static void Main(string[] args)
{
var sim = new QuantumSimulator(throwOnReleasingQubitsNotInZeroState: true);
Console.Write("Enter the number of bits in the system (Less than 6):\n");
var nDatabaseQubits = int.Parse(Console.ReadLine());
if (nDatabaseQubits > 6)
{
Console.WriteLine("Input greater than 6. Value defaulted to 6.");
nDatabaseQubits = 6;
}
Console.Write($"N: {nDatabaseQubits}");
var databaseSize = Math.Pow(2.0, nDatabaseQubits);
var nIterations = (int)Math.Floor(Math.PI * 1 / (Math.Asin(Math.Sqrt(1 / databaseSize))) / 4);
var queries = nIterations * 2 + 1;
var classicalSuccessProbability = 1.0 / databaseSize;
var quantumSuccessProbability = Math.Pow(Math.Sin((2.0 * (double)nIterations + 1.0) * Math.Asin(1.0 / Math.Sqrt(databaseSize))), 2.0);
var repeats = 100;
var successCount = 0;
Console.Write(
$"\n\nQuantum search for marked element in database.\n" +
$" Database size: {databaseSize}.\n" +
$" Classical success probability: {classicalSuccessProbability}\n" +
$" Quantum success probability: {quantumSuccessProbability}\n\n");
foreach (var idxAttempt in Enumerable.Range(0, repeats))
{
var task = ApplyQuantumSearch.Run(sim, nIterations, nDatabaseQubits);
var data = task.Result;
var markedQubit = data.Item1;
var databaseRegister = data.Item2.ToArray();
successCount += markedQubit == Result.One ? 1 : 0;
if ((idxAttempt + 1) % 10 == 0)
{
var empiricalSuccessProbability = Math.Round((double)successCount / ((double)idxAttempt + 1), 3);
var speedupFactor = Math.Round(empiricalSuccessProbability / classicalSuccessProbability / (double)queries, 3);
Console.Write(
$"Attempt {idxAttempt+1}. " +
$"Success: {markedQubit}, " +
$"Probability: {empiricalSuccessProbability} " +
$"Speedup: {speedupFactor} " +
$"Found database index {string.Join(", ", databaseRegister.Select(x => x.ToString()).ToArray())} \n");
}
}
System.Console.WriteLine("\n\nPress any key to continue...\n");
System.Console.ReadKey();
}
static void Main(string[] args)
{
using (var qsim = new QuantumSimulator())
{
//データベースのサイズ(databaseSize)Nに対する
//必要な量子ビット数(nDatabaseQubits)n. N=2^n
var nDatabaseQubits = 6;
var databaseSize = Math.Pow(2.0, nDatabaseQubits);
//振幅増幅を繰り返す回数k。
//確率をほぼ1にするためには PI/4*Sqrt(N)-1/2なので、N=2^6なら6回程度必要。
var nIterations = 3;
// データベースに対する問い合わせ数
var queries = nIterations * 2 + 1;
// 期待される確率を計算して、実際の結果と比較する
// 古典アルゴリズムでの確率は、N個から1つ探す確率なので
var classicalSuccessProbability = 1.0 / databaseSize;
// Groverアルゴリズムでの確率sin^2[(2*k+1)θ]。ただしsinθ=Sqrt(1/N)
var quantumSuccessProbability = Math.Pow(Math.Sin((2.0 * (double)nIterations + 1.0) * Math.Asin(1.0 / Math.Sqrt(databaseSize))), 2.0);
// 一連の測定を繰り返す回数
var repeats = 100;
// 探索がうまく行った回数
var successCount = 0;
Console.Write(
$@"
Quantum search for marked element in database.
