static void SimulateHubbardHamiltonianTest()
{
//////////////////////////////////////////////////////////////////////////
// Introduction //////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////
// In this example, we will estimate the ground state energy of
// 1D Hubbard Hamiltonian using the quantum chemistry library.
// The 1D Hubbard model has `n` sites. Let `i` be the site index,
// `s` = 1,0 be the spin index, where 0 is up and 1 is down, `t` be the
// hopping coefficient, `u` the repulsion coefficient, and aᵢₛ the fermionic
// annihilation operator on the fermion indexed by `(i,s)`. The Hamiltonian
// of this model is
//
// H ≔ - t Σᵢ (a†ᵢₛ aᵢ₊₁ₛ + a†ᵢ₊₁ₛ aᵢₛ) + u Σᵢ a†ᵢ₀ a†ᵢ₁ aᵢ₁ aᵢ₀
//
// Note that we use closed boundary conditions.
#region Building the Hubbard Hamiltonian through orbital integrals
var t = 0.2; // hopping coefficient
var u = 1.0; // repulsion coefficient
var nSites = 6; // number of sites;
// Construct Hubbard Hamiltonian
var hubbardOrbitalIntegralHamiltonian = new OrbitalIntegralHamiltonian();
foreach (var i in Enumerable.Range(0, nSites))
{
hubbardOrbitalIntegralHamiltonian.Add(new OrbitalIntegral(new[] { i, (i + 1) % nSites }, -t));
hubbardOrbitalIntegralHamiltonian.Add(new OrbitalIntegral(new[] { i, i, i, i }, u));
}
// Create fermion representation of Hamiltonian
// In this case, we use the spin-orbital to integer
// indexing convention `x = orbitalIdx + spin * nSites`; as it
// minimizes the length of Jordan–Wigner strings
var hubbardFermionHamiltonian = hubbardOrbitalIntegralHamiltonian.ToFermionHamiltonian(IndexConvention.HalfUp);
#endregion
#region Estimating energies by simulating quantum phase estimation
// Create Jordan–Wigner representation of Hamiltonian
var jordanWignerEncoding = hubbardFermionHamiltonian.ToPauliHamiltonian();
// Create data structure to pass to QSharp.
var qSharpData = jordanWignerEncoding.ToQSharpFormat().Pad();
Console.WriteLine($"Estimate Hubbard Hamiltonian energy:");
#endregion
}
// Checks if any errors occur while building Hamiltonian for both index conventions.
public void BuildFermionHamiltonian()
{
var sourceHamiltonian = new OrbitalIntegralHamiltonian();
sourceHamiltonian.Add(orbitalIntegrals);
var targetHamiltonian0 = sourceHamiltonian.ToFermionHamiltonian(IndexConvention.HalfUp);
var targetHamiltonian1 = sourceHamiltonian.ToFermionHamiltonian(IndexConvention.UpDown);
}
static void Main(string[] args)
{
//////////////////////////////////////////////////////////////////////////
// Introduction //////////////////////////////////////////////////////////
//////////////////////////////////////////////////////////////////////////
// In this example, we will estimate the ground state energy of
// 1D Hubbard Hamiltonian using the quantum chemistry library.
// The 1D Hubbard model has `n` sites. Let `i` be the site index,
// `s` = 1,0 be the spin index, where 0 is up and 1 is down, `t` be the
// hopping coefficient, `u` the repulsion coefficient, and aᵢₛ the fermionic
// annihilation operator on the fermion indexed by `(i,s)`. The Hamiltonian
// of this model is
//
// H ≔ - t Σᵢ (a†ᵢₛ aᵢ₊₁ₛ + a†ᵢ₊₁ₛ aᵢₛ) + u Σᵢ a†ᵢ₀ a†ᵢ₁ aᵢ₁ aᵢ₀
//
// Note that we use closed boundary conditions.
#region Building the Hubbard Hamiltonian through orbital integrals
var t = 0.2; // hopping coefficient
var u = 1.0; // repulsion coefficient
var nSites = 6; // number of sites;
// Construct Hubbard Hamiltonian
var hubbardOrbitalIntegralHamiltonian = new OrbitalIntegralHamiltonian();
foreach (var i in Enumerable.Range(0, nSites))
{
hubbardOrbitalIntegralHamiltonian.Add(new OrbitalIntegral(new[] { i, (i + 1) % nSites }, -t));
hubbardOrbitalIntegralHamiltonian.Add(new OrbitalIntegral(new[] { i, i, i, i }, u));
}
// Create fermion representation of Hamiltonian
// In this case, we use the spin-orbital to integer
// indexing convention `x = orbitalIdx + spin * nSites`; as it
// minimizes the length of Jordan–Wigner strings
var hubbardFermionHamiltonian = hubbardOrbitalIntegralHamiltonian.ToFermionHamiltonian(IndexConvention.HalfUp);
#endregion
#region Estimating energies by simulating quantum phase estimation
// Create Jordan–Wigner representation of Hamiltonian
var jordanWignerEncoding = hubbardFermionHamiltonian.ToPauliHamiltonian();
// Create data structure to pass to QSharp.
