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Adding new tasks to Superposition kata. (#40)
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@ricardo-espinoza @tcNickolas
ricardo-espinoza authored and tcNickolas committed Oct 23, 2018
1 parent bbc8750 commit 13705d3
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57 changes: 49 additions & 8 deletions Superposition/ReferenceImplementation.qs
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Original file line number Diff line number Diff line change
Expand Up @@ -55,7 +55,48 @@ namespace Quantum.Kata.Superposition
adjoint auto;
}

// Task 4. Bell state
// Task 4. Superposition of all basis vectors on two qubits
operation AllBasisVectors_TwoQubits_Reference (qs : Qubit[]) : ()
{
body
{
// Since a Hadamard gate will change |0⟩ into |+⟩ = (|0⟩ + |1⟩)/sqrt(2)
// And the desired state is just a tensor product |+⟩|+⟩, we can apply
// a Hadamard transformation to each qubit.
H(qs[0]);
H(qs[1]);
}
adjoint auto;
}

// Task 5. Superposition of basis vectors with phases
operation AllBasisVectorsWithPhases_TwoQubits_Reference (qs : Qubit[]) : ()
{
body
{
// Question:
// Is this state separable?

// Answer:
// Yes. It is. We can see that:
// ((|0⟩ - |1⟩) / sqrt(2)) ⊗ ((|0⟩ + i*|1⟩) / sqrt(2)) is equal to the desired
// state, so we can create it by doing operations on each qubit independently.

// We can see that the first qubit is in state |-⟩ and the second in state |i⟩,
// so the transformations that we need are:

// Qubit 0 is taken into |+⟩ and then z-rotated into |-⟩.
H(qs[0]);
Z(qs[0]);

// Qubit 1 is taken into |+⟩ and then z-rotated into |i⟩.
H(qs[1]);
S(qs[1]);
}
adjoint auto;
}

// Task 6. Bell state
// Input: two qubits in |00⟩ state (stored in an array of length 2).
// Goal: create a Bell state |Φ⁺⟩ = (|00⟩ + |11⟩) / sqrt(2) on these qubits.
operation BellState_Reference (qs : Qubit[]) : ()
Expand All @@ -68,7 +109,7 @@ namespace Quantum.Kata.Superposition
adjoint auto;
}

// Task 5. All Bell states
// Task 7. All Bell states
// Inputs:
// 1) two qubits in |00⟩ state (stored in an array of length 2)
// 2) an integer index
Expand All @@ -95,7 +136,7 @@ namespace Quantum.Kata.Superposition
adjoint auto;
}

// Task 6. Greenberger–Horne–Zeilinger state
// Task 8. Greenberger–Horne–Zeilinger state
// Input: N qubits in |0...0⟩ state.
// Goal: create a GHZ state (|0...0⟩ + |1...1⟩) / sqrt(2) on these qubits.
operation GHZ_State_Reference (qs : Qubit[]) : ()
Expand All @@ -110,7 +151,7 @@ namespace Quantum.Kata.Superposition
adjoint auto;
}

// Task 7. Superposition of all basis vectors
// Task 9. Superposition of all basis vectors
// Input: N qubits in |0...0⟩ state.
// Goal: create an equal superposition of all basis vectors from |0...0⟩ to |1...1⟩
// (i.e. state (|0...0⟩ + ... + |1...1⟩) / sqrt(2^N) ).
Expand All @@ -125,7 +166,7 @@ namespace Quantum.Kata.Superposition
adjoint auto;
}

// Task 8. Superposition of |0...0⟩ and given bit string
// Task 10. Superposition of |0...0⟩ and given bit string
// Inputs:
// 1) N qubits in |0...0⟩ state
// 2) bit string represented as Bool[]
Expand Down Expand Up @@ -154,7 +195,7 @@ namespace Quantum.Kata.Superposition
adjoint auto;
}

// Task 9. Superposition of two bit strings
// Task 11. Superposition of two bit strings
// Inputs:
// 1) N qubits in |0...0⟩ state
// 2) two bit string represented as Bool[]s
Expand Down Expand Up @@ -207,7 +248,7 @@ namespace Quantum.Kata.Superposition
adjoint auto;
}

