Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterising quantum materials. Recently, a series of quantum algorithms employing block-encoding of Hamiltonians have succeeded in providing efficient simulation of time-evolution operators on quantum computers. While time-independent Hamiltonians can be simulated by the quantum eigenvalue transformation (QET) or quantum singularvalue transformation with the optimal query complexity in time $t$ and desirable accuracy $\varepsilon$ , generic time-dependent Hamiltonians face at larger query complexity and more complicated oracles due to the difficulty of handling time-dependency. In this paper, we establish a QET-based approach for simulating time-dependent Hamiltonians with multiple time-periodicity. Such time-dependent Hamiltonians involve a variety of nonequilibrium systems such as time-periodic systems (Floquet systems) and time-quasiperiodic systems. Overcoming the difficulty of time-dependency, our protocol can simulate the dynamics under multi-periodic time-dependent Hamiltonians with optimal/nearly-optimal query complexity both in time $t$ and desirable accuracy $\varepsilon$ , and simple oracles as well as the optimal algorithm for time-independent cases.Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterising quantum materials. Recently, a series of quantum algorithms employing block-encoding of Hamiltonians have succeeded in providing efficient simulation of time-evolution operators on quantum computers. While time-independent Hamiltonians can be simulated by the quantum eigenvalue transformation (QET) or quantum singularvalue transformation with the optimal query complexity in time $t$ and desirable accuracy $\varepsilon$, generic time-dependent Hamiltonians face at larger query complexity and more complicated oracles due to the difficulty of handling time-dependency. In this paper, we establish a QET-based approach for simulating time-dependent Hamiltonians with multiple time-periodicity. Such time-dependent Hamiltonians involve a variety of nonequilibrium systems such as time-periodic systems (Floquet systems) and time-quasiperiodic systems. Overcoming the difficulty of time-dependency, our protocol can simulate the dynamics under multi-periodic time-dependent Hamiltonians with optimal/nearly-optimal query complexity both in time $t$ and desirable accuracy $\varepsilon$, and simple oracles as well as the optimal algorithm for time-independent cases.

arXiv:2301.06232Jan 16, 20230 citations

Optimal and nearly optimal simulation of multiperiodic time-dependent Hamiltonians

Kaoru Mizuta

Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterizing quantum materials. Recently, a series of quantum algorithms employing block encoding of Hamiltonians have succeeded in providing efficient simulation of time-evolution operators on quantum computers. While time-independent Hamiltonians can be simulated by the quantum eigenvalue transformation (QET) or quantum singular value transformation with the optimal query complexity in time $t$ and desirable accuracy $\ensuremath{\varepsilon}$, generic time-dependent Hamiltonians face at larger query complexity and more complicated oracles due to the difficulty of handling time-dependency. In this paper, we establish a QET-based approach for simulating time-dependent Hamiltonians with multiple time periodicity. Such time-dependent Hamiltonians involve a variety of nonequilibrium systems such as time-periodic systems (Floquet systems) and time-quasiperiodic systems. Overcoming the difficulty of time dependency, our protocol can simulate the dynamics under multiperiodic time-dependent Hamiltonians with optimal and nearly optimal query complexity both in time $t$ and desirable accuracy $\ensuremath{\varepsilon}$, and simple oracles as well as the optimal algorithm for time-independent cases.Simulating Hamiltonian dynamics is one of the most fundamental and significant tasks for characterizing quantum materials. Recently, a series of quantum algorithms employing block encoding of Hamiltonians have succeeded in providing efficient simulation of time-evolution operators on quantum computers. While time-independent Hamiltonians can be simulated by the quantum eigenvalue transformation (QET) or quantum singular value transformation with the optimal query complexity in time $t$ and desirable accuracy $\ensuremath{\varepsilon}$, generic time-dependent Hamiltonians face at larger query complexity and more complicated oracles due to the difficulty of handling time-dependency. In this paper, we establish a QET-based approach for simulating time-dependent Hamiltonians with multiple time periodicity. Such time-dependent Hamiltonians involve a variety of nonequilibrium systems such as time-periodic systems (Floquet systems) and time-quasiperiodic systems. Overcoming the difficulty of time dependency, our protocol can simulate the dynamics under multiperiodic time-dependent Hamiltonians with optimal and nearly optimal query complexity both in time $t$ and desirable accuracy $\ensuremath{\varepsilon}$, and simple oracles as well as the optimal algorithm for time-independent cases.

