QuantumKatas/Measurements/Tests.qs

// Copyright (c) Microsoft Corporation. All rights reserved.
// Licensed under the MIT license.

//////////////////////////////////////////////////////////////////////
// This file contains testing harness for all tasks.
// You should not modify anything in this file.
// The tasks themselves can be found in Tasks.qs file.
//////////////////////////////////////////////////////////////////////

namespace Quantum.Kata.Measurements {
    
    open Microsoft.Quantum.Primitive;
    open Microsoft.Quantum.Canon;
    open Microsoft.Quantum.Extensions.Convert;
    open Microsoft.Quantum.Extensions.Math;
    open Microsoft.Quantum.Extensions.Testing;
    
    
    //////////////////////////////////////////////////////////////////
    
    // "Framework" operation for testing single-qubit tasks for distinguishing states of one qubit
    // with Bool return
    operation DistinguishTwoStates_OneQubit (statePrep : ((Qubit, Int) => Unit), testImpl : (Qubit => Bool)) : Unit {
        let nTotal = 100;
        mutable nOk = 0;
        
        using (qs = Qubit[1]) {
            for (i in 1 .. nTotal) {
                // get a random bit to define whether qubit will be in a state corresponding to true return (1) or to false one (0)
                // state = 0 false return
                // state = 1 true return
                let state = RandomIntPow2(1);
                
                // do state prep: convert |0⟩ to outcome with false return or to outcome with true return depending on state
                statePrep(qs[0], state);
                
                // get the solution's answer and verify that it's a match
                let ans = testImpl(qs[0]);
                if (ans == (state == 1)) {
                    set nOk = nOk + 1;
                }
                
                // we're not checking the state of the qubit after the operation
                Reset(qs[0]);
            }
        }
        
        AssertIntEqual(nOk, nTotal, $"{nTotal - nOk} test runs out of {nTotal} returned incorrect state.");
    }
    
    
    // ------------------------------------------------------
    operation StatePrep_IsQubitOne (q : Qubit, state : Int) : Unit {
        if (state == 0) {
            // convert |0⟩ to |0⟩
        } else {
            // convert |0⟩ to |1⟩
            X(q);
        }
    }
    
    
    operation T101_IsQubitOne_Test () : Unit {
        DistinguishTwoStates_OneQubit(StatePrep_IsQubitOne, IsQubitOne);
    }
    
    
    // ------------------------------------------------------
    operation T102_InitializeQubit_Test () : Unit {
        using (qs = Qubit[1]) {
            for (i in 0 .. 36) {
                let alpha = ((2.0 * PI()) * ToDouble(i)) / 36.0;
                Ry(2.0 * alpha, qs[0]);
                
                // Test Task 1
                InitializeQubit(qs[0]);
                
                // Confirm that the state is |0⟩.
                AssertAllZero(qs);
            }
        }
    }
    
    
    // ------------------------------------------------------
    operation StatePrep_IsQubitPlus (q : Qubit, state : Int) : Unit {
        if (state == 0) {
            // convert |0⟩ to |-⟩
            X(q);
            H(q);
        } else {
            // convert |0⟩ to |+⟩
            H(q);
        }
    }
    
    
    operation T103_IsQubitPlus_Test () : Unit {
        DistinguishTwoStates_OneQubit(StatePrep_IsQubitPlus, IsQubitPlus);
    }
    
    
    // ------------------------------------------------------
    // |A⟩ =   cos(alpha) * |0⟩ + sin(alpha) * |1⟩,
    // |B⟩ = - sin(alpha) * |0⟩ + cos(alpha) * |1⟩.
    operation StatePrep_IsQubitA (alpha : Double, q : Qubit, state : Int) : Unit {
        if (state == 0) {
            // convert |0⟩ to |B⟩
            X(q);
            Ry(2.0 * alpha, q);
        } else {
            // convert |0⟩ to |A⟩
            Ry(2.0 * alpha, q);
        }
    }
    
    
    operation T104_IsQubitA_Test () : Unit {
        // cross-test
        // alpha = 0.0 or PI() => !isQubitOne
        // alpha = PI() / 2.0 => isQubitOne
        DistinguishTwoStates_OneQubit(StatePrep_IsQubitOne, IsQubitA(PI() / 2.0, _));
        
        // alpha = PI() / 4.0 => isQubitPlus
        DistinguishTwoStates_OneQubit(StatePrep_IsQubitPlus, IsQubitA(PI() / 4.0, _));
        
        for (i in 0 .. 10) {
            let alpha = (PI() * ToDouble(i)) / 10.0;
            DistinguishTwoStates_OneQubit(StatePrep_IsQubitA(alpha, _, _), IsQubitA(alpha, _));
        }
    }
    
