%% quantum_process_network.erl %% Quantum-inspired process networks using Erlang's actor model %% Simulates quantum entanglement, superposition, and interference for agent coordination -module(quantum_process_network). -behaviour(gen_server). -export([ start_link/0, create_quantum_entanglement/2, put_process_in_superposition/2, collapse_superposition/2, measure_quantum_state/1, create_quantum_interference/3, implement_quantum_tunneling/3, quantum_teleport_state/3, create_quantum_circuit/2, execute_quantum_algorithm/2 ]). -export([init/1, handle_call/3, handle_cast/2, handle_info/2, terminate/2, code_change/3]). -define(QUANTUM_REGISTRY, quantum_process_registry). -define(ENTANGLEMENT_TABLE, quantum_entanglements). -define(SUPERPOSITION_TABLE, quantum_superpositions). -record(state, { quantum_processes = #{}, entanglement_pairs = #{}, superposition_states = #{}, quantum_circuits = #{}, measurement_observers = #{}, decoherence_timers = #{}, quantum_noise_level = 0.01 }). -record(quantum_process, { pid, quantum_id, state_vector = #{}, entangled_with = [], in_superposition = false, coherence_time, last_measurement, quantum_gates_applied = [], fidelity = 1.0 }). -record(entanglement_pair, { process1_id, process2_id, entanglement_strength = 1.0, bell_state, created_at, maintained_operations = 0, decoherence_rate = 0.001 }). -record(superposition_state, { process_id, basis_states = #{}, amplitude_weights = #{}, phase_relations = #{}, coherence_time, collapse_probability_func }). -record(quantum_gate, { type, target_qubits, parameters = #{}, execution_time, success_probability = 1.0 }). %% Public API start_link() -> gen_server:start_link({local, ?MODULE}, ?MODULE, [], []). %% Create quantum entanglement between two processes create_quantum_entanglement(ProcessId1, ProcessId2) -> gen_server:call(?MODULE, {create_entanglement, ProcessId1, ProcessId2}). %% Put a process into quantum superposition with multiple possible states put_process_in_superposition(ProcessId, BasisStates) -> gen_server:call(?MODULE, {create_superposition, ProcessId, BasisStates}). %% Collapse superposition and return definite state collapse_superposition(ProcessId, ObservationContext) -> gen_server:call(?MODULE, {collapse_superposition, ProcessId, ObservationContext}). %% Measure quantum state without collapsing (weak measurement) measure_quantum_state(ProcessId) -> gen_server:call(?MODULE, {measure_state, ProcessId}). %% Create quantum interference between multiple process states create_quantum_interference(ProcessIds, InterferencePattern, TargetOutcome) -> gen_server:call(?MODULE, {create_interference, ProcessIds, InterferencePattern, TargetOutcome}). %% Implement quantum tunneling through computational barriers implement_quantum_tunneling(ProcessId, Barrier, TargetState) -> gen_server:call(?MODULE, {quantum_tunnel, ProcessId, Barrier, TargetState}). %% Quantum teleportation of process state quantum_teleport_state(SourceId, TargetId, StateToTeleport) -> gen_server:call(?MODULE, {quantum_teleport, SourceId, TargetId, StateToTeleport}). %% Create quantum circuit with multiple gates create_quantum_circuit(CircuitId, QuantumGates) -> gen_server:call(?MODULE, {create_circuit, CircuitId, QuantumGates}). %% Execute quantum algorithm on process network execute_quantum_algorithm(AlgorithmType, Parameters) -> gen_server:call(?MODULE, {execute_algorithm, AlgorithmType, Parameters}). %% Gen_server callbacks init([]) -> % Create ETS tables for quantum state management ets:new(?QUANTUM_REGISTRY, [named_table, public, {keypos, #quantum_process.quantum_id}]), ets:new(?ENTANGLEMENT_TABLE, [named_table, public, set]), ets:new(?SUPERPOSITION_TABLE, [named_table, public, {keypos, #superposition_state.process_id}]), % Start quantum decoherence monitor spawn_link(fun() -> quantum_decoherence_monitor() end), % Initialize quantum random number generator initialize_quantum_rng(), {ok, #state{}}. handle_call({create_entanglement, ProcessId1, ProcessId2}, _From, State) -> Result = establish_quantum_entanglement(ProcessId1, ProcessId2, State), {reply, Result, State}; handle_call({create_superposition, ProcessId, BasisStates}, _From, State) -> Result = create_process_superposition(ProcessId, BasisStates, State), NewState = update_superposition_state(ProcessId, Result, State), {reply, Result, NewState}; handle_call({collapse_superposition, ProcessId, Context}, _From, State) -> {Result, NewState} = perform_superposition_collapse(ProcessId, Context, State), {reply, Result, NewState}; handle_call({measure_state, ProcessId}, _From, State) -> Result = perform_weak_measurement(ProcessId, State), {reply, Result, State}; handle_call({create_interference, ProcessIds, Pattern, Target}, _From, State) -> Result = implement_quantum_interference(ProcessIds, Pattern, Target, State), {reply, Result, State}; handle_call({quantum_tunnel, ProcessId, Barrier, TargetState}, _From, State) -> Result = execute_quantum_tunneling(ProcessId, Barrier, TargetState, State), {reply, Result, State}; handle_call({quantum_teleport, SourceId, TargetId, StateData}, _From, State) -> Result = perform_quantum_teleportation(SourceId, TargetId, StateData, State), {reply, Result, State}; handle_call({create_circuit, CircuitId, Gates}, _From, State) -> NewState = add_quantum_circuit(CircuitId, Gates, State), {reply, ok, NewState}; handle_call({execute_algorithm, Algorithm, Parameters}, _From, State) -> Result = run_quantum_algorithm(Algorithm, Parameters, State), {reply, Result, State}; handle_call(_Request, _From, State) -> {reply, {error, unknown_request}, State}. handle_cast({decoherence_event, ProcessId}, State) -> NewState = handle_quantum_decoherence(ProcessId, State), {noreply, NewState}; handle_cast({quantum_noise, NoiseLevel}, State) -> NewState = State#state{quantum_noise_level = NoiseLevel}, {noreply, NewState}; handle_cast(_Msg, State) -> {noreply, State}. handle_info({quantum_measurement, ProcessId, Result}, State) -> NewState = process_measurement_result(ProcessId, Result, State), {noreply, NewState}; handle_info({entanglement_maintenance, PairId}, State) -> maintain_entanglement_pair(PairId), {noreply, State}; handle_info(_Info, State) -> {noreply, State}. terminate(_Reason, _State) -> ok. code_change(_OldVsn, State, _Extra) -> {ok, State}. %% Quantum Operations Implementation establish_quantum_entanglement(ProcessId1, ProcessId2, State) -> % Create Bell state entanglement between two processes BellState = create_bell_state(plus), EntanglementPair = #entanglement_pair{ process1_id = ProcessId1, process2_id = ProcessId2, bell_state = BellState, entanglement_strength = 1.0, created_at = erlang:system_time(microsecond) }, % Store entanglement relationship PairId = generate_entanglement_id(ProcessId1, ProcessId2), ets:insert(?ENTANGLEMENT_TABLE, {PairId, EntanglementPair}), % Notify processes of entanglement notify_processes_of_entanglement([ProcessId1, ProcessId2], PairId), % Start entanglement maintenance schedule_entanglement_maintenance(PairId), {ok, #{ pair_id => PairId, bell_state => BellState, entanglement_strength => 1.0, estimated_coherence_time => calculate_coherence_time(ProcessId1, ProcessId2) }}. create_process_superposition(ProcessId, BasisStates, State) -> % Calculate normalized amplitude weights for superposition NumStates = length(BasisStates), EqualWeight = 1.0 / math:sqrt(NumStates), AmplitudeWeights = lists:foldl(fun(BasisState, Acc) -> maps:put(BasisState, EqualWeight, Acc) end, #{}, BasisStates), % Generate random phase relationships for quantum interference PhaseRelations = generate_quantum_phases(BasisStates), % Create superposition state record SuperpositionState = #superposition_state{ process_id = ProcessId, basis_states = list_to_map_with_index(BasisStates), amplitude_weights = AmplitudeWeights, phase_relations = PhaseRelations, coherence_time = calculate_superposition_coherence_time(), collapse_probability_func = fun(ObsContext) -> calculate_collapse_probability(BasisStates, ObsContext) end }, % Store in ETS table ets:insert(?SUPERPOSITION_TABLE, SuperpositionState), % Schedule decoherence schedule_superposition_decoherence(ProcessId), {ok, #{ superposition_id => ProcessId, basis_states => BasisStates, amplitude_weights => AmplitudeWeights, phase_relations => PhaseRelations, coherence_time => SuperpositionState#superposition_state.coherence_time }}. perform_superposition_collapse(ProcessId, ObservationContext, State) -> case ets:lookup(?SUPERPOSITION_TABLE, ProcessId) of [SuperpositionState] -> % Calculate collapse probabilities based on observation context CollapseProbs = calculate_context_dependent_probabilities( SuperpositionState, ObservationContext), % Quantum measurement - probabilistic collapse CollapsedState = quantum_measurement_collapse(CollapseProbs), % Remove from superposition ets:delete(?SUPERPOSITION_TABLE, ProcessId), % Notify entangled processes of collapse notify_entangled_processes_of_collapse(ProcessId, CollapsedState, State), Result = #{ collapsed_to => CollapsedState, measurement_context => ObservationContext, collapse_probability => maps:get(CollapsedState, CollapseProbs), measurement_time => erlang:system_time(microsecond) }, {ok, Result, State}; [] -> {{error, not_in_superposition}, State} end. perform_weak_measurement(ProcessId, State) -> % Perform weak measurement without fully collapsing the quantum state case ets:lookup(?SUPERPOSITION_TABLE, ProcessId) of [SuperpositionState] -> % Extract current quantum state BasisStates = SuperpositionState#superposition_state.basis_states, AmplitudeWeights = SuperpositionState#superposition_state.amplitude_weights, % Perform weak measurement with minimal disturbance MeasurementStrength = 0.1, % Weak coupling parameter % Calculate measurement probabilities without full collapse Probabilities = maps:map(fun(_State, Amplitude) -> math:pow(erlang:abs(Amplitude), 2) end, AmplitudeWeights), % Determine most likely state without collapsing {MostLikelyState, MaxProb} = maps:fold(fun(State, Prob, {MaxState, MaxP}) -> if Prob > MaxP -> {State, Prob}; true -> {MaxState, MaxP} end end, {undefined, 0}, Probabilities), % Apply small perturbation based on measurement PerturbedWeights = maps:map(fun(State, Amplitude) -> if State == MostLikelyState -> Amplitude * (1 + MeasurementStrength); true -> Amplitude * (1 - MeasurementStrength * 0.1) end end, AmplitudeWeights), % Renormalize amplitudes NormalizedWeights = normalize_amplitudes(PerturbedWeights), % Update superposition state with perturbed weights UpdatedSuperposition = SuperpositionState#superposition_state{ amplitude_weights = NormalizedWeights }, ets:insert(?SUPERPOSITION_TABLE, UpdatedSuperposition), {ok, #{ measurement_type => weak, most_likely_state => MostLikelyState, probability => MaxProb, measurement_strength => MeasurementStrength, state_disturbed => true, disturbance_level => minimal }}; [] -> % Process not in superposition, perform classical measurement {ok, #{ measurement_type => classical, state => get_classical_process_state(ProcessId), probability => 1.0, state_disturbed => false }} end. implement_quantum_interference(ProcessIds, InterferencePattern, TargetOutcome, State) -> % Collect quantum states from all participating processes QuantumStates = collect_quantum_states(ProcessIds), % Calculate interference amplitudes InterferenceAmplitudes = calculate_interference_amplitudes( QuantumStates, InterferencePattern), % Apply constructive/destructive interference ModifiedAmplitudes = apply_interference_pattern( InterferenceAmplitudes, TargetOutcome), % Update process states with interfered amplitudes UpdateResults = lists:map(fun(ProcessId) -> update_process_quantum_state(ProcessId, ModifiedAmplitudes) end, ProcessIds), % Calculate interference success probability SuccessProbability = calculate_interference_success( ModifiedAmplitudes, TargetOutcome), {ok, #{ interference_pattern => InterferencePattern, participating_processes => ProcessIds, success_probability => SuccessProbability, modified_amplitudes => ModifiedAmplitudes, update_results => UpdateResults }}. execute_quantum_tunneling(ProcessId, Barrier, TargetState, State) -> % Calculate tunneling probability based on barrier properties TunnelingProbability = calculate_tunneling_probability(ProcessId, Barrier), % Quantum tunneling attempt TunnelingSuccess = quantum_random() < TunnelingProbability, case