// Task 10. W state on 2^k qubits
// Task 12. W state on 2^k qubits
// Input: N = 2^k qubits in |0...0⟩ state.
// Goal: create a W state (https://en.wikipedia.org/wiki/W_state) on these qubits.
// W state is an equal superposition of all basis states on N qubits of Hamming weight 1.
Expand Down Expand Up @@ -241,7 +282,7 @@ namespace Quantum.Kata.Superposition
adjoint auto;
}

// Task 11. W state on arbitrary number of qubits
// Task 13. W state on arbitrary number of qubits
// Input: N qubits in |0...0⟩ state (N is not necessarily a power of 2).
// Goal: create a W state (https://en.wikipedia.org/wiki/W_state) on these qubits.
// W state is an equal superposition of all basis states on N qubits of Hamming weight 1.
Expand Down
49 changes: 40 additions & 9 deletions Superposition/Tasks.qs
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Original file line number Diff line number Diff line change
Expand Up @@ -35,7 +35,7 @@ namespace Quantum.Kata.Superposition
{
// Hadamard gate H will convert |0⟩ state to |+⟩ state.
// The first qubit of the array can be accessed as qs[0].
// Type H(qs[0]);
// Type the following: H(qs[0]);
// Then rebuild the project and rerun the tests - T01_PlusState_Test should now pass!

// ...
Expand Down Expand Up @@ -71,7 +71,38 @@ namespace Quantum.Kata.Superposition
}
}

// Task 4. Bell state
// Task 4. Superposition of all basis vectors on two qubits
// Input: two qubits in |00⟩ state (stored in an array of length 2).
// Goal: create the following state on these qubits: (|00⟩ + |01⟩ + |10⟩ + |11⟩) / 2.
operation AllBasisVectors_TwoQubits (qs : Qubit[]) : ()
{
body
{
// The following lines enforce the constraints on the input that you are given.
// You don't need to modify them. Feel free to remove them, this won't cause your code to fail.
AssertIntEqual(Length(qs), 2, "The array should have exactly 2 qubits.");

// ...
}
}

// Task 5. Superposition of basis vectors with phases
// Input: two qubits in |00⟩ state (stored in an array of length 2).
// Goal: create the following state on these qubits: (|00⟩ + i*|01⟩ - |10⟩ - i*|11⟩) / 2.
operation AllBasisVectorsWithPhases_TwoQubits (qs : Qubit[]) : ()
{
body
{
// The following lines enforce the constraints on the input that you are given.
// You don't need to modify them. Feel free to remove them, this won't cause your code to fail.
AssertIntEqual(Length(qs), 2, "The array should have exactly 2 qubits.");

// Hint: Is this state separable?
// ...
}
}

// Task 6. Bell state
// Input: two qubits in |00⟩ state (stored in an array of length 2).
// Goal: create a Bell state |Φ⁺⟩ = (|00⟩ + |11⟩) / sqrt(2) on these qubits.
operation BellState (qs : Qubit[]) : ()
Expand All @@ -82,7 +113,7 @@ namespace Quantum.Kata.Superposition
}
}

// Task 5. All Bell states
// Task 7. All Bell states
// Inputs:
// 1) two qubits in |00⟩ state (stored in an array of length 2)
// 2) an integer index
Expand All @@ -99,7 +130,7 @@ namespace Quantum.Kata.Superposition
}
}

// Task 6. Greenberger–Horne–Zeilinger state
// Task 8. Greenberger–Horne–Zeilinger state
// Input: N qubits in |0...0⟩ state.
// Goal: create a GHZ state (|0...0⟩ + |1...1⟩) / sqrt(2) on these qubits.
operation GHZ_State (qs : Qubit[]) : ()
Expand All @@ -112,7 +143,7 @@ namespace Quantum.Kata.Superposition
}
}

// Task 7. Superposition of all basis vectors
// Task 9. Superposition of all basis vectors
// Input: N qubits in |0...0⟩ state.
// Goal: create an equal superposition of all basis vectors from |0...0⟩ to |1...1⟩
// (i.e. state (|0...0⟩ + ... + |1...1⟩) / sqrt(2^N) ).
Expand All @@ -124,7 +155,7 @@ namespace Quantum.Kata.Superposition
}
}

