Algorithms

Ground state computation

Using DMRG, we can compute ground states for States and Simulations

ITensorMPS.dmrg — Function

dmrg(hamiltonian, ::State; options...)
dmrg(hamiltonian, ::Simulation; options...)

optimize for ground state of the given Hamiltonian starting with state / simulation using dmrg.

Note that Dmrg does not work for mixed representations.

Options

nsweeps: number of sweeps
observer!: observer (see DmrgObserver)
limits: constraints on the mps (cutoff and `maxdim may be vectors with different values for each sweep)
others identical to ITensorMPS.dmrg

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TensorMixedStates.DmrgObserver — Type

struct DmrgObserver
DmrgObserver(sim, measurements, period, tol)

an observer for dmrg which makes and outputs measurements every period steps and stops it when energy improvements are smaller than tol

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Time evolution

Using TDVP or ApproxW, we can do time evolution (Hamiltonian or Lindbladian)

ITensorMPS.tdvp — Function

tdvp(evolver, t, ::State; options...)
tdvp(evolver, t, ::Simulation; options...)

do time evolution with tdvp algorithm on a state / sim for the given time t. Also see TdvpObserver

Options

nsweeps: number sweeps to do (time step = t / nsweeps)
coefs: coefficients for time dependent evolver
n_expand: do expansion steps every n_expand steps (default 0 means no expansion)
n_hermitianize: make hermitian (for mixed states) every n_hermitianize steps (default 0 for no corrections)
others are identical to ITensorMPS.tdvp

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TensorMixedStates.approx_W — Function

approx_W(evolver, t, ::State; options...)
approx_W(evolver, t, ::Simulation; options...)

time evolution using approximation WI or WII at a given order. Also see ApproxWObserver

Options

coefs: coefficients for time dependent evolution
n_hermitianize: make hermitian (for mixed states) every n_hermitianize steps (default 0 for no corrections)
nsweeps: number of steps (time step is t / nsweeps)
order: order of approximation
w: 1 or 2 for WI or WII
observer!: observer (see ApproxWObserver)
time_start: the simulation time at the beginning of evolution
limits: MPS constraints

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TensorMixedStates.TdvpObserver — Type

struct TdvpObserver
TdvpObserver(sim, measurements, period)

an observer for tdvp which make measurements every period steps

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TensorMixedStates.ApproxWObserver — Type

struct ApproxWObserver
ApproxWObserver(sim, measurements, period)

an observer for approx_W which make measurements every period steps

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Gate application

ITensors.apply — Function

apply(op, ::State; limits::Limits)
apply(mps, ::State; limits::Limits)
apply(op, ::Simulation; limits::Limits)

Apply the given gates to the state and truncate the result according to limits. It is much more efficient to apply all the gates in a single call to apply.

Examples

apply(CZ(1,3)*H(2)*CNOT(3,4), state)

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