    
    // ------------------------------------------------------
    
    // "Framework" operation for testing multi-qubit tasks for distinguishing states of an array of qubits
    // with Int return
    operation DistinguishStates_MultiQubit (Nqubit : Int, Nstate : Int, statePrep : ((Qubit[], Int) => Unit), testImpl : (Qubit[] => Int)) : Unit {
        let nTotal = 100;
        mutable nOk = 0;
        
        using (qs = Qubit[Nqubit]) {
            for (i in 1 .. nTotal) {
                // get a random integer to define the state of the qubits
                let state = RandomInt(Nstate);
                
                // do state prep: convert |0...0⟩ to outcome with return equal to state
                statePrep(qs, state);
                
                // get the solution's answer and verify that it's a match
                let ans = testImpl(qs);
                if (ans == state) {
                    set nOk = nOk + 1;
                }
                
                // we're not checking the state of the qubit after the operation
                ResetAll(qs);
            }
        }
        
        AssertIntEqual(nOk, nTotal, $"{nTotal - nOk} test runs out of {nTotal} returned incorrect state.");
    }
    
    
    // ------------------------------------------------------
    operation StatePrep_ZeroZeroOrOneOne (qs : Qubit[], state : Int) : Unit {
        if (state == 1) {
            // |11⟩
            X(qs[0]);
            X(qs[1]);
        }
    }
    
    
    operation T105_ZeroZeroOrOneOne_Test () : Unit {
        DistinguishStates_MultiQubit(2, 2, StatePrep_ZeroZeroOrOneOne, ZeroZeroOrOneOne);
    }
    
    
    // ------------------------------------------------------
    operation StatePrep_BasisStateMeasurement (qs : Qubit[], state : Int) : Unit {
        
        if (state / 2 == 1) {
            // |10⟩ or |11⟩
            X(qs[0]);
        }
        
        if (state % 2 == 1) {
            // |01⟩ or |11⟩
            X(qs[1]);
        }
    }
    
    
    operation T106_BasisStateMeasurement_Test () : Unit {
        DistinguishStates_MultiQubit(2, 4, StatePrep_BasisStateMeasurement, BasisStateMeasurement);
    }
    
    
    // ------------------------------------------------------
    operation StatePrep_Bitstring (qs : Qubit[], bits : Bool[]) : Unit {
        for (i in 0 .. Length(qs) - 1) {
            if (bits[i]) {
                X(qs[i]);
            }
        }
    }
    
    
    operation StatePrep_TwoBitstringsMeasurement (qs : Qubit[], bits1 : Bool[], bits2 : Bool[], state : Int) : Unit {
        if (state == 0) {
            StatePrep_Bitstring(qs, bits1);
        } else {
            StatePrep_Bitstring(qs, bits2);
        }
    }
    
    
    operation T107_TwoBitstringsMeasurement_Test () : Unit {
        for (i in 1 .. 1) {
            let b1 = [false, true];
            let b2 = [true, false];
            DistinguishStates_MultiQubit(2, 2, StatePrep_TwoBitstringsMeasurement(_, b1, b2, _), TwoBitstringsMeasurement(_, b1, b2));
        }
        
        for (i in 1 .. 1) {
            let b1 = [true, true, false];
            let b2 = [false, true, true];
            DistinguishStates_MultiQubit(3, 2, StatePrep_TwoBitstringsMeasurement(_, b1, b2, _), TwoBitstringsMeasurement(_, b1, b2));
        }
        
        for (i in 1 .. 1) {
            let b1 = [false, true, true, false];
            let b2 = [false, true, true, true];
            DistinguishStates_MultiQubit(4, 2, StatePrep_TwoBitstringsMeasurement(_, b1, b2, _), TwoBitstringsMeasurement(_, b1, b2));
        }
        
        for (i in 1 .. 1) {
            let b1 = [true, false, false, false];
            let b2 = [true, false, true, true];
            DistinguishStates_MultiQubit(4, 2, StatePrep_TwoBitstringsMeasurement(_, b1, b2, _), TwoBitstringsMeasurement(_, b1, b2));
        }
    }
    
