The full requirements for a functional quantum computer are not entirely known, but there are many generally accepted requirements.
David DiVincenzo outlined several of these
criteria for quantum computing. The system's initial state for quantum computation can therefore be described by the ions in their hyperfine and motional ground states, resulting in an initial center of mass phonon state of |0\rangle (zero phonons).
Arbitrary single qubit rotation One of the requirements of universal quantum computing is to coherently change the state of a single qubit. For example, this can transform a qubit starting out in 0 into any arbitrary superposition of 0 and 1 defined by the user. In a trapped-ion system, this is often done using
magnetic dipole transitions or stimulated
Raman transitions for hyperfine qubits and electric quadrupole transitions for optical qubits. The term "rotation" alludes to the
Bloch sphere representation of a qubit pure state. Gate fidelity can be greater than 99%. The
rotation operators R_x(\theta) and R_y(\theta) can be applied to individual ions by manipulating the frequency of an external electromagnetic field from and exposing the ions to the field for specific amounts of time. These controls create a
Hamiltonian of the form H_I^i=\hbar\Omega/2(S_+\exp(i\phi)+S_-\exp(-i\phi)). Here, S_+ and S_- are the raising and lowering operators of spin (see
Ladder operator). These rotations are the universal building blocks for single-qubit gates in quantum computing.
Scalable trap designs Quantum computers must be capable of initializing, storing, and manipulating many qubits at once in order to solve difficult computational problems. However, as previously discussed, a finite number of qubits can be stored in each trap while still maintaining their computational abilities. It is therefore necessary to design interconnected ion traps that are capable of transferring information from one trap to another. Ions can be separated from the same interaction region to individual storage regions and brought back together without losing the quantum information stored in their internal states. Ions can also be made to turn corners at a "T" junction, allowing a two dimensional trap array design. Semiconductor fabrication techniques have also been employed to manufacture the new generation of traps, making the 'ion trap on a chip' a reality. An example is the
quantum charge-coupled device (QCCD) designed by D. Kielpinski,
Christopher Monroe and
David J. Wineland. QCCDs resemble mazes of electrodes with designated areas for storing and manipulating qubits. The variable electric potential created by the electrodes can both trap ions in specific regions and move them through the transport channels, which negates the necessity of containing all ions in a single trap. Ions in the QCCD's memory region are isolated from any operations and therefore the information contained in their states is kept for later use. Gates, including those that entangle two ion states, are applied to qubits in the interaction region by the method already described in this article.
Decoherence in scalable traps When an ion is being transported between regions in an interconnected trap and is subjected to a nonuniform magnetic field, decoherence can occur in the form of the equation below (see
Zeeman effect). This effectively changes the relative phase of the quantum state. The up and down arrows correspond to a general superposition qubit state, in this case the ground and excited states of the ion. \left|\uparrow\right\rangle + \left|\downarrow\right\rangle\longrightarrow \exp(i\alpha)\left|\uparrow\right\rangle + \left|\downarrow\right\rangle Additional relative phases could arise from physical movements of the trap or the presence of unintended electric fields. If the user could determine the parameter α, accounting for this decoherence would be relatively simple, as known quantum information processes exist for correcting a relative phase. However, since α from the interaction with the magnetic field is path-dependent, the problem is highly complex. Considering the multiple ways that decoherence of a relative phase can be introduced in an ion trap, reimagining the ion state in a new basis that minimizes decoherence could be a way to eliminate the issue. One way to combat decoherence is to represent the quantum state in a new basis called the
decoherence-free subspaces, or DFS., with basis states \left|\uparrow\downarrow\right\rangle and \left|\downarrow\uparrow\right\rangle. The DFS is actually the subspace of two ion states, such that if both ions acquire the same relative phase, the total quantum state in the DFS will be unaffected. ==Challenges==