Physical Review ResearchJul 31, 20235 citations

Time dependent quadratic Hamiltonians and

P. Croxson

Physics Letters AFeb 20, 20061 citation

Derivative of Unitary is not always -iHU

A S Muddu

$i\dot{U} = HU$ (or $\dot{U} = -iHU$ ) is the equation that is said to govern the evolution of a unitary matrix $U$ given the Hamiltonian $H$ of the system. This equation is said to hold true even if the Hamiltonian is time dependent. We show iU = HU (or $\dot{U} = -iHU$ ) is the equation that is said to govern the evolution of a unitary matrix $U$ given the Hamiltonian $H$ of the system. This equation is said to hold true even if the Hamiltonian is time dependent. We show in this paper that $i\dot{U} = HU$ may not always hold for time dependent Hamiltonians.this paper that $i\dot{U} = HU$ may not always hold for time dependent Hamiltonians.$i\dot{U} = HU$ (or $\dot{U} = -iHU$) is the equation that is said to govern the evolution of a unitary matrix $U$ given the Hamiltonian $H$ of the system. This equation is said to hold true even if the Hamiltonian is time dependent. We show iU = HU (or $\dot{U} = -iHU$) is the equation that is said to govern the evolution of a unitary matrix $U$ given the Hamiltonian $H$ of the system. This equation is said to hold true even if the Hamiltonian is time dependent. We show in this paper that $i\dot{U} = HU$ may not always hold for time dependent Hamiltonians.this paper that $i\dot{U} = HU$ may not always hold for time dependent Hamiltonians.

Dec 23, 20200 citations

t

and desirable accuracy

\varepsilon

, generic time-dependent Hamiltonians face at larger query complexity and more complicated oracles due to the difficulty of handling time-dependency. In this paper, we establish a QET-based approach for simulating time-dependent Hamiltonians with multiple time-periodicity. Such time-dependent Hamiltonians involve a variety of nonequilibrium systems such as time-periodic systems (Floquet systems) and time-quasiperiodic systems. Overcoming the difficulty of time-dependency, our protocol can simulate the dynamics under multi-periodic time-dependent Hamiltonians with optimal/nearly-optimal query complexity both in time

t

and desirable accuracy

\varepsilon

, and simple oracles as well as the optimal algorithm for time-independent cases.

t

and desirable accuracy $\ensuremath{\varepsilon}$, generic time-dependent Hamiltonians face at larger query complexity and more complicated oracles due to the difficulty of handling time-dependency. In this paper, we establish a QET-based approach for simulating time-dependent Hamiltonians with multiple time periodicity. Such time-dependent Hamiltonians involve a variety of nonequilibrium systems such as time-periodic systems (Floquet systems) and time-quasiperiodic systems. Overcoming the difficulty of time dependency, our protocol can simulate the dynamics under multiperiodic time-dependent Hamiltonians with optimal and nearly optimal query complexity both in time

t

and desirable accuracy $\ensuremath{\varepsilon}$, and simple oracles as well as the optimal algorithm for time-independent cases.

i\dot{U} = HU

(or

\dot{U} = -iHU

) is the equation that is said to govern the evolution of a unitary matrix

U

given the Hamiltonian

H

of the system. This equation is said to hold true even if the Hamiltonian is time dependent. We show iU = HU (or

\dot{U} = -iHU

) is the equation that is said to govern the evolution of a unitary matrix

U

given the Hamiltonian

H

of the system. This equation is said to hold true even if the Hamiltonian is time dependent. We show in this paper that

i\dot{U} = HU

may not always hold for time dependent Hamiltonians.this paper that

i\dot{U} = HU

may not always hold for time dependent Hamiltonians.