データベースのサイズ: {databaseSize}
古典アルゴリズムでの確率: {classicalSuccessProbability}
1回当たりの問い合わせ数: {queries}
量子アルゴリズムでの確率: {quantumSuccessProbability}
");
foreach (var idxAttempt in Enumerable.Range(0, repeats))
{
//必要なパラメーターを渡してQ#のコードを実行
// GetAwaiter().GetResult() はC#のasync/await構文
// var () = ... という書き方はタプル構文を参照してください
var(markedQubit, databaseRegister) = ApplyQuantumSearch.Run(qsim, nIterations, nDatabaseQubits).GetAwaiter().GetResult();
// 探索に成功していればカウントアップ
successCount += markedQubit == Result.One ? 1 : 0;
// 10回ごとに結果を表示する (10回ごとに特に意味はない)
if ((idxAttempt + 1) % 10 == 0)
{
// 成功した割合を表示
var empiricalSuccessProbability = Math.Round((double)successCount / ((double)idxAttempt + 1), 3);
// 古典アルゴリズムよりどけだけよかったか（割合の比）
var speedupFactor = Math.Round(empiricalSuccessProbability / classicalSuccessProbability / (double)queries, 3);
Console.WriteLine($"試行回数 {idxAttempt}. 成功: {markedQubit}, 確率: {empiricalSuccessProbability} 高速化比: {speedupFactor} 検出したインデックス {databaseRegister}");
}
}
}
}
/// <summary>
/// The aim of this program is to find out the maximum |11…1> in the
/// n-qubits domain with grover algorithm speeding up.
/// </summary>
static void Main(string[] args)
{
var sim = new QuantumSimulator(throwOnReleasingQubitsNotInZeroState: true);
// Quantum Database Search with Manual Oracle Definitions
// N = 2^n
var nDatabaseQubits = 6;
var databaseSize = (int)Math.Pow(2.0, nDatabaseQubits);
double overallProbability = 0.0;
double overallIteration = 0.0;
double overallAcceleration = 0.0;
double overallMutationSuccess = 0.0;
double overallMutationAcceleration = 0.0;
int totalMutation = 0;
int caseNum = 50;
foreach (var cs in Enumerable.Range(0, caseNum))
{
// We define the marked elements. These must be smaller than `databaseSize`
//var markedElements = new long[] { 255, 250, 251, 254, 234 };
var markedElements = new long[] { };
List <long> Elements = markedElements.ToList();
//Generate some random integers for grover to find
Random rnd = new Random();
//At least one individual is marked
int ranLength = rnd.Next(1, (int)Math.Sqrt(databaseSize));
foreach (var i in Enumerable.Range(0, ranLength))
{
int ranNum = rnd.Next(0, databaseSize);
Elements.Add(ranNum);
}
markedElements = Elements.ToArray();
var nMarkedElements = markedElements.Length;
// Grover iteration times to amplify the marked subspace
// Note that the domain is 64 and the solution to this
// problem can only be one, so the number of iterations
// is (π/4)(√N/1)
var nIterations = Statics(databaseSize, nMarkedElements);
// Number of queries to database oracle.
var queries = nIterations * 2 + 1;
var quantumSuccessProbability = Math.Pow(Math.Sin((2.0 * (double)nIterations + 1.0) * Math.Asin(1.0 / Math.Sqrt(databaseSize))), 2.0);
int iterationsTest = (int)((Math.PI / 2.0 / (Math.Asin(Math.Sqrt(nMarkedElements) / Math.Sqrt(databaseSize))) - 1) / 2.0) + 1;
var repeats = 50;
Console.Write(
$"Marked elements: {string.Join(",", markedElements.Select(x => x.ToString()).ToArray())}" +
$" Initial iteration: {iterationsTest}" +
$" Iterations: {nIterations}" +
//$" Theoretical probability: {quantumSuccessProbability}\n\n" +
"\n");
//Perform mutaion or not
var mutate = 1;
//Record the maximun probability of find a result and its corresponding iteration number
var maxProbability = 0.0;
var correspondingIterations = 0;
//More iteration numbers can be tested in the following line
foreach (var iterAttempt in Enumerable.Range(1, nIterations + (int)Math.Sqrt(nIterations)))
{
Console.WriteLine($"-------------------No.{iterAttempt} iteration attempt in No.{cs+1} case test-------------------");
var probsWithoutMutation = 0.0;
for (int mutation = 0; mutation <= mutate; mutation++)
{
var successCount = 0;
