quimb.tensor.circuit.pepo

PEPO simple-update circuit simulator.

Classes

CircuitPEPOSimpleUpdate

Quantum circuit simulator that evolves an observable backwards in time,

Module Contents

class quimb.tensor.circuit.pepo.CircuitPEPOSimpleUpdate(N=None, *, edges=None, gates=None, max_bond=None, cutoff=1e-10, gate_contract='reduce-split', gate_opts=None, **circuit_opts)

Bases: quimb.tensor.circuit.simple_update.CircuitSimpleUpdate

Quantum circuit simulator that evolves an observable backwards in time, in the Heisenberg picture, by representing it as an arbitrary geometry PEPO and applying the gates with the simple update rule.

Rather than evolving a state forwards, gates are simply recorded as they are applied; no contraction happens until an expectation value is requested. When local_expectation() (or get_evolved_operator()) is called, the local observable is built as a bond dimension 1 PEPO on the supplied edges and the recorded gates are applied in reverse order as \(O \rightarrow G^\dagger O G\), using tensor_network_ag_gate_simple() (Vidal-style gauging plus compression). Gates that fall outside the reverse lightcone of the observable are skipped, since \(G^\dagger G = 1\). The evolved operator is finally projected onto the |00...0> initial state.

This is the Heisenberg-picture companion to CircuitPEPSSimpleUpdate, useful on lattices where evolving the full state is intractable but a single local observable can be evolved in a truncated, gauged operator network.

Parameters:

• N (int, optional) – The number of qubits. If not given it is inferred from the geometry. Supply it to pad the geometry up to N sites.

• edges (sequence[tuple[hashable, hashable]], optional) – The edges defining the geometry. A bond is placed between each pair of sites, and two-qubit gates are only supported on these edges. If not given the geometry is inferred from the two-qubit gates.

• gates (sequence, optional) – If edges is not given, infer the geometry from the two-qubit gates in this sequence (the gates are only inspected here, not applied).

• max_bond (int, optional) – The maximum bond dimension to compress the operator to as gates are applied during the backwards evolution.

• cutoff (float, optional) – The singular value cutoff to use when compressing.

• gate_contract (str, optional) – How to split a two site gate, see tensor_network_ag_gate_simple().

• gate_opts (dict, optional) – Default options forwarded to gate_simple_ such as max_bond, cutoff and renorm. This is the single source of truth for the compression options; max_bond and cutoff are also exposed as properties.

edges

The unique edges defining the geometry.

Type:

tuple[tuple[hashable, hashable]]

sites

The sites (qubit labels).

Type:

tuple[hashable]

gates

The gates recorded so far.

Type:

tuple[Gate]

Examples

>>> import quimb.tensor as qtn
>>> edges = [(0, 1), (1, 2), (2, 3)]
>>> circ = qtn.CircuitPEPOSimpleUpdate(edges=edges, max_bond=16)
>>> circ.apply_gates(gates)            # no computation happens here
>>> circ.local_expectation(qu.pauli("Z"), 1)   # evolve + contract here

See also

CircuitPEPSSimpleUpdate, CircuitMPS

property max_bond

The maximum bond dimension to compress to.

property cutoff

The singular value cutoff to use when compressing.

_init_state(N, dtype='complex128')

_apply_gate(gate, tags=None, **gate_opts)

Apply a Gate to this Circuit. This is the main method that all calls to apply a gate should go through.

Parameters:

• gate (Gate) – The gate to apply.

• tags (str or sequence of str, optional) – Tags to add to the gate tensor(s).

apply_gates(gates, progbar=False, **gate_opts)

Apply a sequence of gates to this tensor network quantum circuit.

Parameters:

• gates (Sequence[Gate] or Sequence[Tuple]) – The sequence of gates to apply.

• gate_opts – Supplied to apply_gate().

_parse_where(where)

_initial_operator(G, where)

Build the bond dimension 1 PEPO of G acting at where and the identity elsewhere, on the circuit geometry.

get_evolved_operator(G, where, *, max_bond=None, cutoff=None)

Evolve the local observable G at where backwards through the recorded circuit, returning the Heisenberg-picture operator \(U^\dagger G U\) as a gauged PEPO. Gates outside the reverse lightcone of the observable are skipped.

Parameters:

• G (array_like) – The local operator acting on the site(s) in where.

• where (hashable or sequence[hashable]) – The site or sites the operator acts on.

• max_bond (optional) – Override the compression options for this call.

• cutoff (optional) – Override the compression options for this call.

Return type:

TensorNetworkGenOperator

get_evolved_operator_with_state(G, where, *, max_bond=None, cutoff=None)

Return the evolved operator \(U^\dagger G U\) projected onto the |00...0> initial state on both sides, i.e. the tensor network whose full contraction is \(\langle 0 | U^\dagger G U | 0 \rangle\). The physical indices are projected with isel; the caller can contract the returned network however they like.

local_expectation(G, where, *, max_bond=None, cutoff=None, optimize='auto-hq', **contract_opts)

Compute \(\langle 0 | U^\dagger G U | 0 \rangle\), the expectation of the local operator G at where in the state prepared by the recorded circuit U acting on |00...0>.

Parameters:

• G (array_like) – The local operator acting on the site(s) in where.

• where (hashable or sequence[hashable]) – The site or sites the operator acts on.

• max_bond (optional) – Override the compression options for this call.

• cutoff (optional) – Override the compression options for this call.

• optimize (str, optional) – The contraction path optimizer for the final contraction.

• contract_opts – Supplied to the final contract().

Return type:

scalar

abstractmethod _unsupported(name)

get_psi()

Get a copy of the current state tensor network. This is the single method each representation must implement to expose its state, and is what the psi property calls.

to_dense(*args, **kwargs)