Non-unitary probabilistic quantum computing circuit and method
A quantum circuit performing quantum computation in a quantum computer. A chosen transformation of an initial n-qubit state is probabilistically obtained. The circuit comprises a unitary quantum operator obtained from a non-unitary quantum operator, operating on an n-qubit state and an ancilla state. When operation on the ancilla state provides a success condition, computation is stopped. When operation on the ancilla state provides a failure condition, computation is performed again on the ancilla state and the n-qubit state obtained in the previous computation, until a success condition is obtained.
1. A quantum circuit adapted to perform quantum computation in a quantum computer to probabilistically achieve a chosen transformation of an initial n-qubit state, comprising:
a unitary quantum operator operating on a qubit state and an ancilla state to obtain an evolved qubit state and an evolved ancilla state; and
a measurement operator to measure the evolved ancilla state, the evolved ancilla state being adapted to assume a success condition or a failure condition,
wherein when the evolved ancilla state assumes a success condition the chosen transformation is obtained, and when the evolved ancilla state assumes a failure condition the unitary quantum operator further operates on the ancilla state and the evolved qubit state, the unitary quantum operator further operating on the ancilla state and previously evolved qubit states until the evolved ancilla state assumes a success condition.
2. The quantum circuit of claim 1 , wherein the unitary quantum operator is formed from a non-unitary quantum operator.
3. The quantum circuit of claim 2 , wherein the unitary quantum operator is induced from a Hamiltonian containing the non-unitary quantum operator.
4. The quantum circuit of claim 1 , wherein the ancilla state is a |1 1| state.
5. The quantum circuit of claim 4 , wherein the success condition corresponds to the |0 evolved ancilla state.
6. The quantum circuit of claim 4 , wherein the failure condition corresponds to the |1 evolved ancilla state.
7. The quantum circuit of claim 1 , wherein the unitary quantum operator depends on a non-unitary matrix N and a constant ε.
8. The quantum circuit of claim 7 , wherein the unitary quantum operator is defined through a Hamiltonian built from N.
9. The quantum circuit of claim 7 , wherein the unitary quantum operator has an expression
Ω
=
exp
(
ⅈ
ɛ
(
0
-
ⅈ
N
ⅈ
N
+
0
)
)
.
10. The quantum circuit of claim 2 , wherein the quantum computation is a transformation
ρ in −>Nρ in N † /tr ( Nρ in N † ),
wherein N is the non-unitary quantum operator and wherein ρ in is the qubit state.
11. The quantum circuit of claim 10 , wherein the qubit state is an n-dimensional qubit state and N is a 2 n ×2 n dimensional matrix.
12. A quantum computer comprising the quantum circuit according to claim 1 .
13. A method for probabilistic performance of quantum computation in a quantum circuit adapted to be used in a quantum computer, comprising:
providing an arbitrary non-unitary transformation N;
obtaining a unitary quantum operator from the non-unitary transformation N;
providing an ancilla qubit;
providing a qubit state;
evolving the ancilla qubit under the unitary quantum operator;
evolving the qubit state under the unitary quantum operator;
measuring the evolved ancilla state;
stopping computation if the evolved ancilla state assumes a success condition;
further evolving the ancilla qubit and the evolved qubit state under the unitary quantum operator if the evolved ancilla state assumes a failure condition;
further evolving the ancilla qubit and a previously evolved qubit state under the unitary quantum operator until the evolved ancilla state assumes a success condition.
14. The method of claim 13 wherein N is amended to form a 2 n ×2 n matrix.
15. A quantum circuit operating according to the method of claim 14 .
16. A quantum computer operating according to the method of claim 14 .