//This loop controls whether mutation should be performed or not
foreach (var idxAttempt in Enumerable.Range(0, repeats))
{
//Which qubit should perform Hadamard transformation
var H = new long[] { };
List <long> HList = H.ToList();
//Which qubit should flip
var X = new long[] { };
List <long> XList = X.ToList();
//Which qubit should control
var CNOTLeft = new long[] { };
List <long> CNOTLeftList = CNOTLeft.ToList();
//Which qubit should be controlled to flip
var CNOTRight = new long[] { };
List <long> CNOTRightList = CNOTRight.ToList();
//Note: the number of Hize is yet to reconsider
//int HSize = rnd.Next((int)Math.Sqrt(databaseSize), databaseSize / 2);
int HSize = rnd.Next(0, (int)Math.Sqrt(databaseSize));
foreach (var idxRan in Enumerable.Range(0, HSize))
{
HList.Add(rnd.Next(0, nDatabaseQubits));
}
H = HList.ToArray();
//Not working
int XSize = rnd.Next(0, (int)Math.Sqrt(databaseSize));
foreach (var idxRan in Enumerable.Range(0, XSize))
{
XList.Add(rnd.Next(0, nDatabaseQubits));
}
X = XList.ToArray();
//Note: the number of CNOTSize is yet to reconsider
int CNOTSize = rnd.Next(databaseSize / 2, databaseSize);
foreach (var idxRan in Enumerable.Range(0, CNOTSize))
{
CNOTLeftList.Add(rnd.Next(0, nDatabaseQubits));
CNOTRightList.Add(rnd.Next(0, nDatabaseQubits));
}
CNOTLeft = CNOTLeftList.ToArray();
CNOTRight = CNOTRightList.ToArray();
var task = ApplyQuantumSearch.Run(sim, new QArray <long>(markedElements), iterAttempt, nDatabaseQubits,
new QArray <long>(H), new QArray <long>(X), new QArray <long>(CNOTLeft), new QArray <long>(CNOTRight), mutation);
//Extract the marked qubit and the database register
var data = task.Result;
var markedQubit = data.Item1;
var databaseRegister = data.Item2;
//var resultTest = data.Item3 == Result.One ? 1 : 0;
//If the returned marked qubit is One,
//that means the grover search succeed.
successCount += markedQubit == Result.One ? 1 : 0;
}
var Probability = Math.Round((double)successCount / ((double)repeats), 5);
if (mutation == 0)
{
Console.WriteLine("Random initial State");
probsWithoutMutation = Probability;
}
else
{
Console.WriteLine("With Mutation");
}
if (Probability > maxProbability && mutation == 0)
{
maxProbability = Probability;
correspondingIterations = iterAttempt;
}
else if (mutation == 1 && Probability > probsWithoutMutation)
{
overallMutationSuccess++;
overallMutationAcceleration += (Probability - probsWithoutMutation);
}
Console.WriteLine("Iterations: " + iterAttempt + " Probability: " + Probability);
}
totalMutation++;
}
double acclerationRate = (double)(nIterations > iterationsTest ? nIterations : iterationsTest) / correspondingIterations;
Console.WriteLine("\nIterations: " + correspondingIterations + " Probability: " + maxProbability + " Accleration Rate: " + acclerationRate);
Console.WriteLine("Total mutation: " + totalMutation + " Overall mutation success: " + overallMutationSuccess);
Console.WriteLine("Contemporary Mutation Success: " + overallMutationSuccess / totalMutation + " and Mutation Acceleration : " + overallMutationAcceleration / overallMutationSuccess + "\n");
overallIteration += correspondingIterations;
overallProbability += maxProbability;
overallAcceleration += acclerationRate;
}
Console.WriteLine("Overall probability: " + overallProbability / caseNum + " iterations: " + overallIteration / caseNum + " Acceleration Rate: " + overallAcceleration / caseNum);
Pause();
}
static void Main(string[] args)
{
#region Simulator Setup
// We begin by defining a quantum simulator to be our target
// machine.
var sim = new QuantumSimulator(throwOnReleasingQubitsNotInZeroState: true);
#endregion
#region Random (Classical) Database Search
// Let us investigate the success probability of classical random search.