    
    // ------------------------------------------------------
    operation WState_Arbitrary_Reference (qs : Qubit[]) : Unit {
        
        body (...) {
            let N = Length(qs);
            
            if (N == 1) {
                // base case of recursion: |1⟩
                X(qs[0]);
            } else {
                // |W_N> = |0⟩|W_(N-1)> + |1⟩|0...0⟩
                // do a rotation on the first qubit to split it into |0⟩ and |1⟩ with proper weights
                // |0⟩ -> sqrt((N-1)/N) |0⟩ + 1/sqrt(N) |1⟩
                let theta = ArcSin(1.0 / Sqrt(ToDouble(N)));
                Ry(2.0 * theta, qs[0]);
                
                // do a zero-controlled W-state generation for qubits 1..N-1
                X(qs[0]);
                Controlled WState_Arbitrary_Reference(qs[0 .. 0], qs[1 .. N - 1]);
                X(qs[0]);
            }
        }
        
        adjoint invert;
        controlled distribute;
        controlled adjoint distribute;
    }
    
    
    operation StatePrep_AllZerosOrWState (qs : Qubit[], state : Int) : Unit {
        
        if (state == 1) {
            // prep W state
            WState_Arbitrary_Reference(qs);
        }
    }
    
    
    operation T108_AllZerosOrWState_Test () : Unit {
        
        for (i in 2 .. 6) {
            DistinguishStates_MultiQubit(i, 2, StatePrep_AllZerosOrWState, AllZerosOrWState);
        }
    }
    
    
    // ------------------------------------------------------
    operation GHZ_State_Reference (qs : Qubit[]) : Unit {
        
        body (...) {
            H(qs[0]);
            for (i in 1 .. Length(qs) - 1) {
                CNOT(qs[0], qs[i]);
            }
        }
        
        adjoint invert;
    }
    
    
    operation StatePrep_GHZOrWState (qs : Qubit[], state : Int) : Unit {
        
        if (state == 0) {
            // prep GHZ state
            GHZ_State_Reference(qs);
        } else {
            // prep W state
            WState_Arbitrary_Reference(qs);
        }
    }
    
    
    operation T109_GHZOrWState_Test () : Unit {
        for (i in 2 .. 6) {
            DistinguishStates_MultiQubit(i, 2, StatePrep_GHZOrWState, GHZOrWState);
        }
    }
    
    
    // ------------------------------------------------------
    // 0 - |Φ⁺⟩ = (|00⟩ + |11⟩) / sqrt(2)
    // 1 - |Φ⁻⟩ = (|00⟩ - |11⟩) / sqrt(2)
    // 2 - |Ψ⁺⟩ = (|01⟩ + |10⟩) / sqrt(2)
    // 3 - |Ψ⁻⟩ = (|01⟩ - |10⟩) / sqrt(2)
    operation StatePrep_BellState (qs : Qubit[], state : Int) : Unit {
        H(qs[0]);
        CNOT(qs[0], qs[1]);
        
        // now we have |00⟩ + |11⟩ - modify it based on state arg
        if (state % 2 == 1) {
            // negative phase
            Z(qs[1]);
        }
        if (state / 2 == 1) {
            X(qs[1]);
        }
    }
    
    
    operation T110_BellState_Test () : Unit {
        DistinguishStates_MultiQubit(2, 4, StatePrep_BellState, BellState);
    }
    
    
    // ------------------------------------------------------
    // 0 - (|00⟩ + |01⟩ + |10⟩ + |11⟩) / 2
    // 1 - (|00⟩ - |01⟩ + |10⟩ - |11⟩) / 2
    // 2 - (|00⟩ + |01⟩ - |10⟩ - |11⟩) / 2
    // 3 - (|00⟩ - |01⟩ - |10⟩ + |11⟩) / 2
    operation StatePrep_TwoQubitState (qs : Qubit[], state : Int) : Unit {
        // start with state prep of basis vectors
        StatePrep_BasisStateMeasurement(qs, state);
        H(qs[0]);
        H(qs[1]);
    }
    
    
    // ------------------------------------------------------
    // 0 - ( |00⟩ - |01⟩ - |10⟩ - |11⟩) / 2
    // 1 - (-|00⟩ + |01⟩ - |10⟩ - |11⟩) / 2
    // 2 - (-|00⟩ - |01⟩ + |10⟩ - |11⟩) / 2
    // 3 - (-|00⟩ - |01⟩ - |10⟩ + |11⟩) / 2
    operation StatePrep_TwoQubitStatePartTwo (qs : Qubit[], state : Int) : Unit {
        
        // start with state prep of basis vectors
        StatePrep_BasisStateMeasurement(qs, state);
        
