Qiskit Spacetime Bridge

Outcome-code and spacetime-code construction for Qiskit Clifford circuits, implementing Algorithm 1 and the back-cumulant construction (Section 5.1) from Delfosse & Paetznick, "Spacetime codes of Clifford circuits" (arXiv:2304.05943).

Install

pip install -e .

Depends on qiskit>=2.0,<3 and numpy. Confirmed installing and running correctly from a built wheel in a clean virtualenv (not just from source).

Usage

from qiskit import QuantumCircuit
from spacetime_bridge import Circuit, analyze

qc = QuantumCircuit(2, 2)
qc.measure(0, 0)
qc.measure(1, 1)
qc.cx(0, 1)
qc.measure(1, 1)   # redundant: forced to equal the XOR of the first two

circuit = Circuit.from_qiskit_circuit(qc)
checks, depth = circuit.finalize()
generators = [circuit.build_spacetime_generator(tag) for (_, tag) in checks]
analyze(generators)

Supported instructions: h, s, sdg, cx, measure (Z-basis, as standard for Qiskit). Anything else raises NotImplementedError rather than silently mishandling it.

What's implemented and validated

• algorithm1.py — Algorithm 1 (outcome code), augmented stabilizer tableau with sign-only phase tracking (justified in-module). 7 tests including two specifically stressing sign correctness.
• spacetime.py — back-cumulant construction (Section 5.1) turning each outcome-code check into a spacetime stabilizer generator. One test case independently hand-verified against the paper's closed-form formula (Proposition 2), separately from the iterative code.
• Circuit.from_qiskit_circuit — real integration with qiskit.QuantumCircuit (not a standalone reimplementation with a Qiskit-flavored API). Validated against a real Qiskit circuit reproducing the hand-verified CNOT case.
• analysis.py — symplectic matrix conversion, [[N,K]] parameters (Theorem 2), pairwise-commutativity sanity check.
• Full test suite re-verified against the actual built wheel installed in a clean virtualenv, not just against local source files.

What's explicitly NOT implemented (honest scope limits)

• No CZ or SWAP gate rules — same pattern as H/S/CNOT to add.
• No Algorithm 3 (LDPC sparsification) or logical operators (Proposition 10) — the harder phase-2 work; not started.
• No code distance or distance bound anywhere — distance requires logical operators; a generator's weight is not a valid stand-in, and analyze() explicitly does not report one.
• One level per instruction, not true parallel scheduling — always correct, but produces larger/non-minimal spacetime codes than an optimally-scheduled circuit would. Improving this is a performance concern, not correctness.
• analysis.py is a generic, package-agnostic implementation — not wired into qiskit-cayley-codes' actual CDZ analysis code (that source wasn't available in the session this was built in). to_symplectic_matrix()'s output is the standard stabilizer-matrix format and should drop in directly once that wiring happens.

Running the tests

pip install -e ".[test]"
pytest tests/

All currently pass.