// This corresponds to the case where we only prepare the start state, and
// do not perform any Grover iterations to amplify the marked subspace
var nIterations = 0;
// We now define the size `N` = 2^n of the database to search in terms of
// number of qubits `n`
var nDatabaseQubits = 6;
// 2^6 = 64
var databaseSize = Math.Pow(2.0, nDatabaseQubits);
// We now execute the classical random search.
// Repeat 1000 times to collect enough data.
var repeats = 1000;
var successCount = 0;
Console.Write(
$"Classical random search for marked element in database (no Grover iterations).\n" +
$" Database size: {databaseSize}\n" +
$" Looking for marked element: One One One One One One\n\n");
foreach (var idxAttempt in Enumerable.Range(0, repeats))
{
// Each operation has a static method called Run which takes a simulator as
// an argument, along with all the arguments defined by the operation itself.
var task = ApplyQuantumSearch.Run(sim, nIterations, nDatabaseQubits);
// We extract the return value of the operation by getting the Results property.
var data = task.Result;
// Extract the marked qubit state
var markedQubit = data.Item1;
var databaseRegister = data.Item2.ToArray();
successCount += markedQubit == Result.One ? 1 : 0;
// Print the results of the search every 100 attempts
if ((idxAttempt + 1) % 100 == 0)
{
var success = false;
if (markedQubit == Result.One)
{
success = true;
}
Console.Write(
$"Attempt: {idxAttempt}. " +
$"Success: {success}. " +
$"Probability: {Math.Round((double)successCount / ((double)idxAttempt + 1), 3)}. " +
$"Found database index: {string.Join(", ", databaseRegister.Select(x => x.ToString()).ToArray())} \n");
}
}
Console.Write($"\nTotal success count over {repeats} attempts: {successCount}.\n");
#endregion
#region Quantum Database Search
// Let us investigate the success probability of the quantum search.
// Wedefine the size `N` = 2^n of the database to searched in terms of
// number of qubits `n`.
nDatabaseQubits = 6;
databaseSize = Math.Pow(2.0, nDatabaseQubits);
// We now perform Grover iterates to amplify the marked subspace.
nIterations = 3;
// Number of queries to database oracle.
var queries = nIterations * 2 + 1;
// We now execute the quantum search.
repeats = 1000;
successCount = 0;
Console.Write(
$"\nQuantum search for marked element in database. Number of Grover iterations: {nIterations}\n" +
$" Database size: {databaseSize}\n" +
$" Looking for marked element: One One One One One One\n\n");
foreach (var idxAttempt in Enumerable.Range(0, repeats))
{
// Each operation has a static method called Run which takes a simulator as
// an argument, along with all the arguments defined by the operation itself.
var task = ApplyQuantumSearch.Run(sim, nIterations, nDatabaseQubits);
// We extract the return value of the operation by getting the Results property.
var data = task.Result;
// Extract the marked qubit state
var markedQubit = data.Item1;
var databaseRegister = data.Item2.ToArray();
successCount += markedQubit == Result.One ? 1 : 0;
// Print the results of the search every 10 attemps
if ((idxAttempt + 1) % 100 == 0)
{
var success = false;
if (markedQubit == Result.One)
{
success = true;
}
Console.Write(
$"Attempt: {idxAttempt}. " +
$"Success: {success}. " +
$"Found database index: {string.Join(", ", databaseRegister.Select(x => x.ToString()).ToArray())} \n");
}
}
Console.Write($"\nTotal success count over {repeats} attempts: {successCount}.\n");
Console.WriteLine("\nPress any key to exit.\n");
Console.ReadKey();
#endregion
}
static void Main(string[] args)
{
#region Setup
// We begin by defining a quantum simulator to be our target
// machine.
var sim = new QuantumSimulator(throwOnReleasingQubitsNotInZeroState: true);
#endregion
#region Random Database Search with Manual Oracle Definitions
// Let us investigate the success probability of classical random search.
