Custom and Qiskit Gates in YAQS

Note

This is a reference guide with static code blocks; it is not executed during the documentation build. Runnable circuit examples are in Noisy Circuit Simulation and Equivalence Checking.

YAQS represents every digital gate as a BaseGate instance from GateLibrary. Circuits enter YAQS as Qiskit qiskit.circuit.QuantumCircuit objects; the library converts each DAG operation into an internal gate, then applies that gate during circuit simulation or equivalence checking.

This page explains that pipeline, how built-in and custom gates are translated, and how to supply an analytic generator when you want long-range two-qubit gates to use the TDVP window path.

How YAQS handles gates end-to-end

flowchart TD
  qc[QuantumCircuit] --> dag[DAGCircuit]
  dag --> convert[convert_dag_to_tensor_algorithm]
  convert --> hardcoded[GateLibrary alias]
  convert --> fallback[GateLibrary.custom matrix]
  hardcoded --> bg[BaseGate]
  fallback --> bg
  bg --> sim[Simulator / digital_tjm]
  bg --> equiv[EquivalenceChecker]
  sim --> mps[MPS site updates]
  equiv --> mpo[MPO or dense tensor backend]

Internal gate objects

Each BaseGate carries:

Field	Role
matrix	Dense unitary as a 2^n × 2^n complex matrix (n = number of qubits the gate acts on).
tensor	Tensor layout used in MPS/MPO contractions (for two-qubit gates: shape (2, 2, 2, 2) after set_sites).
interaction	Number of qubits (1, 2, …); inferred from matrix size (dim = 2**interaction).
sites	MPS site indices the gate acts on, set via set_sites(...).
generator	Optional. For two-qubit built-ins that support TDVP: a list of two 2×2 local operators used to build a generator MPO. Not set by plain GateLibrary.custom(...).
name	Qiskit operation name or "custom".

Built-in gates (cx, h, rxx, …) are classes on GateLibrary. GateLibrary.custom(matrix) returns a generic BaseGate backed only by the unitary matrix.

Translation from Qiskit

convert_dag_to_tensor_algorithm() walks a qiskit.dagcircuit.DAGCircuit and produces a list of BaseGate objects.

For each operation node:

1. Unsupported instructions raise ValueError: reset, delay, store, mid-circuit measure, classically controlled ops, and control-flow instructions (if_else, for_loop, …).

2. barrier nodes are skipped during conversion (ignored for unitary evolution).

3. Known Qiskit names (for example h, cx, u3, u1, swap, rxx) map to hardcoded GateLibrary classes via getattr(GateLibrary, name).

4. Any other one- or two-qubit unitary falls back to the matrix path: Qiskit’s to_matrix() / qiskit.quantum_info.Operator data is wrapped as GateLibrary.custom(matrix) with the Qiskit op.name preserved.

Note

Three-qubit and larger gates (including Toffoli / CCX) are not supported by the Qiskit translation layer. Only one- and two-qubit unitaries are accepted on the matrix fallback path.

Symbolic parameters must be bound before translation; unbound qiskit.circuit.Parameter objects raise ValueError.

Application during circuit simulation

Simulator runs digital circuits through digital_tjm:

• Single-qubit gates — contract the gate tensor onto the corresponding MPS site.

• Two-qubit gates — routed by StrongSimParams.gate_mode / WeakSimParams.gate_mode (see Configuring Simulation Parameters):

  • mpo (default) — TEBD/SVD on nearest-neighbor pairs; long-range gates via extended gate MPO.

  • swaps — TEBD with SWAP routing for long-range pairs.

  • tdvp — TEBD on nearest-neighbor pairs; long-range pairs use 2TDVP only when the gate has a generator; otherwise the MPO path is used.

  • full-tdvp — 2TDVP on every two-qubit gate that has a generator; generator-less gates fall back to TEBD (NN) or MPO (long-range).