TunnelingSuccess of true -> % Successful tunneling - instantaneous state transition PreviousState = get_process_quantum_state(ProcessId), update_process_state(ProcessId, TargetState), % Notify system of quantum tunneling event notify_quantum_tunneling_event(ProcessId, PreviousState, TargetState), {ok, #{ tunneling_successful => true, previous_state => PreviousState, target_state => TargetState, tunneling_probability => TunnelingProbability, barrier_overcome => Barrier }}; false -> {ok, #{ tunneling_successful => false, tunneling_probability => TunnelingProbability, barrier_strength => Barrier, retry_suggested => true }} end. perform_quantum_teleportation(SourceId, TargetId, StateToTeleport, State) -> % Quantum teleportation protocol implementation % Step 1: Verify entanglement between source and target case verify_entanglement(SourceId, TargetId) of {ok, EntanglementPair} -> % Step 2: Perform Bell measurement on source + state to teleport BellMeasurement = perform_bell_measurement(SourceId, StateToTeleport), % Step 3: Classical communication of measurement results ClassicalBits = extract_classical_bits(BellMeasurement), % Step 4: Apply corrective operations on target based on measurement CorrectiveOps = determine_corrective_operations(ClassicalBits), apply_corrective_operations(TargetId, CorrectiveOps), % Step 5: Verify teleportation fidelity TeleportationFidelity = calculate_teleportation_fidelity( StateToTeleport, get_process_quantum_state(TargetId)), % Step 6: Destroy original state (no-cloning theorem) destroy_quantum_state(SourceId, StateToTeleport), {ok, #{ teleportation_successful => TeleportationFidelity > 0.9, fidelity => TeleportationFidelity, classical_bits => ClassicalBits, corrective_operations => CorrectiveOps, entanglement_consumed => true }}; {error, no_entanglement} -> {error, #{ reason => no_entanglement_available, suggestion => "Create entanglement first between source and target" }} end. run_quantum_algorithm(AlgorithmType, Parameters, State) -> case AlgorithmType of grovers_search -> execute_grovers_algorithm(Parameters, State); shors_factoring -> execute_shors_algorithm(Parameters, State); quantum_fourier_transform -> execute_qft_algorithm(Parameters, State); variational_quantum_eigensolver -> execute_vqe_algorithm(Parameters, State); quantum_approximate_optimization -> execute_qaoa_algorithm(Parameters, State); quantum_machine_learning -> execute_qml_algorithm(Parameters, State) end. execute_grovers_algorithm(Parameters, State) -> % Grover's search algorithm for unstructured search SearchSpace = maps:get(search_space, Parameters), TargetItem = maps:get(target, Parameters), % Calculate optimal number of iterations N = length(SearchSpace), OptimalIterations = round(math:pi() / 4 * math:sqrt(N)), % Initialize uniform superposition InitialState = create_uniform_superposition(SearchSpace), % Apply Grover iterations FinalState = apply_grover_iterations(InitialState, TargetItem, OptimalIterations), % Measure result MeasurementResult = quantum_measurement(FinalState), % Calculate success probability SuccessProbability = calculate_grovers_success_probability(N, OptimalIterations), {ok, #{ algorithm => grovers_search, search_space_size => N, iterations_performed => OptimalIterations, measurement_result => MeasurementResult, success_probability => SuccessProbability, quantum_speedup => math:sqrt(N) }}. %% Utility Functions create_bell_state(Type) -> case Type of plus -> #{state => "1/sqrt(2) * (|00⟩ + |11⟩)", entanglement_type => maximally_entangled}; minus -> #{state => "1/sqrt(2) * (|00⟩ - |11⟩)", entanglement_type => maximally_entangled}; phi_plus -> #{state => "1/sqrt(2) * (|01⟩ + |10⟩)", entanglement_type => maximally_entangled}; phi_minus -> #{state => "1/sqrt(2) * (|01⟩ - |10⟩)", entanglement_type => maximally_entangled} end. generate_quantum_phases(BasisStates) -> lists:foldl(fun(State, Acc) -> Phase = 2 * math:pi() * quantum_random(), maps:put(State, Phase, Acc) end, #{}, BasisStates). quantum_random() -> % True quantum random number generation simulation % In practice, this could interface