Quantum Computation Language

• Data types
  • Quantum - qureg, quvoid, quconst, quscratch, qucond
  • Classical - int, real, complex, boolean, string, vector, matrix, tensor
• Function types
  • qufunct - Pseudo-classic operators. Can only change the permutation of basis states.
  • operator - General unitary operators. Can change the amplitude.
  • procedure - Can call measure, print, and dump inside this function. This function is non-invertible.
• Built-in functions
  • Quantum
    • qufunct - Fanout, Swap, Perm2, Perm4, Perm8, Not, CNot
    • operator - Matrix2x2, Matrix4x4, Matrix8x8, Rot, Mix, H, CPhase, SqrtNot, X, Y, Z, S, T
    • procedure - measure, dump, reset
  • Classical
    • Arithmetic - sin, cos, tan, log, sqrt, ...
    • Complex - Re, Im, conj

The basic built-in quantum data type in QCL is the qureg (quantum register). It can be interpreted as an array of qubits (quantum bits).

qureg x1[2]; // 2-qubit quantum register x1
qureg x2[2]; // 2-qubit quantum register x2
H(x1); // Hadamard operation on x1
H(x2[1]); // Hadamard operation on the first qubit of the register x2

Since the qcl interpreter uses qlib simulation library, it is possible to observe the internal state of the quantum machine during execution of the quantum program.

qcl> dump
: STATE: 4 / 32 qubits allocated, 28 / 32 qubits free
0.35355 |0> + 0.35355 |1> + 0.35355 |2> + 0.35355 |3>
+ 0.35355 |8> + 0.35355 |9> + 0.35355 |10> + 0.35355 |11>

Note that the dump operation is different from measurement, since it does not influence the state of the quantum machine and can be realized only using a simulator.

Like in modern programming languages, it is possible to define new operations which can be used to manipulate quantum data. For example:

operator diffuse (qureg q) {
  H(q);                 // Hadamard Transform
  Not(q);               // Invert q
  CPhase(pi, q);        // Rotate if q=1111..
  !Not(q);              // undo inversion
  !H(q);                // undo Hadamard Transform
}

defines inverse about the mean operator used in Grover's algorithm (it is sometimes called Grover's diffusion operator). This allows one to define algorithms on a higher level of abstraction and extend the library of functions available for programmers.