen lattices. Our results showed that the resource efficiency of OSE is strongly affected by the spatial locality of the underlying single-particle basis. We find that OSE is outperformed by JW when the orbitals in the underlying single-particle basis are highly overlapping, which limits its applicability to near-term quantum chemistry simulations utilizing standard basis sets. In contrast, when orbitals are overlapping with only few others, as is the case of hydrogen lattices with very tight orbitals, OSE fares comparatively better. Our results illustrate the importance of choosing the right combination of basis sets and fermion-to-qubit mapping to get the most out of a quantum device when simulating physical systems.