Measurements are handled differently from unitary conversion:

• During simulation, terminal measure nodes are removed from the live DAG so evolution can proceed; sampling uses the remaining circuit structure.

• During equivalence checking, final measurements are stripped from both circuits before comparison; mid-circuit measurements raise ValueError.

Plain barrier instructions are dropped in simulation except barriers labelled SAMPLE_OBSERVABLES (used for strong-simulation layer sampling).

Equivalence checking

EquivalenceChecker compares two circuits by forming \(W = U_2^\dagger U_1\) and testing whether \(W\) is identity-like up to global phase. Custom and QASM-defined gates use the same translation path as simulation; unknown one- and two-qubit unitaries work via matrix fallback. See Equivalence Checking for backend choice (representation="mpo" recommended).

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Custom gates from Qiskit (most common)

You do not need to register custom gates manually when they come from Qiskit.

UnitaryGate

import numpy as np
from qiskit import QuantumCircuit
from qiskit.circuit.library import UnitaryGate

u = np.array([[0, 1], [1, 0]], dtype=complex)
qc = QuantumCircuit(1)
qc.append(UnitaryGate(u), [0])

YAQS translates this to a matrix-backed BaseGate named "unitary" with no generator attribute.

OpenQASM 2 custom gates

OpenQASM 2 lets you declare reusable gate bodies (fixed or parameterized) and call them like built-in instructions. Pass a file path or raw OpenQASM string directly to check() or run(), or load with qiskit.qasm2.loads / load first. Qiskit produces a qiskit.circuit.QuantumCircuit whose operations retain the user-defined gate names.

YAQS does not maintain a separate registry of QASM gate definitions. Each DAG node is translated by name: if the name matches a GateLibrary entry, the hardcoded class is used; otherwise, for one- and two-qubit gates, YAQS builds a matrix-backed gate from Qiskit’s unitary representation (matrix fallback). You do not need to inline or transpile custom gates to a fixed basis set before simulation or equivalence checking.

from mqt.yaqs import EquivalenceChecker, Simulator, State, WeakSimParams

qasm = """
OPENQASM 2.0;
include "qelib1.inc";

gate entangle a,b {
  h a;
  cx a,b;
}

qreg q[2];
entangle q[0], q[1];
"""

checker = EquivalenceChecker(representation="mpo")
checker.check(qasm, qasm)

state = State(2, initial="zeros")
Simulator(show_progress=False).run(state, qasm, WeakSimParams(shots=128, max_bond_dim=4))

The same rules apply to legacy or backend-specific Qiskit gate names that are not in the hardcoded alias list: if Qiskit can supply a unitary matrix and the gate acts on at most two qubits, translation succeeds via matrix fallback. Names that already have GateLibrary aliases (including common single-qubit parameterizations) continue to use the built-in implementations.

TDVP behaviour for matrix-backed custom gates

Matrix-backed custom gates have no analytic generator. In gate_mode="tdvp" or "full-tdvp":

Gate width	Routing
Nearest-neighbor (|i − j| = 1)	TEBD/SVD
Long-range (|i − j| > 1)	Extended gate MPO (same as gate_mode="mpo")

This is intentional: 2TDVP requires a split local generator; a bare unitary matrix does not provide one. Use gate_mode="mpo" if you want consistent long-range handling for all custom unitaries without defining generators.

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Manually defining custom gates

Use this path for library code, tests, or workflows that construct gates directly in YAQS (without Qiskit).

Matrix-only custom gate

import numpy as np
from mqt.yaqs.core.libraries.gate_library import GateLibrary

unitary = np.eye(4, dtype=complex)  # example 2-qubit unitary
gate = GateLibrary.custom(unitary)
gate.name = "my_gate"
gate.set_sites(0, 1)
# gate.matrix, gate.tensor, gate.sites are ready for TEBD/MPO application

GateLibrary.custom validates that the matrix is square with dimension \(2^n\).