// This corresponds to the case where we only prepare the start state, and
// do not perform any Grover iterates to amplify the marked subspace.
var nIterations = 0;
// We now define the size `N` = 2^n of the database to searched in terms of
// number of qubits `n`.
var nDatabaseQubits = 3;
var databaseSize = Math.Pow(2.0, nDatabaseQubits);
// We now execute the classical random search and verify that the success
// probability matches the classical result of 1/N. Let us repeat 100
// times to collect enough statistics.
var classicalSuccessProbability = 1.0 / databaseSize;
var repeats = 3;
var successCount = 0;
/*
* Console.Write(
* $"Classical random search for marked element in database.\n" +
* $" Database size: {databaseSize}.\n" +
* $" Success probability: {classicalSuccessProbability}\n\n");
*
*
*
* foreach (var idxAttempt in Enumerable.Range(0, repeats))
* {
* // Each operation has a static method called Run which takes a simulator as
* // an argument, along with all the arguments defined by the operation itself.
* var task = ApplyQuantumSearch.Run(sim, nIterations, nDatabaseQubits);
*
* // We extract the return value of the operation by getting the Results property.
* var data = task.Result;
*
* // Extract the marked qubit state
* var markedQubit = data.Item1;
* var databaseRegister = data.Item2.ToArray();
*
* successCount += markedQubit == Result.One ? 1 : 0;
*
* // Print the results of the search every 100 attemps
* //if ((idxAttempt + 1) % 1 == 0)
* if(markedQubit == Result.One)
* {
*
* Console.Write(
* $"Attempt {idxAttempt}. " +
* $"Success: {markedQubit}, " +
* $"Probability: {Math.Round((double)successCount / ((double)idxAttempt + 1),3)} " +
* $"Found database index {string.Join(", ", databaseRegister.Select(x => x.ToString()).ToArray())} \n");
* }
* }
* Console.Write("Total Success = " + successCount);
* Pause();
*/
#endregion
#region Quantum Database Search with Manual Oracle Definitions
// Let us investigate the success probability of the quantum search.
// Wedefine the size `N` = 2^n of the database to searched in terms of
// number of qubits `n`.
nDatabaseQubits = 6;
databaseSize = Math.Pow(2.0, nDatabaseQubits);
// We now perform Grover iterates to amplify the marked subspace.
nIterations = 3;
// Number of queries to database oracle.
var queries = nIterations * 2 + 1;
// We now execute the quantum search and verify that the success
// probability matches the theoretical prediction.
classicalSuccessProbability = 1.0 / databaseSize;
var quantumSuccessProbability = Math.Pow(Math.Sin((2.0 * (double)nIterations + 1.0) * Math.Asin(1.0 / Math.Sqrt(databaseSize))), 2.0);
repeats = 8;
successCount = 0;
Console.Write("Searching in 6 bit Register - 2^6=64");
Console.Write(
$"\n\n Quantum search for marked element (63 - (1,1,1,1,1,1))in database. \n" +
$" Database size: {databaseSize}.\n" +
$" Classical success probability: {classicalSuccessProbability}\n" +
// $" Queries per search: {queries} \n" +
$" No of Iterations = {repeats}.\n" +
$" Quantum success probability: {quantumSuccessProbability}\n\n");
foreach (var idxAttempt in Enumerable.Range(0, repeats))
{
// Each operation has a static method called Run which takes a simulator as
// an argument, along with all the arguments defined by the operation itself.
var task = ApplyQuantumSearch.Run(sim, nIterations, nDatabaseQubits);
// We extract the return value of the operation by getting the Results property.
var data = task.Result;
// Extract the marked qubit state
var markedQubit = data.Item1;
var databaseRegister = data.Item2.ToArray();
successCount += markedQubit == Result.One ? 1 : 0;
// Print the results of the search every 10 attemps
//if ((idxAttempt + 1) % 10 == 0)
//if (markedQubit == Result.One )
{
var empiricalSuccessProbability = Math.Round((double)successCount / ((double)idxAttempt + 1), 3);
// This is how much faster the quantum algorithm performs on average
// over the classical search.
var speedupFactor = Math.Round(empiricalSuccessProbability / classicalSuccessProbability / (double)queries, 3);
Console.Write(
$"Attempt {idxAttempt+1}. " +
$"Success: {markedQubit}, " +
$"Probability: {empiricalSuccessProbability} " +
// $"Speedup: {speedupFactor} " +
$"Found database index {string.Join(", ", databaseRegister.Select(x => x.ToString()).ToArray())} \n");
}
}
Console.Write("\n\nTotal Success = " + successCount);
Pause();
#endregion
#region Multiple Element Quantum Database Search with the Canon
// Let us investigate the success probability of the quantum search with multiple
// marked elements.
