codes.h

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/*
 * This file is part of Quantum++.
 *
 * MIT License
 *
 * Copyright (c) 2013 - 2020 Vlad Gheorghiu.
 *
 * Permission is hereby granted, free of charge, to any person obtaining a copy
 * of this software and associated documentation files (the "Software"), to deal
 * in the Software without restriction, including without limitation the rights
 * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 * copies of the Software, and to permit persons to whom the Software is
 * furnished to do so, subject to the following conditions:
 *
 * The above copyright notice and this permission notice shall be included in
 * all copies or substantial portions of the Software.
 *
 * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
 * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
 * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
 * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
 * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
 * SOFTWARE.
 */

#ifndef CLASSES_CODES_H_
#define CLASSES_CODES_H_

namespace qpp {
class Codes final : public internal::Singleton<const Codes> // const Singleton
{
    friend class internal::Singleton<const Codes>;

  public:
    enum class Type {
        FIVE_QUBIT,         
        SEVEN_QUBIT_STEANE, 
        NINE_QUBIT_SHOR,    
    };

  private:
    Codes() {} // = default; // clang++ spits the error below if defaulted:
    //    error:
    //    default initialization of an object of const type 'const qpp::Codes'
    //    requires a user-provided default constructor

    ~Codes() = default;

  public:
    ket codeword(Type type, idx i) const {
        ket result;
        switch (type) {
            // [[5,1,3]] Five qubit code, as described in Nielsen and Chuang
            case Type::FIVE_QUBIT:
                switch (i) {
                    case 0:
                        result =
                            (mket({0, 0, 0, 0, 0}) + mket({1, 0, 0, 1, 0}) +
                             mket({0, 1, 0, 0, 1}) + mket({1, 0, 1, 0, 0}) +
                             mket({0, 1, 0, 1, 0}) - mket({1, 1, 0, 1, 1}) -
                             mket({0, 0, 1, 1, 0}) - mket({1, 1, 0, 0, 0}) -
                             mket({1, 1, 1, 0, 1}) - mket({0, 0, 0, 1, 1}) -
                             mket({1, 1, 1, 1, 0}) - mket({0, 1, 1, 1, 1}) -
                             mket({1, 0, 0, 0, 1}) - mket({0, 1, 1, 0, 0}) -
                             mket({1, 0, 1, 1, 1}) + mket({0, 0, 1, 0, 1})) /
                            4.;
                        break;
                    case 1:
                        result =
                            (mket({1, 1, 1, 1, 1}) + mket({0, 1, 1, 0, 1}) +
                             mket({1, 0, 1, 1, 0}) + mket({0, 1, 0, 1, 1}) +
                             mket({1, 0, 1, 0, 1}) - mket({0, 0, 1, 0, 0}) -
                             mket({1, 1, 0, 0, 1}) - mket({0, 0, 1, 1, 1}) -
                             mket({0, 0, 0, 1, 0}) - mket({1, 1, 1, 0, 0}) -
                             mket({0, 0, 0, 0, 1}) - mket({1, 0, 0, 0, 0}) -
                             mket({0, 1, 1, 1, 0}) - mket({1, 0, 0, 1, 1}) -
                             mket({0, 1, 0, 0, 0}) + mket({1, 1, 0, 1, 0})) /
                            4.;
                        break;
                    default:
                        throw exception::NoCodeword("qpp::Codes::codeword()");
                }
                break;
            // [[7,1,3]] Steane code, as described in Nielsen and Chuang
            case Type::SEVEN_QUBIT_STEANE:
                switch (i) {
                    case 0:
                        result = (mket({0, 0, 0, 0, 0, 0, 0}) +
                                  mket({1, 0, 1, 0, 1, 0, 1}) +
                                  mket({0, 1, 1, 0, 0, 1, 1}) +
                                  mket({1, 1, 0, 0, 1, 1, 0}) +
                                  mket({0, 0, 0, 1, 1, 1, 1}) +
                                  mket({1, 0, 1, 1, 0, 1, 0}) +
                                  mket({0, 1, 1, 1, 1, 0, 0}) +
                                  mket({1, 1, 0, 1, 0, 0, 1})) /
                                 std::sqrt(8.);

                        break;
                    case 1:
                        result = (mket({1, 1, 1, 1, 1, 1, 1}) +
                                  mket({0, 1, 0, 1, 0, 1, 0}) +
                                  mket({1, 0, 0, 1, 1, 0, 0}) +
                                  mket({0, 0, 1, 1, 0, 0, 1}) +
                                  mket({1, 1, 1, 0, 0, 0, 0}) +
                                  mket({0, 1, 0, 0, 1, 0, 1}) +
                                  mket({1, 0, 0, 0, 0, 1, 1}) +
                                  mket({0, 0, 1, 0, 1, 1, 0})) /
                                 std::sqrt(8.);
                        break;
                    default:
                        throw exception::NoCodeword("qpp::Codes::codeword()");
                }
                break;
            // [[9,1,3]] Shor code
            case Type::NINE_QUBIT_SHOR:
                ket shora = mket({0, 0, 0}) + mket({1, 1, 1});
                ket shorb = mket({0, 0, 0}) - mket({1, 1, 1});
                switch (i) {
                    case 0:
                        result =
                            kron(shora, kron(shora, shora)) / std::sqrt(8.);
                        break;
                    case 1:
                        result =
                            kron(shorb, kron(shorb, shorb)) / std::sqrt(8.);
                        break;
                    default:
                        throw exception::NoCodeword("qpp::Codes::codeword()");
                }
        }

        return result;
    }
}; /* class Codes */

} /* namespace qpp */

#endif /* CLASSES_CODES_H_ */