Fault-Tolerant Resource Estimation

How many logical qubits and T gates would a real first-wall simulation need? Honest estimates set the horizon for Kronos quantum materials work.

Turning a use case into qubit and gate counts

Resource estimation is the discipline of computing, before any hardware exists, how large a fault-tolerant machine a target problem needs. For a first-wall or blanket electronic-structure calculation this means counting logical qubits (from the number of spin-orbitals) and non-Clifford T gates (from the qubitization query cost and target precision).

# Rough scaling for a QPE/qubitization chemistry run:
logical_qubits  ~  O(N)          # N = spin-orbitals in active space
T_gate_count    ~  O( N^3 / eps )  to  O( N^4 )   (method-dependent)
#   eps = target energy error (chemical accuracy ~1.6e-3 Hartree)
# then multiply by surface-code overhead for PHYSICAL resources

Why the numbers are sobering

Even a modest correlated active space, tens of spin-orbitals, translates into hundreds to low thousands of logical qubits and billions to trillions of T gates once precision is demanded. Each logical qubit is hundreds of physical qubits under the surface code, and T gates require magic-state distillation factories that dominate footprint and runtime.

# Illustrative chain for a small first-wall defect cluster:
N ~ 50 spin-orbitals
  -> ~10^2 logical qubits
  -> ~10^9-10^{12} T gates for chemical accuracy
  -> x (10^2-10^3 physical qubits/logical) = 10^4-10^5 physical qubits
  -> plus distillation -> runtime hours-to-days on a machine not yet built

What Kronos does with these numbers

• Prioritize use cases: the smallest active space that answers a real first-wall question comes first.
• Track hardware roadmaps against these targets to know when, not whether, to invest.
• Refuse to promise results the resource estimate says are a decade-plus away.

Resource estimation is how we stay honest: it converts vague quantum optimism into concrete, checkable requirements. It is also why the Kronos machines' physics, validated at FOAK around 2030, will not wait on quantum computing for any decision. Quantum materials simulation is a patient bet whose payoff, if it comes, benefits fleet-scale material choices. See the roadmap.