// We define the size `N` = 2^n of the database to searched in terms of
// number of qubits `n`.
nDatabaseQubits = 8;
databaseSize = Math.Pow(2.0, nDatabaseQubits);
// We define the marked elements. These must be smaller than `databaseSize`
//Microsoft.Quantum.Simulation.Core.QArray<long>[]
Console.Write("\nEnter the no to find below 256:");
long xart = 0;
try
{
xart = Convert.ToInt64(Console.ReadLine());
}
catch (Exception)
{
Console.Write("Since no input given, randomly taking 84\n\n");
xart = 84;
}
QArray <long> markedElements = new QArray <long>()
{
xart
};
var nMarkedElements = markedElements.Length;
// We now perform Grover iterates to amplify the marked subspace.
nIterations = 3;
// Number of queries to database oracle.
queries = nIterations * 2 + 1;
// We now execute the quantum search and verify that the success
// probability matches the theoretical prediction.
classicalSuccessProbability = (double)(nMarkedElements) / databaseSize;
quantumSuccessProbability = Math.Pow(Math.Sin((2.0 * (double)nIterations + 1.0) * Math.Asin(Math.Sqrt(nMarkedElements) / Math.Sqrt(databaseSize))), 2.0);
repeats = 16;
successCount = 0;
Console.Write(
$"\n\nQuantum search for marked element in database.\n" +
$" Database size: {databaseSize}.\n" +
$" Marked elements: {string.Join(",", markedElements.Select(x => x.ToString()).ToArray())}\n" +
$" Classical success probability: {classicalSuccessProbability}\n" +
// $" Queries per search: {queries} \n" +
$" Quantum success probability: {quantumSuccessProbability}\n\n");
//Pause();
foreach (var idxAttempt in Enumerable.Range(0, repeats))
{
//Console.Write(idxAttempt); // Bharath Code
// Each operation has a static method called Run which takes a simulator as
// an argument, along with all the arguments defined by the operation itself.
var task = ApplyGroverSearch.Run(sim, markedElements, nIterations, nDatabaseQubits);
// We extract the return value of the operation by getting the Results property.
var data = task.Result;
// Extract the marked qubit state
var markedQubit = data.Item1;
var databaseRegister = data.Item2;
successCount += markedQubit == Result.One ? 1 : 0;
// Print the results of the search every 1 attemps
//if ((idxAttempt + 1) % 1 == 0)
//if (markedQubit == Result.One)
{
var empiricalSuccessProbability = Math.Round((double)successCount / ((double)idxAttempt + 1), 3);
// This is how much faster the quantum algorithm performs on average
// over the classical search.
var speedupFactor = Math.Round(empiricalSuccessProbability / classicalSuccessProbability / (double)queries, 3);
Console.Write(
$"Attempt {idxAttempt+1}. " +
$"Success: {markedQubit}, " +
$"Probability: {empiricalSuccessProbability} " +
// $"Speedup: {speedupFactor} " +
$"Found database index {databaseRegister} \n");
}
}
Console.Write("\n\nTotal Success = " + successCount);
Pause();
#endregion
/* */
}
static void Main(string[] args)
{
#region Setup
// We begin by defining a quantum simulator to be our target
// machine.
var sim = new QuantumSimulator(throwOnReleasingQubitsNotInZeroState: true);
#endregion
#region Quantum Database Search with Manual Oracle Definitions
// Let us investigate the success probability of the quantum search.
