THC FeMoco compliation

In this notebook we provide an example of the CCZ cost model functionalities by attempting to reproduce results from section IV.C of Lee et al. 2021 (surface code compliation of quantum phase estimation on the THC-encoded Li et al. FeMoco Hamiltonian).

manual choice of distillation and data parameters

The physical costs can be computed by specifying manually the factories used for magic state distillation and the surface code parameters.

from qualtran.surface_code.gidney_fowler_model import get_ccz2t_costs
from qualtran.surface_code import CCZ2TFactory, MultiFactory, SimpleDataBlock
from qualtran.resource_counting import GateCounts

n_logical_gates = GateCounts(toffoli=6665400000) # pag. 26
n_algo_qubits = 696 # Fig. 10 
factory = MultiFactory(base_factory=CCZ2TFactory(distillation_l1_d=19, distillation_l2_d=31),
                       n_factories=4)
data_block = SimpleDataBlock(data_d=31, routing_overhead=0.5) 

cost = get_ccz2t_costs(
    n_logical_gates=n_logical_gates,
    n_algo_qubits=n_algo_qubits,
    phys_err=1e-3,
    cycle_time_us=1,
    factory=factory,
    data_block=data_block
)

print(f'failure probability: {cost.failure_prob:.3%}')
print(f'wall time: {cost.duration_hr/24} days') # ref: 3 days
print(f'footprint: {cost.footprint*1e-6:.2f} million qubits') # ref: 4 million qubits 

failure probability: 0.442%
wall time: 4.1369453125 days
footprint: 2.81 million qubits

Grid search for distillation and data code distances

Alternatively, qualtran provides a function to perform grid search over factories and data blocks, optimizing the cost (in terms of spacetime volume, total time or any other given ordering).

from qualtran.surface_code import LogicalErrorModel, QECScheme
err_model = LogicalErrorModel(qec_scheme=QECScheme.make_gidney_fowler(), physical_error=1e-3)

from qualtran.surface_code.gidney_fowler_model import (
    get_ccz2t_costs_from_grid_search,
    iter_ccz2t_factories
)

best_cost, best_factory, best_data_block = get_ccz2t_costs_from_grid_search(
    n_logical_gates=n_logical_gates,
    n_algo_qubits=n_algo_qubits,
    error_budget=1e-2,
    phys_err=err_model.physical_error,
    factory_iter=iter_ccz2t_factories(n_factories=4), # use 4 CCZ factories in parallel
    cost_function=(lambda pc: pc.duration_hr) # optimize over total time
)

distillation_error = best_factory.factory_error(n_logical_gates, logical_error_model=err_model)
data_error = best_data_block.data_error(
    n_algo_qubits=n_algo_qubits, 
    n_cycles=best_factory.n_cycles(n_logical_gates, logical_error_model=err_model),
    logical_error_model=err_model,
)

print(f"distillation error: {distillation_error:.3%}")  # ref: 0.1% per 1e10 Toffolis
print(f"data error: {data_error:.3%}")
print(f"total failure probability: {best_cost.failure_prob:.3%}")
print(f"wall time: {best_cost.duration_hr / 24} days")  # ref: 3 days
print(f"footprint: {best_cost.footprint * 1e-6:.2f} million qubits")  # ref: 4 million qubits

distillation error: 0.739%
data error: 0.033%
total failure probability: 0.773%
wall time: 3.7126432291666664 days
footprint: 2.93 million qubits

The optimization result does not match the THC paper results exactly. The cost model used is similar, but the results from the THC paper include a detailed study of the lattice surgery layout. Here, instead, we just assume a 50% space overhead for routing and we compute the time as only limited by the CCZ generation rate. The shorter runtime, at a cost of an increased number of physical qubits, might be due to this.