with actual quantum hardware rand:uniform(). calculate_coherence_time(ProcessId1, ProcessId2) -> % Estimate based on process characteristics and environmental factors BaseCoherence = 1000, % microseconds NoiseLevel = 0.01, EnvironmentalFactors = analyze_environmental_decoherence(ProcessId1, ProcessId2), BaseCoherence * (1 - NoiseLevel) * EnvironmentalFactors. quantum_decoherence_monitor() -> % Continuous monitoring of quantum coherence receive {monitor_process, ProcessId} -> spawn(fun() -> monitor_process_coherence(ProcessId) end), quantum_decoherence_monitor(); {stop_monitoring, ProcessId} -> stop_process_monitoring(ProcessId), quantum_decoherence_monitor(); stop -> ok after 1000 -> perform_periodic_coherence_check(), quantum_decoherence_monitor() end. %% Placeholder implementations for complex quantum operations generate_entanglement_id(Id1, Id2) -> list_to_binary([atom_to_list(Id1), "_", atom_to_list(Id2)]). notify_processes_of_entanglement(_Processes, _PairId) -> ok. schedule_entanglement_maintenance(_PairId) -> ok. list_to_map_with_index(List) -> lists:foldl(fun({Index, Item}, Acc) -> maps:put(Item, Index, Acc) end, #{}, lists:zip(lists:seq(1, length(List)), List)). calculate_superposition_coherence_time() -> 5000. % microseconds schedule_superposition_decoherence(_ProcessId) -> ok. calculate_context_dependent_probabilities(_State, _Context) -> #{}. quantum_measurement_collapse(_Probs) -> default_state. notify_entangled_processes_of_collapse(_ProcessId, _State, _SystemState) -> ok. collect_quantum_states(_ProcessIds) -> []. calculate_interference_amplitudes(_States, _Pattern) -> #{}. apply_interference_pattern(_Amplitudes, _Target) -> #{}. update_process_quantum_state(_ProcessId, _Amplitudes) -> ok. calculate_interference_success(_Amplitudes, _Target) -> 0.8. calculate_tunneling_probability(_ProcessId, _Barrier) -> 0.3. get_process_quantum_state(_ProcessId) -> default_state. update_process_state(_ProcessId, _State) -> ok. notify_quantum_tunneling_event(_ProcessId, _Previous, _Target) -> ok. verify_entanglement(_Id1, _Id2) -> {error, no_entanglement}. perform_bell_measurement(_ProcessId, _State) -> #{}. extract_classical_bits(_Measurement) -> [0, 1]. determine_corrective_operations(_Bits) -> []. apply_corrective_operations(_ProcessId, _Ops) -> ok. calculate_teleportation_fidelity(_Original, _Final) -> 0.95. destroy_quantum_state(_ProcessId, _State) -> ok. execute_shors_algorithm(_Params, _State) -> {ok, #{}}. execute_qft_algorithm(_Params, _State) -> {ok, #{}}. execute_vqe_algorithm(_Params, _State) -> {ok, #{}}. execute_qaoa_algorithm(_Params, _State) -> {ok, #{}}. execute_qml_algorithm(_Params, _State) -> {ok, #{}}. create_uniform_superposition(_SearchSpace) -> #{}. apply_grover_iterations(_State, _Target, _Iterations) -> #{}. quantum_measurement(_State) -> measurement_result. calculate_grovers_success_probability(_N, _Iterations) -> 0.9. analyze_environmental_decoherence(_Id1, _Id2) -> 0.8. monitor_process_coherence(_ProcessId) -> ok. stop_process_monitoring(_ProcessId) -> ok. perform_periodic_coherence_check() -> ok. initialize_quantum_rng() -> ok. update_superposition_state(_ProcessId, _Result, State) -> State. handle_quantum_decoherence(_ProcessId, State) -> State. process_measurement_result(_ProcessId, _Result, State) -> State. maintain_entanglement_pair(_PairId) -> ok. add_quantum_circuit(_CircuitId, _Gates, State) -> State. calculate_collapse_probability(_States, _Context) -> 0.5. normalize_amplitudes(AmplitudeMap) -> % Calculate sum of squared amplitudes SumSquared = maps:fold(fun(_State, Amplitude, Sum) -> Sum + math:pow(erlang:abs(Amplitude), 2) end, 0, AmplitudeMap), % Normalization factor NormFactor = math:sqrt(SumSquared), % Normalize each amplitude maps:map(fun(_State, Amplitude) -> Amplitude / NormFactor end, AmplitudeMap). get_classical_process_state(ProcessId) -> % Return classical state for a process not in superposition % This would typically query the process state from another system #{ process_id => ProcessId, state => classical, properties => #{ deterministic => true, quantum_properties => none } }.