Realization of Universal Ion-Trap Quantum Computation with Decoherence-Free Qubits

Any residual coupling of a quantum computer to the environment results in computational errors. Encoding quantum information in a so-called decoherence-free subspace provides means to avoid these errors. Despite tremendous progress in employing this technique to extend memory storage times by orders of magnitude, computation within such subspaces has been scarce. Here, we demonstrate the realization of a universal set of quantum gates acting on decoherence-free ion qubits. We combine these gates to realize the first controlled-NOT gate towards a decoherence-free, scalable quantum computer.

Figure 1

Set of logical gate operations—${\sigma }^z$ rotation, ${\sigma }^x$ rotation, and conditional phase gate: A single ion ac-Stark shift pulse allows for arbitrary rotation of the logical qubit around the $z$ axis; the MS gate represents a rotation about the $x$ axis of the corresponding Bloch sphere of the logical qubit; the phase gate is realized by a copropagating bichromatic light field as described in 21, applied on adjacent ions of two logical qubits.

Figure 2

Pulse sequence to realize a controlled-NOT operation within a DFS—The logical pulse sequence (a) and the operations on the physical qubits (b) are depicted: A logical phase gate is performed on two logical qubits. For the target qubit, the phase gate is enclosed by two Ramsey pulses, respectively $\pi /2$ rotations along the $x$ and $y$ axis of the corresponding Bloch sphere (represented by a composite ${\sigma }^z{\sigma }^x{\sigma }^z$ rotation).

Figure 3

The DFS-CNOT gate can be used to generate Bell states in the logical qubit Hilbert space. For a given superposition between $|0{⟩}_L$ and $|1{⟩}_L$ on the control qubit, the resulting output state will be one of the four Bell states. The real part of the obtained density matrices for all four Bell states is shown above. On average, a fidelity of 91(2)% is achieved within the decoherence-free subspace.