MPS Backend

The MPS (Matrix Product State) backend is the default backend and the package's namesake: it represents the quantum state as a matrix product state via ITensors.jl and ITensorMPS.jl, truncating the bond dimension at every gate application according to cutoff/maxdim. This is what lets it scale to L = 100+ qubits for the entangling-but-not- maximally-entangling circuits typical of MIPT/CIPT studies, at the cost of a controlled truncation error.

When to use it: the general-purpose default — production runs at L = 100+, or any circuit whose entanglement growth stays bounded by a reasonable maxdim (measurement-induced and control-induced phase transitions are exactly this regime, by construction: measurements and resets keep entanglement in check).

When not to use it: when you need an exact zero-truncation-error reference (see State Vector Backend), or when the circuit is built entirely from Clifford-group gates and you want to push L into the hundreds or thousands (see Clifford Backend).

Quick Example

using QuantumCircuitsMPS

state = SimulationState(L=12, bc=:periodic, maxdim=64,
    rng=RNGRegistry(gates_spacetime=42, gates_realization=1, born_measurement=2))
initialize!(state, ProductState(binary_int=0))
track!(state, :entropy => EntanglementEntropy(; cut=6))

apply!(state, HaarRandom(), Bricklayer(:even))
apply!(state, HaarRandom(), Bricklayer(:odd))
record!(state)
println("Entropy: $(state.observables[:entropy][end])")

backend=:mps is the default and can be omitted from SimulationState(...). cutoff (SVD truncation threshold, default 1e-10) and maxdim (maximum bond dimension, default 100) are MPS-only keywords — they are silently ignored on the other two backends for cross-backend API consistency (see the Backend Interface Contract).

Internal Engine

Every apply! call resolves a gate to an ITensor via build_operator, then contracts and truncates it back into the MPS via apply_op_internal! (SVD-based contraction with re-orthogonalization). See Design Philosophy for the full layered picture and Backend Interface Contract for the developer-facing method table every backend (including this one) must implement.

PBC Indexing Caveat

Under bc=:periodic, the MPS backend stores sites in a folded RAM ordering (src/Core/basis.jl) so that periodic boundary conditions can be represented by a 1-D chain topology. All public geometry/gate/observable APIs speak physical site indices and translate transparently — except EntanglementEntropy(cut=k), whose cut is the RAM bond index of the folded MPS, not the physical bipartition {1..k} (only cut = L÷2 is fold-aligned). See the Backend Interface Contract's PBC section and EntropyProfile's docstring for the full detail; cross-backend entropy comparisons under PBC should use cut = L÷2 or bc=:open.