Surface-Code Hardware Hamiltonian

  1. Xuexin Xu,
  2. Kuljeet Kaur,
  3. Chloé Vignes,
  4. Mohammad H. Ansari,
  5. and John M. Martinis
We present a scalable framework for accurately modeling many-body interactions in surface-code quantum processor units (QPUs). Combining a concise diagrammatic formalism with high-precision
numerical methods, our approach efficiently evaluates high-order, long-range Pauli string couplings and maps complete chip layouts onto exact effective Hamiltonians. Applying this method to surface-code architectures, such as Google’s Sycamore lattice, we identify three distinct operational regimes: computationally stable, error-dominated, and hierarchy-inverted. Our analysis reveals that even modest increases in residual qubit-qubit crosstalk can invert the interaction hierarchy, driving the system from a computationally favorable phase into a topologically ordered regime. This framework thus serves as a powerful guide for optimizing next-generation high-fidelity surface-code hardware and provides a pathway to investigate emergent quantum many-body phenomena.

Absence of spin-boson quantum phase transition for transmon qubits

  1. Kuljeet Kaur,
  2. Théo Sépulcre,
  3. Nicolas Roch,
  4. Izak Snyman,
  5. Serge Florens,
  6. and Soumya Bera
Superconducting circuits are currently developed as a versatile platform for the exploration of many-body physics, both at the analog and digital levels. Their building blocks are often
idealized as two-level qubits, drawing powerful analogies to quantum spin models. For a charge qubit that is capacitively coupled to a transmission line, this analogy leads to the celebrated spin-boson description of quantum dissipation. We put here into evidence a failure of the two-level paradigm for realistic superconducting devices, due to electrostatic constraints which limit the maximum strength of dissipation. These prevent the occurence of the spin-boson quantum phase transition for transmons, even up to relatively large non-linearities. A different picture for the many-body ground state describing strongly dissipative transmons is proposed, showing unusual zero point fluctuations.