        // now apply all gates for unitary in reference impl (in reverse + adjoint)
        ApplyToEach(X, qs);
        Controlled Z([qs[0]], qs[1]);
        ApplyToEach(X, qs);
        ApplyToEach(H, qs);
        ApplyToEach(X, qs);
        Controlled Z([qs[0]], qs[1]);
        ApplyToEach(X, qs);
        SWAP(qs[0], qs[1]);
    }
    
    
    operation T111_TwoQubitState_Test () : Unit {
        DistinguishStates_MultiQubit(2, 4, StatePrep_TwoQubitState, TwoQubitState);
    }
    
    
    operation T112_TwoQubitStatePartTwo_Test () : Unit {
        DistinguishStates_MultiQubit(2, 4, StatePrep_TwoQubitStatePartTwo, TwoQubitStatePartTwo);
    }
    
    
    // ------------------------------------------------------
    
    operation StatePrep_ThreeQubitMeasurement (qs : Qubit[], state : Int) : Unit {
        
        body (...) {
            WState_Arbitrary_Reference(qs);
            
            if (state == 0) {
                // prep 1/sqrt(3) ( |100⟩ + ω |010⟩ + ω² |001⟩ )
                R1(2.0 * PI() / 3.0, qs[1]);
                R1(4.0 * PI() / 3.0, qs[2]);
            } else {
                //  prep 1/sqrt(3) ( |100⟩ + ω² |010⟩ + ω |001⟩ )
                R1(4.0 * PI() / 3.0, qs[1]);
                R1(2.0 * PI() / 3.0, qs[2]);
            }
        }
        
        adjoint invert;
    }
    
    operation T113_ThreeQubitMeasurement_Test () : Unit {
        DistinguishStates_MultiQubit(3, 2, StatePrep_ThreeQubitMeasurement, ThreeQubitMeasurement);
    }
    

    //////////////////////////////////////////////////////////////////
    operation StatePrep_IsQubitZeroOrPlus (q : Qubit, state : Int) : Unit {
        
        if (state == 0) {
            // convert |0⟩ to |0⟩
        } else {
            // convert |0⟩ to |+⟩
            H(q);
        }
    }
    
    
    // "Framework" operation for testing multi-qubit tasks for distinguishing states of an array of qubits
    // with Int return. Framework tests against a threshold parameter for the fraction of runs that must succeed.
    operation DistinguishStates_MultiQubit_Threshold (Nqubit : Int, Nstate : Int, threshold : Double, statePrep : ((Qubit, Int) => Unit), testImpl : (Qubit => Bool)) : Unit {
        let nTotal = 1000;
        mutable nOk = 0;
        
        using (qs = Qubit[Nqubit]) {
            for (i in 1 .. nTotal) {
                // get a random integer to define the state of the qubits
                let state = RandomInt(Nstate);
                
                // do state prep: convert |0⟩ to outcome with return equal to state
                statePrep(qs[0], state);
                
                // get the solution's answer and verify that it's a match
                let ans = testImpl(qs[0]);
                if (ans == (state == 0)) {
                    set nOk = nOk + 1;
                }
                
                // we're not checking the state of the qubit after the operation
                ResetAll(qs);
            }
        }
        
        if (ToDouble(nOk) < threshold * ToDouble(nTotal)) {
            fail $"{nTotal - nOk} test runs out of {nTotal} returned incorrect state which does not meet the required threshold of at least {threshold * 100.0}%.";
        }
    }
    
    
    // "Framework" operation for testing multi-qubit tasks for distinguishing states of an array of qubits
    // with Int return. Framework tests against a threshold parameter for the fraction of runs that must succeed.
    // Framework tests in the USD scenario, i.e., it is allowed to respond "inconclusive" (with some probability)
    // up to given threshold, but it is never allowed to err if an actual conclusive response is given.
    operation USD_DistinguishStates_MultiQubit_Threshold (Nqubit : Int, Nstate : Int, thresholdInconcl : Double, thresholdConcl : Double, statePrep : ((Qubit, Int) => Unit), testImpl : (Qubit => Int)) : Unit {
        let nTotal = 10000;
        
        // counts total inconclusive answers
        mutable nInconc = 0;
        
        // counts total conclusive |0⟩ state identifications
        mutable nConclOne = 0;
        
        // counts total conclusive |+> state identifications
        mutable nConclPlus = 0;
        
        using (qs = Qubit[Nqubit]) {
            for (i in 1 .. nTotal) {
                
                // get a random integer to define the state of the qubits
                let state = RandomInt(Nstate);
                
                // do state prep: convert |0⟩ to outcome with return equal to state
                statePrep(qs[0], state);
                
                // get the solution's answer and verify that it's a match
                let ans = testImpl(qs[0]);
                