// Wedefine the size `N` = 2^n of the database to searched in terms of
// number of qubits `n`.
var nDatabaseQubits = 6;
var databaseSize = Math.Pow(2.0, nDatabaseQubits);
// We now perform Grover iterates to amplify the marked subspace.
var nIterations = 3;
// Number of queries to database oracle.
var queries = nIterations * 2 + 1;
// We now execute the quantum search and verify that the success
// probability matches the theoretical prediction.
var classicalSuccessProbability = 1.0 / databaseSize;
var quantumSuccessProbability = Math.Pow(Math.Sin((2.0 * (double)nIterations + 1.0) * Math.Asin(1.0 / Math.Sqrt(databaseSize))), 2.0);
var repeats = 100;
var numberSuccess = 0;
var numberTotal = 0;
foreach (var idxAttempt in Enumerable.Range(0, repeats))
{
// Each operation has a static method called Run which takes a simulator as
// an argument, along with all the arguments defined by the operation itself.
var task = ApplyQuantumSearch.Run(sim, nIterations, nDatabaseQubits);
// We extract the return value of the operation by getting the Results property.
var data = task.Result;
// Extract the marked qubit state
var markedQubit = data.Item1;
var databaseRegister = data.Item2.ToArray();
var isSuccess = true;
foreach (var elt in databaseRegister)
{
if (elt.ToString() == "Zero")
{
isSuccess = false;
}
}
if (isSuccess)
{
numberSuccess += 1;
}
Console.Write("Output of Grover's search in binary\n");
Console.Write(string.Join(", ", databaseRegister) + "\n");
numberTotal += 1;
Console.WriteLine("Statistics so far...");
Console.WriteLine($"Total number of attempts = {numberTotal}");
Console.WriteLine($"Total number of successes = {numberSuccess}");
Pause();
}
// Pause();
#endregion
}
static void Main(string[] args)
{
#region Setup
// We begin by defining a quantum simulator to be our target
// machine.
var sim = new QuantumSimulator(throwOnReleasingQubitsNotInZeroState: true);
#endregion
#region Random Database Search with Manual Oracle Definitions
// Let us investigate the success probability of classical random search.
// This corresponds to the case where we only prepare the start state, and
// do not perform any Grover iterates to amplify the marked subspace.
var nIterations = 0;
// We now define the size `N` = 2^n of the database to searched in terms of
// number of qubits `n`.
var nDatabaseQubits = 3;
var databaseSize = Pow(2.0, nDatabaseQubits);
// We now execute the classical random search and verify that the success
// probability matches the classical result of 1/N. Let us repeat 100
// times to collect enough statistics.
var classicalSuccessProbability = 1.0 / databaseSize;
var repeats = 1000;
var successCount = 0;
Console.Write(
$"Classical random search for marked element in database.\n" +
$" Database size: {databaseSize}.\n" +
$" Success probability: {classicalSuccessProbability}\n\n");
foreach (var idxAttempt in Enumerable.Range(0, repeats))
{
// Each operation has a static method called Run which takes a simulator as
// an argument, along with all the arguments defined by the operation itself.
var task = ApplyQuantumSearch.Run(sim, nIterations, nDatabaseQubits);
// We extract the return value of the operation by getting the Results property.
var data = task.Result;
// Extract the marked qubit state
var markedQubit = data.Item1;
var databaseRegister = data.Item2.ToArray();
successCount += markedQubit == Result.One ? 1 : 0;
// Print the results of the search every 100 attempts
if ((idxAttempt + 1) % 100 == 0)
{
Console.Write(
$"Attempt {idxAttempt}. " +
$"Success: {markedQubit}, " +
$"Probability: {Round((double)successCount / ((double)idxAttempt + 1),3)} " +
$"Found database index {string.Join(", ", databaseRegister.Select(x => x.ToString()).ToArray())} \n");
}
}
Pause();
#endregion
#region Quantum Database Search with Manual Oracle Definitions
// Let us investigate the success probability of the quantum search.
// We define the size `N` = 2^n of the database to searched in terms of
// number of qubits `n`.
nDatabaseQubits = 6;
databaseSize = Pow(2.0, nDatabaseQubits);
// We now perform Grover iterates to amplify the marked subspace.
nIterations = 3;
// Number of queries to database oracle.
var queries = nIterations * 2 + 1;
// We now execute the quantum search and verify that the success
// probability matches the theoretical prediction.
