Fig. 1: Frequency optimization.
From: Optimizing quantum gates towards the scale of logical qubits
a Our quantum processor with N = 68 frequency-tunable superconducting transmon qubits represented as a graph. Nodes are qubits (e.g., black dot) and edges are engineered interactions between them (e.g., blue and green bars). b A quantum algorithm (A) comprising single- and two-qubit gates with one qubit (qj) distinguished. c Corresponding qubit frequency trajectories (F), parameterized by single-qubit idle (fj for qubit qj) and two-qubit interaction (fij for qi and qj) frequencies. Quantum computational errors depend strongly on frequency trajectories since most physical error mechanisms are frequency dependent (red dots are non-exhaustive examples). Namely, pulse distortion errors (1) increase with larger frequency excursions. Relaxation errors (2) increase near relaxation hotspots, for example due to two-level-system defects (TLS, horizontal resonance). Stray coupling errors (3) increase near frequency collisions between coupled computational elements. Dephasing errors (4) increase towards lower frequencies, where qubit flux-sensitivity grows. d We leverage our understanding of physical error mechanisms (M) to estimate the algorithm’s error (E) and then optimize it with respect to qubit frequency trajectories. e We employ the Snake optimizer, which can solve optimization problems at an arbitrary dimension (D), controlled by the scope parameter (S). These graphs show possible idle (nodes) and interaction (edges) frequency optimization variables (blue) at one Snake optimization step for scopes ranging from \(S={S}_{\max }\) (global limit, ∣F∣D optimization) to S = 1 (local limit, 1D optimization). f Snake optimization threads (progress horizontally) for three scopes (increase downwards). Snake’s high configurability enables it to scalably overcome frequency optimization complexity and be adapted to a variety of quantum operations, algorithms, and architectures.