                // check that the answer is actually in allowed range
                if (ans < -1 or ans > 1) {
                    fail $"state {state} led to invalid response {ans}.";
                }
                
                // keep track of the number of inconclusive answers given
                if (ans == -1) {
                    set nInconc = nInconc + 1;
                }
                
                if (ans == 0 and state == 0) {
                    set nConclOne = nConclOne + 1;
                }
                
                if (ans == 1 and state == 1) {
                    set nConclPlus = nConclPlus + 1;
                }
                
                // check if upon conclusive result the answer is actually correct
                if (ans == 0 and state == 1 or ans == 1 and state == 0) {
                    fail $"state {state} led to incorrect conclusive response {ans}.";
                }
                
                // we're not checking the state of the qubit after the operation
                ResetAll(qs);
            }
        }
        
        if (ToDouble(nInconc) > thresholdInconcl * ToDouble(nTotal)) {
            fail $"{nInconc} test runs out of {nTotal} returned inconclusive which does not meet the required threshold of at most {thresholdInconcl * 100.0}%.";
        }
        
        if (ToDouble(nConclOne) < thresholdConcl * ToDouble(nTotal)) {
            fail $"Only {nConclOne} test runs out of {nTotal} returned conclusive |0⟩ which does not meet the required threshold of at least {thresholdConcl * 100.0}%.";
        }
        
        if (ToDouble(nConclPlus) < thresholdConcl * ToDouble(nTotal)) {
            fail $"Only {nConclPlus} test runs out of {nTotal} returned conclusive |+> which does not meet the required threshold of at least {thresholdConcl * 100.0}%.";
        }
    }
    
    
    operation T201_IsQubitZeroOrPlus_Test () : Unit {
        DistinguishStates_MultiQubit_Threshold(1, 2, 0.8, StatePrep_IsQubitZeroOrPlus, IsQubitPlusOrZero);
    }
    
    
    operation T202_IsQubitZeroOrPlusSimpleUSD_Test () : Unit {
        USD_DistinguishStates_MultiQubit_Threshold(1, 2, 0.8, 0.1, StatePrep_IsQubitZeroOrPlus, IsQubitPlusZeroOrInconclusiveSimpleUSD);
    }
    
    
    // ------------------------------------------------------
    operation StatePrep_IsQubitNotInABC (q : Qubit, state : Int) : Unit {
        let alpha = (2.0 * PI()) / 3.0;
        H(q);
        
        if (state == 0) {
            // convert |0⟩ to 1/sqrt(2) (|0⟩ + |1⟩)
        }
        elif (state == 1) {
            // convert |0⟩ to 1/sqrt(2) (|0⟩ + ω |1⟩), where ω = exp(2iπ/3)
            R1(alpha, q);
        }
        else {
            // convert |0⟩ to 1/sqrt(2) (|0⟩ + ω² |1⟩), where ω = exp(2iπ/3)
            R1(2.0 * alpha, q);
        }
    }
    
    
    // "Framework" operation for testing multi-qubit tasks for distinguishing states of an array of qubits
    // with Int return. Framework tests instances of the Peres/Wootters game. In this game, one of three
    // "trine" states is presented and the algorithm must answer with a label that does not correspond
    // to one of the label of the input state.
    operation ABC_DistinguishStates_MultiQubit_Threshold (Nqubit : Int, Nstate : Int, statePrep : ((Qubit, Int) => Unit), testImpl : (Qubit => Int)) : Unit {
        
        let nTotal = 1000;
        
        using (qs = Qubit[Nqubit]) {
            
            for (i in 1 .. nTotal) {
                // get a random integer to define the state of the qubits
                let state = RandomInt(Nstate);
                
                // do state prep: convert |0⟩ to outcome with return equal to state
                statePrep(qs[0], state);
                
                // get the solution's answer and verify that it's a match
                let ans = testImpl(qs[0]);
                
                // check that the value of ans is 0, 1 or 2
                if (ans < 0 or ans > 2) {
                    fail "You can not return any value other than 0, 1 or 2.";
                }
                
                // check if upon conclusive result the answer is actually correct
                if (ans == state) {
                    fail $"State {state} led to incorrect conclusive response {ans}.";
                }
                
                // we're not checking the state of the qubit after the operation
                ResetAll(qs);
            }
        }
    }
    
    operation T203_IsQubitNotInABC_Test () : Unit {
        ABC_DistinguishStates_MultiQubit_Threshold(1, 3, StatePrep_IsQubitNotInABC, IsQubitNotInABC);
    }
}