Computational supplement

def solver_audit(benchN,bench_error): tests = [("identity",(a,b):E for a,b,E in units(),0.), ("constant",(a,b):dep(E) for a,b,E in units(),.75), ("dephasing",(a,b):(E+Z@E@Z)/2 for a,b,E in units(),.5), ("flagged_even",benchN,bench_error)] for name,N,target in tests: result = recovery(N,"validation_"+name) check("solver_expected_"+name,np.array(result["estimate"]), np.array(target),STOL) check("solver_achieved_"+name, np.array(result["achieved_distance"]["repaired_dual"]), np.array(target),STOL) DATA["records"].append("validation":name,"result":result)

def dashboard(entries,pi,K,U,t,name): A,dk,ek = dense(entries) N = channel(A) check(name+"_isometry",A.reshape(-1,2).conj()[email protected](-1,2),I) C,ck,SDF = core_density(entries) actual_pi = np.array([sum(C[i,i].real for i,(m,b) in enumerate(ck) if m==n) for n in range(K+1)]) check(name+"_population",actual_pi,np.array(list(map(float,pi)))) check(name+"_entropy_purity",np.array(entropy(C)),np.array(SDF)) ec = sum(n*float(p) for n,p in enumerate(pi)) ed = sum(N[0,0][i,i].real*sum(len(p) for p in d) for i,d in enumerate(dk)) ef = sum(np.linalg.norm(A[:,i,0])**2*sum(len(p) for p in f) for i,(core,f) in enumerate(ek)) check(name+"_energy",np.array(ec+ed+ef),np.array(float(K))) save(name+"_channel",A=A,core=C,Choi=choi(N)) return A,dk,N,"population":list(map(float,pi)), "emitted_count_distribution":list(reversed(list(map(float,pi)))), "S_core":entropy(C),"S_accessible":entropy(N[0,0]),"S_DF":SDF, "decoupling":decoupling(A),"energy":[ec,ed,ef]