classicalSuccessProbability = 1.0 / databaseSize;
var quantumSuccessProbability = Pow(Sin((2.0 * (double)nIterations + 1.0) * Asin(1.0 / Sqrt(databaseSize))), 2.0);
repeats = 100;
successCount = 0;
Console.Write(
$"\n\nQuantum search for marked element in database.\n" +
$" Database size: {databaseSize}.\n" +
$" Classical success probability: {classicalSuccessProbability}\n" +
$" Queries per search: {queries} \n" +
$" Quantum success probability: {quantumSuccessProbability}\n\n");
foreach (var idxAttempt in Enumerable.Range(0, repeats))
{
// Each operation has a static method called Run which takes a simulator as
// an argument, along with all the arguments defined by the operation itself.
var task = ApplyQuantumSearch.Run(sim, nIterations, nDatabaseQubits);
// We extract the return value of the operation by getting the Results property.
var data = task.Result;
// Extract the marked qubit state
var markedQubit = data.Item1;
var databaseRegister = data.Item2.ToArray();
successCount += markedQubit == Result.One ? 1 : 0;
// Print the results of the search every 10 attempts
if ((idxAttempt + 1) % 10 == 0)
{
var empiricalSuccessProbability = Round((double)successCount / ((double)idxAttempt + 1), 3);
// This is how much faster the quantum algorithm performs on average
// over the classical search.
var speedupFactor = Round(empiricalSuccessProbability / classicalSuccessProbability / (double)queries, 3);
Console.Write(
$"Attempt {idxAttempt}. " +
$"Success: {markedQubit}, " +
$"Probability: {empiricalSuccessProbability} " +
$"Speedup: {speedupFactor} " +
$"Found database index {string.Join(", ", databaseRegister.Select(x => x.ToString()).ToArray())} \n");
}
}
Pause();
#endregion
#region Multiple Element Quantum Database Search with the Canon
// Let us investigate the success probability of the quantum search with multiple
// marked elements.
// We define the size `N` = 2^n of the database to searched in terms of
// number of qubits `n`.
nDatabaseQubits = 8;
databaseSize = Pow(2.0, nDatabaseQubits);
// We define the marked elements. These must be smaller than `databaseSize`.
var markedElements = new long[] { 0, 39, 101, 234 };
var nMarkedElements = markedElements.Length;
// We now perform Grover iterates to amplify the marked subspace.
nIterations = 3;
// Number of queries to database oracle.
queries = nIterations * 2 + 1;
// We now execute the quantum search and verify that the success
// probability matches the theoretical prediction.
classicalSuccessProbability = (double)(nMarkedElements) / databaseSize;
quantumSuccessProbability = Pow(Sin((2.0 * (double)nIterations + 1.0) * Asin(Sqrt(nMarkedElements) / Sqrt(databaseSize))), 2.0);
repeats = 10;
successCount = 0;
Console.Write(
$"\n\nQuantum search for marked element in database.\n" +
$" Database size: {databaseSize}.\n" +
$" Marked elements: {string.Join(",", markedElements.Select(x => x.ToString()).ToArray())}" +
$" Classical success probability: {classicalSuccessProbability}\n" +
$" Queries per search: {queries} \n" +
$" Quantum success probability: {quantumSuccessProbability}\n\n");
foreach (var idxAttempt in Enumerable.Range(0, repeats))
{
// Each operation has a static method called Run which takes a simulator as
// an argument, along with all the arguments defined by the operation itself.
var task = ApplyGroverSearch.Run(sim, new QArray <long>(markedElements), nIterations, nDatabaseQubits);
// We extract the return value of the operation by getting the Results property.
var data = task.Result;
// Extract the marked qubit state
var markedQubit = data.Item1;
var databaseRegister = data.Item2;
successCount += markedQubit == Result.One ? 1 : 0;
// Print the results of the search every 1 attempt
if ((idxAttempt + 1) % 1 == 0)
{
var empiricalSuccessProbability = Round((double)successCount / ((double)idxAttempt + 1), 3);
// This is how much faster the quantum algorithm performs on average
// over the classical search.
var speedupFactor = Round(empiricalSuccessProbability / classicalSuccessProbability / (double)queries, 3);
Console.Write(
$"Attempt {idxAttempt}. " +
$"Success: {markedQubit}, " +
$"Probability: {empiricalSuccessProbability} " +
$"Speedup: {speedupFactor} " +
$"Found database index {databaseRegister} \n");
}
}
Pause();
#endregion
}