var qSharpData = jordanWignerEncoding.ToQSharpFormat().Pad();
Console.WriteLine($"Estimate Hubbard Hamiltonian energy:");
// Bits of precision in phase estimation.
var bits = 7;
// Repetitions to find minimum energy.
var reps = 5;
// Trotter step size
var trotterStep = 0.5;
using (var qsim = new QuantumSimulator())
{
for (int i = 0; i < reps; i++)
{
// EstimateEnergyByTrotterization
// Name should make clear that it does it by trotterized
var(phaseEst, energyEst) = GetEnergy.Run(qsim, qSharpData, bits, trotterStep).Result;
Console.WriteLine($"Rep #{i}: Energy estimate: {energyEst}; Phase estimate: {phaseEst}");
}
}
Console.WriteLine("Press Enter to continue...");
if (System.Diagnostics.Debugger.IsAttached)
{
Console.ReadLine();
}
#endregion
}
void BuildOrbitalIntegralHamiltonian()
{
var hamiltonian = new OrbitalIntegralHamiltonian();
hamiltonian.Add(orbitalIntegrals);
}
/// <summary>
/// Deserializes an FCIDUMP-formatted problem description.
/// </summary>
/// <param name="reader">A stream for reading FCIDUMP data.</param>
/// <returns>
/// An electronic structure problem deserialized from the file.
/// </returns>
public static IEnumerable <ElectronicStructureProblem> Deserialize(TextReader reader)
{
// FCIDUMP files begin with a FORTRAN-formatted namelist, delimited
// by &FCI and &END. We start by extracting that namelist.
var allText = reader.ReadToEnd();
var lines = Regex.Split(allText, "\r\n|\r|\n");
if (lines == null)
{
throw new IOException("Expected a non-empty FCIDUMP file.");
}
var header = System.String.Join("\n", lines.TakeWhile(line => line.Trim() != "&END")).Trim();
var body = lines !.SkipWhile(line => line.Trim() != "&END").Skip(1).ToList();
// Make sure that the header starts with &FCI, as expected.
if (!header.StartsWith("&FCI"))
{
throw new IOException("FCIDUMP file did not start with \"&FCI\" as expected.");
}
// Split out the &FCI and &END lines, turn the rest into a dictionary of namelist items.
var namelist = Regex.Matches(
header
.Replace("&FCI", "")
.Replace("&END", ""),
pattern: "\\s*(?<identifier>\\w+)\\s*=\\s*(?<value>[^=]+),\\s*"
)
.ToDictionary(
match => match.Groups["identifier"].Value,
match => match.Groups["value"].Value
);
var hamiltonian = new OrbitalIntegralHamiltonian();
var arrayData = body
.Select(line => line.Trim())
.Where(line => line.Length > 0)
.Select(
line => line.Split(" ", StringSplitOptions.RemoveEmptyEntries)
)
.Select(
row => (
Double.Parse(row[0]),
row[1..].Select(Int32.Parse).Where(idx => idx != 0).ToZeroBasedIndices()
)
);
var(coulomb, _) = arrayData.Where(item => item.Item2.Length == 0).Single();
hamiltonian.Add(arrayData
.Where(row => row.Item2.Length > 0)
.SelectMaybe(
row => row.Item2.Length % 2 == 0
? new OrbitalIntegral(
row.Item2, row.Item1, OrbitalIntegral.Convention.Mulliken
).ToCanonicalForm()
: null
)
.Distinct()
);
// The identity term in deserialized Hamiltonians is the sum of the
// Coloumb repulsion and the energy offset. Since only the former
// exists in FCIDUMP, we set the identity term accordingly.
