Doped Clifford Sampling #245

Circuit ID

ibm_boston_dcs_nq64_depth73_checks12

Circuit file

dcs_nq64_depth73_checks12_t314.qasm.zip

Qubits

64 logical (76 physical)

Gates

2,336 logical CZ (2,644 physical CZ), 314 logical T

Problem category

Active candidates

Problem description

Doped Clifford Sampling

We demonstrate doped Clifford sampling on a 64-qubit, depth-73 circuit with 314 T gates. The qubits are arranged on a ring. The circuit is protected in the quantum experiment by spacetime codes using 12 ancilla qubits, yielding a fidelity of 0.38(1) after post-selection on the zero-syndrome of the code.

Verification process

Verification is by lower-bounding the fidelity of the prepared state, even when it is beyond simulation.
An encoded Clifford circuit’s state fidelity F1 and its syndrome distributions S1 are measured efficiently. The circuit is doped with T gates that commute with code stabilizers, yielding statistically indistinguishable syndromes S2. This leads to a lower bound on the fidelity F2 of the (hard) doped circuit. The code projects both states to the same subspace, and doping only rotates within this subspace. A lower bound on F2 can be efficiently estimated from the classification of Pauli faults affecting the Clifford circuit. The set of rejected faults and the no-fault probability remain invariant with doping. Any loss in fidelity is only possible due to the conversion of harmless faults, which are rare in random Cliffords.

Experimental results

We see experimentally that the (easy) Clifford and the (hard) doped circuits have the same post-selection probability.. we can also numerically bound the probability of harmless faults in our circuit instance. We therefore obtain a lower bound of 0.349 with 95% confidence.

We can also validate this further by doping with lower amounts of magic such that the circuit remains simulable. We observe a fidelity consistent with our estimated lower bound across these doping regimes, as well as consistent code syndromes.

Classical simulation cost

We explored many classical simulation methods, including tensor network contraction, Clifford+T simulation, and hybrid methods combining the two. The best classical runtime estimate is shown below.

We ran Cotengra’s hyper optimizer on our circuit truncated at various depths and compared the contraction cost (in FLOPs, left panel) and contraction memory (in number of complex scalars, right panel) with those of the deterministic paths. In a first run, we imposed no memory limitation (w = ∞). At depth 73, the deterministic and Cotengra paths have maximum tensor sizes of 264 and 271 scalars, respectively. In a second run, we limited the maximum memory footprint to 243 scalars (w = 43), resulting in higher contraction costs. Solid lines show the deterministic paths, plus markers show the best completed cotengra paths, and open circles show the exact minimum unsliced widths certified by Ratcatcher.

Name

ibm_boston_dcs_nq64_depth73_checks12

Value

0.38

Method

Quantum

Method proof

Preprint: https://arxiv.org/abs/2607.25941

Quantum runtime (seconds)

870

Classical runtime (seconds)

No response

Compute resources (quantum)

IBM Heron r3 (ibm_boston)

Compute resources (classical)

No response

Notes

No response

Authors

Simon Martiel, Jay-U Chung, Alireza Seif, Soumik Ghosh, Ian Hincks, Abhinav Deshpande, Hidetaka Manabe, Hanfeng Gu, Feng Pan, Bill Fefferman, Jay M. Gambetta, and Ali Javadi-Abhari

Institutions

IBM, UChicago, Singapore University of Technology and Design, Nvidia