// Task 8. Superposition of |0...0⟩ and given bit string
// Task 10. Superposition of |0...0⟩ and given bit string
// Inputs:
// 1) N qubits in |0...0⟩ state
// 2) bit string represented as Bool[]
Expand All @@ -146,7 +177,7 @@ namespace Quantum.Kata.Superposition
}
}

// Task 9. Superposition of two bit strings
// Task 11. Superposition of two bit strings
// Inputs:
// 1) N qubits in |0...0⟩ state
// 2) two bit string represented as Bool[]s
Expand All @@ -164,7 +195,7 @@ namespace Quantum.Kata.Superposition
}
}

// Task 10**. W state on 2^k qubits
// Task 12**. W state on 2^k qubits
// Input: N = 2^k qubits in |0...0⟩ state.
// Goal: create a W state (https://en.wikipedia.org/wiki/W_state) on these qubits.
// W state is an equal superposition of all basis states on N qubits of Hamming weight 1.
Expand All @@ -179,7 +210,7 @@ namespace Quantum.Kata.Superposition
}
}

// Task 11**. W state on arbitrary number of qubits
// Task 13**. W state on arbitrary number of qubits
// Input: N qubits in |0...0⟩ state (N is not necessarily a power of 2).
// Goal: create a W state (https://en.wikipedia.org/wiki/W_state) on these qubits.
// W state is an equal superposition of all basis states on N qubits of Hamming weight 1.
Expand Down
36 changes: 28 additions & 8 deletions Superposition/Tests.qs
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Original file line number Diff line number Diff line change
Expand Up @@ -72,7 +72,27 @@ namespace Quantum.Kata.Superposition
}

// ------------------------------------------------------
operation T04_BellState_Test () : ()
operation T04_AllBasisVectors_TwoQubits_Test () : ()
{
body
{
// We only check for 2 qubits.
AssertEqualOnZeroState(2, AllBasisVectors_TwoQubits, AllBasisVectors_TwoQubits_Reference);
}
}

// ------------------------------------------------------
operation T05_AllBasisVectorsWithPhases_TwoQubits_Test () : ()
{
body
{
// We only check for 2 qubits.
AssertEqualOnZeroState(2, AllBasisVectorsWithPhases_TwoQubits, AllBasisVectorsWithPhases_TwoQubits_Reference);
}
}

// ------------------------------------------------------
operation T06_BellState_Test () : ()
{
body
{
Expand All @@ -81,7 +101,7 @@ namespace Quantum.Kata.Superposition
}

// ------------------------------------------------------
operation T05_AllBellStates_Test () : ()
operation T07_AllBellStates_Test () : ()
{
body
{
Expand All @@ -92,7 +112,7 @@ namespace Quantum.Kata.Superposition
}

// ------------------------------------------------------
operation T06_GHZ_State_Test () : ()
operation T08_GHZ_State_Test () : ()
{
body
{
Expand All @@ -107,7 +127,7 @@ namespace Quantum.Kata.Superposition
}

// ------------------------------------------------------
operation T07_AllBasisVectorsSuperposition_Test () : ()
operation T09_AllBasisVectorsSuperposition_Test () : ()
{
body
{
Expand All @@ -121,7 +141,7 @@ namespace Quantum.Kata.Superposition
}

// ------------------------------------------------------
operation T08_ZeroAndBitstringSuperposition_Test () : ()
operation T10_ZeroAndBitstringSuperposition_Test () : ()
{
body
{
Expand Down Expand Up @@ -149,7 +169,7 @@ namespace Quantum.Kata.Superposition
}

// ------------------------------------------------------
operation T09_TwoBitstringSuperposition_Test () : ()
operation T11_TwoBitstringSuperposition_Test () : ()
{
body
{
Expand Down Expand Up @@ -194,7 +214,7 @@ namespace Quantum.Kata.Superposition
}

// ------------------------------------------------------
operation T10_WState_PowerOfTwo_Test () : ()
operation T12_WState_PowerOfTwo_Test () : ()
{
body
{
Expand All @@ -213,7 +233,7 @@ namespace Quantum.Kata.Superposition
}

// ------------------------------------------------------
operation T11_WState_Arbitrary_Test () : ()
operation T13_WState_Arbitrary_Test () : ()
{
body
{
Expand Down

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