For equivalence checking, comparing two circuits that use the same custom unitary (or a custom gate versus an equivalent decomposition) works the same as for built-in gates.

Subclassing BaseGate

Built-in gates subclass BaseGate and often override set_sites to set tensor, optional mpo_tensors, and— for TDVP-capable two-qubit gates—generator. See CX in gate_library for a reference implementation.

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Generators and the TDVP path

Some two-qubit GateLibrary gates (cx, cz, cp, rxx, ryy, rzz, …) define a generator: a list of two 2×2 complex matrices [G_a, G_b], one per qubit, ordered by increasing site index after set_sites.

construct_generator_mpo() embeds these local operators on the gate support and places identity 2×2 blocks elsewhere, producing an MPO that represents the sum generator on the full chain. apply_two_qubit_gate_tdvp() then runs two-site TDVP (tdvp_mode="2site") on a window around the gate for a total evolution time of 1 (split across tdvp_sweeps substeps on StrongSimParams).

The controlled-NOT gate illustrates the pattern (see source for exact matrices):

from mqt.yaqs.core.libraries.gate_library import GateLibrary

gate = GateLibrary.cx()
gate.set_sites(0, 1)
# gate.generator is a list of two 2x2 arrays, set inside set_sites
assert len(gate.generator) == 2

Routing checks getattr(gate, "generator", None) is not None in apply_two_qubit_gate(). Plain GateLibrary.custom(...) does not set generator; TDVP long-range application therefore does not activate unless you add one yourself.

Attaching a generator to a custom gate

Advanced use: if you know a two-local generator decomposition compatible with YAQS digital TDVP, you can assign it after set_sites:

import numpy as np
from mqt.yaqs.core.libraries.gate_library import GateLibrary

unitary = ...  # 4x4 unitary on qubits (i, j), i < j
G_i = ...  # 2x2 local operator on site i
G_j = ...  # 2x2 local operator on site j

gate = GateLibrary.custom(unitary)
gate.set_sites(i, j)
gate.generator = [G_i, G_j]

Warning

YAQS does not verify that exp(-i (G_i ⊗ I + I ⊗ G_j)) at evolution time 1 reproduces unitary. Deriving consistent local generators is the caller’s responsibility; use built-in gates as templates. Reversed qubit order is handled internally when building the generator MPO, but the local matrices must match the increasing site index convention used in construct_generator_mpo().

Generators apply only to two-qubit digital gates. Single-qubit custom gates always use direct MPS contraction; there is no single-qubit TDVP gate path in circuit simulation.

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Quick reference

Source	generator	TDVP long-range (gate_mode="tdvp")	Equivalence check
Built-in cx, rxx, …	Yes (in set_sites)	2TDVP window	Supported
Qiskit UnitaryGate / QASM custom	No	MPO fallback	Supported (matrix fallback)
GateLibrary.custom(matrix)	No (unless you set it)	MPO fallback	Supported
GateLibrary.custom + manual .generator	Yes (if you set it)	2TDVP window	Supported
3+ qubit Qiskit gates	—	Not translated	Not supported

Rejected Qiskit instructions (translation)

Instruction	Conversion	Simulation	Equivalence
barrier	Skipped	Removed (except SAMPLE_OBSERVABLES)	Skipped in MPO zones
Final measure	Rejected in raw conversion	Removed from DAG	Stripped before check
Mid-circuit measure	Rejected	Removed only if per-qubit terminal	ValueError
reset, delay, control-flow	Rejected	—	—

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Related topics

• Configuring Simulation Parameters — gate_mode, tdvp_sweeps, tdvp_mode

• Equivalence Checking — comparing original and transpiled circuits

• Noisy Circuit Simulation — running circuits with Simulator

• dag_utils — translation implementation and SUPPORTED_QISKIT_GATE_NAMES

• gate_library — built-in gate definitions and generator examples