hamiltonian.Add(new OrbitalIntegral(), coulomb);
return(new List <ElectronicStructureProblem>
{
new ElectronicStructureProblem
{
EnergyOffset = 0.0.WithUnits("hartree"),
CoulombRepulsion = coulomb.WithUnits("hartree"),
Metadata = new Dictionary <string, object>
{
["Comment"] = "Imported from FCIDUMP"
},
NElectrons = Int32.Parse(namelist["NELEC"]),
NOrbitals = Int32.Parse(namelist["NORB"]),
OrbitalIntegralHamiltonian = hamiltonian
}
});
}
internal static ElectronicStructureProblem DeserializeSingleProblem(string line)
{
var problem = new ElectronicStructureProblem()
{
Metadata = new Dictionary <string, object>()
};
var regexMiscellaneous = new Regex(@"((info=(?<info>[^\s]*)))");
var regexnuc = new Regex(@"nuc=(?<nuc>-?\s*\d*.\d*)");
var regexPQ = new Regex(@"(^|\s+)(?<p>\d+),(?<q>\d+)\D*=\s*(?<coeff>-?\s*\d*.\d*)e?(?<exponent>-?\d*)");
var regexPQRS = new Regex(@"(^|\s+)(?<p>\d+)\D+(?<q>\d+)\D+(?<r>\d+)\D+(?<s>\d+)\D*=\s*(?<coeff>-?\s*\d*.\d*)e?(?<exponent>-?\d*)");
double coulombRepulsion = 0.0;
var fileHIJTerms = new Dictionary <int[], double>(new Extensions.ArrayEqualityComparer <int>());
var fileHIJKLTerms = new Dictionary <int[], double>(new Extensions.ArrayEqualityComparer <int>());
var hamiltonian = new OrbitalIntegralHamiltonian();
var nOrbitals = 0L;
Match stringMisc = regexMiscellaneous.Match(line);
if (stringMisc.Success)
{
problem.Metadata["misc_info"] = stringMisc.Groups["info"].ToString();
}
Match stringnuc = regexnuc.Match(line);
if (stringnuc.Success)
{
coulombRepulsion = double.Parse(stringnuc.Groups["nuc"].ToString()).ToDoubleCoeff();
hamiltonian.Add(TermType.OrbitalIntegral.Identity, new OrbitalIntegral(), coulombRepulsion);
}
foreach (Match stringPQ in regexPQ.Matches(line))
{
if (stringPQ.Success)
{
var p = int.Parse(stringPQ.Groups["p"].ToString());
var q = int.Parse(stringPQ.Groups["q"].ToString());
var coeff = double.Parse(stringPQ.Groups["coeff"].ToString());
var exponentString = stringPQ.Groups["exponent"].ToString();
var exponent = 0.0;
if (exponentString != "")
{
exponent = double.Parse(stringPQ.Groups["exponent"].ToString());
}
nOrbitals = new long[] { nOrbitals, p + 1, q + 1 }.Max();
var orbitalIntegral = new OrbitalIntegral(new int[] { p, q }, coeff * (10.0).Pow(exponent));
var orbitalIntegralCanonical = orbitalIntegral.ToCanonicalForm();
if (fileHIJTerms.ContainsKey(orbitalIntegralCanonical.OrbitalIndices))
{
// Check consistency
if (fileHIJTerms[orbitalIntegralCanonical.OrbitalIndices] != orbitalIntegral.Coefficient)
{
// Consistency check failed.
throw new System.NotSupportedException(
$"fileHPQTerm Consistency check fail. " +
$"Orbital integral {orbitalIntegral} coefficient {orbitalIntegral.Coefficient}" +
$"does not match recorded {orbitalIntegralCanonical} coefficient {fileHIJTerms[orbitalIntegral.OrbitalIndices]}.");
}
else
{
// Consistency check passed.
}
}
else
{
fileHIJTerms.Add(orbitalIntegralCanonical.OrbitalIndices, orbitalIntegralCanonical.Coefficient);
}
}
}
foreach (Match stringPQRS in regexPQRS.Matches(line))
{
if (stringPQRS.Success)
{
var p = int.Parse(stringPQRS.Groups["p"].ToString());
var q = int.Parse(stringPQRS.Groups["q"].ToString());
var r = int.Parse(stringPQRS.Groups["r"].ToString());
var s = int.Parse(stringPQRS.Groups["s"].ToString());
var coeff = double.Parse(stringPQRS.Groups["coeff"].ToString());
var exponentString = stringPQRS.Groups["exponent"].ToString();
var exponent = 0.0;
if (exponentString != "")
{
exponent = double.Parse(stringPQRS.Groups["exponent"].ToString());
}
nOrbitals = new long[] { nOrbitals, p + 1, q + 1, r + 1, s + 1 }.Max();
var orbitalIntegral = new OrbitalIntegral(new int[] { p, q, r, s }, coeff * (10.0).Pow(exponent));
var orbitalIntegralCanonical = orbitalIntegral.ToCanonicalForm();
if (fileHIJKLTerms.ContainsKey(orbitalIntegralCanonical.OrbitalIndices))
{
// Check consistency
if (fileHIJKLTerms[orbitalIntegralCanonical.OrbitalIndices] != orbitalIntegral.Coefficient)
{
// Consistency check failed.
throw new System.NotSupportedException(
$"fileHPQRSTerm Consistency check fail. " +
$"Orbital integral {orbitalIntegral.OrbitalIndices} coefficient {orbitalIntegral.Coefficient}" +
$"does not match recorded {orbitalIntegralCanonical.OrbitalIndices} coefficient {fileHIJKLTerms[orbitalIntegral.OrbitalIndices]}.");
}
else
{
// Consistency check passed.
}
}
else
{
fileHIJKLTerms.Add(orbitalIntegralCanonical.OrbitalIndices, orbitalIntegralCanonical.Coefficient);
}
}
}
hamiltonian.Add(fileHIJTerms.Select(o => new OrbitalIntegral(o.Key, o.Value)).ToList());
hamiltonian.Add(fileHIJKLTerms.Select(o => new OrbitalIntegral(o.Key, o.Value)).ToList());
problem.OrbitalIntegralHamiltonian = hamiltonian;
problem.NOrbitals = System.Convert.ToInt32(nOrbitals);
problem.CoulombRepulsion = coulombRepulsion.WithUnits("hartree");
return(problem);
}
