Computational supplement

def labels(d): return tuple(tuple(r for r,a in p) for p in d)

def blocks(M,dk): groups = {} for i,d in enumerate(dk): groups.setdefault(labels(d),[]).append(i) for lab,ix in groups.items(): e = sum(map(len,lab)) B = np.zeros((2**e,2**e),complex) bi = i:integer([a for p in dk[i] for r,a in p]) for i in ix for i in ix: for j in ix: B[bi[i],bi[j]] += M[i,j] yield lab,B

def core_density(entries): ck = sorted(core for core,d,f in entries) ci = c:i for i,c in enumerate(ck) rk = sorted((d,f) for core,d,f in entries) ri = r:i for i,r in enumerate(rk) A = np.zeros((len(ck),len(rk)),complex) for (core,d,f),v in entries.items(): A[ci[core],ri[d,f]] += v[0] C = [email protected]().T s = np.linalg.svd(A,compute_uv=False)**2 emitted_entropy = float(-sum(x*np.log2(x) for x in s if x>1e-12)) return C,ck,emitted_entropy

def popstep(pi,law): q = [F(0)]*len(pi) for n,p in enumerate(pi): for k,r in enumerate(law[n]): q[n-k] += p*r return q

def transport_decode(M,dk,target,retain,t): out = np.zeros((2,2),complex) for lab,B in blocks(M,dk): positions = [i for i,r in enumerate([r for S in lab for r in S]) if r==target] if not positions: out += dep(B) continue e = sum(map(len,lab)) R = ptrace(B,positions,e) j = next(j for j,S in enumerate(lab) if target in S) out += R if retain or j==t-1 else (R+Z@R@Z)/2 return out

def transport_ledger(lab,target,retain,h): """S0 final direct-return path is not logged as preparation.""" q,live,held,record = h+1,0,False,False events,peak = [],0 for j,S in enumerate(lab): live += q peak = max(peak,live) events.append(["arrival",j,live]) live -= h if target in S and (retain or j==len(lab)-1): held = True events.append(["retain_target",j,live]) else: if target in S: record = True events.append(["Z_target_readout",j,live]) live -= 1 events.append(["consume_rail_or_dummy",j,live]) if held: events.append(["direct_return",len(lab),live]) live -= 1 else: live += 1 peak = max(peak,live) events.append(["prepare_eigenstate" if record else "prepare_I_over_2", len(lab),live]) live -= 1 need(live==0 and peak<=q+int(retain),"transport occupancy") return "labels":lab,"retain":retain,"events":events,"peak":peak