Samplers

In v0.2 there are two types of monte carlo samplers implemented:

Exact Sampler

ExactSampler, to be used only for relatively small systems, constructs the full probability distribution and samples it directly. This has exponential memory cost.

The only parameter for this sampler is the number of desired samples and an optional starting seed.

MetropolisSampler, can be used on arbitrarily big system. It samples from a Markov Chain where states are updated according to the Metropolis-Hastings rule. In a nutshell, the Metropolis sampler starts from a state sampled from the system's hilbert space, then proposes a new state according to some rule, and accepts or rejects this new state depending on some probability.

MetropolisSampler takes 3 parameters: rule, chain_length and passes. The second, chain_length specifies how many samples should the chain have, while passes specifies how many times rule must be applied between two returned samples. The effective chain length will actually be chain_length * passes, but only a fraction will be returned, in order to reduce correlation among different samples.

For ergodicity, passes should always be even.

Metropolis Rules

Local

LocalRule is a transition rule for Metropolis-Hastings sampling where at every step a random site is switched to another random state.

This rule does not preserve any particular property or symmetry of the hilbert space or of the operator.

Exchange

ExchangeRule is a transition rule for Metropolis-Hastings sampling where at every step a random couple of sites i,j is selected, and their states switched. The couples of sites i,j considered are those coupled by the hamiltonian, for example from tight binding terms.

This rule does preserve total magnetization or particle number, and related symmetries of the hamiltonian.

Operator

OperatorRule is a transition rule for Metropolis-Hastings sampling where at every step the state is changed to any other state to which it is coupled by an Operator (usually the hamiltonian).

This rule preserves symmetries of the operator.

Reference

Samplers

NeuralQuantum.ExactSampler — Type

ExactSampler(n_samples; seed=rand)

Constructs an exact sampler, which builds the full pdf of the quantum state and samples it exactly.

This sampler can only be used on indexable spaces, and should be used only for somewhat small systems (Closed N<14, Open N<7), as the computational cost increases exponentially with the number of sites.

Initial seed can be set bu specifying seed.

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NeuralQuantum.MetropolisSampler — Type

MetropolisSampler(rule, chain_length, passes; burn=0, seed=rand)

Constructs a Metropolis-Hastings sampler which samples Markov chains of length chain_length + burn, ignoring the first burn samples. Transition rules are specified by the rule rule. To reduce auto-correlation, passes number of metropolis-hastings steps are performed for each sample returned (minimum 1).

Effectively, this means that the chain is actually passes * (chain_lenght + burn) long, but only 1 every passes elements are stored and used to compute expectation values.

Initial seed can be set bu specifying seed.

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### Metropolis Rules

NeuralQuantum.LocalRule — Type

LocalRule()

Transition rule for Metropolis-Hastings sampling where at every step a random site is switched to another random state.

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NeuralQuantum.ExchangeRule — Type

ExchangeRule(graph)

Transition rule for Metropolis-Hastings sampling where at every step a random couple of sites i,j is switched.

Couples of sites are generated from the graph graph (or operator), where all sites that are connected (or coupled by a 2-body term) are considered for switches.

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NeuralQuantum.OperatorRule — Type

OperatorRule(Ô)

Transition rule for Metropolis-Hastings sampling where at every step a move is drawn from those allowed by the Operator Ô.

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