Quantum Computing

Error Correction

Quantum error correction is essential if quantum computer is to work properly because of the fragility of quantum states in the presence of noise. In conventional computer, error correction methods usually involve the gathering of information from the system (such as creating redundant bits). For a quantum system this would cause the unavoidable disturbance associated with observation. It is not possible to generate copies of the original state without destroying it.

Prepare the primary physical qubit such as P = a |1 + b |0, which is to be protected from error.
Prepare two auxiliary A1 = |1, A2 = |1, which are then entangled with the primary qubit to form a logical state.
Noise (causing random error) is applied to this logical state, which is represented by P, A1, A2 in Figure 13.
The primary qubit is decoded from the auxiliary qubits. Now P is separated from A1, A2.
Syndrome measurement, which can determine if the error is a bit flip, or a sign (of the phase) flip, or both, is performed on the four possibilities for the auxiliary states A1, A2, e.g.,
1. |1|1 for no error - association of the most often outcome with the most easily distinguishable measurement.
2. |1|0 for auxiliary state 2 flipped - no correction required.
3. |0|1 for auxiliary state 1 flipped - no correction required.
4. |0|0 for primary qubit flipped - e.g., both the bit and sign are flipped: P = -a |0 + b |1.
The primary state has been altered in Case 4. Appropriate correction is applied to recover the primary qubit initial state.

Such error-correction protocols have been implemented in 2004 using three beryllium atomic-ion qubits (the qubits comprise the two electronic ground state hyperfine levels, which are equated to the two spin 1/2 states - up and down) confined to a linear, multi-zone trap. The trap acts like a quantum register with the internal state of each ion playing the role of a qubit. It has been demonstrated that fidelity of 0.7 - 0.8 can be achieved in the experiments. However, the method works well only when at most one of the three qubits undergoes a spin-flip error. Figure 13 shows the transportation of the ions in the trap during the error-correction protocol as a function of time. Each experiment requires approximately 4 ms to perform. The ions are kept together by careful tuning of the phases of the optical-dipole force. Refocusing operations are required to counteract qubit dephasing caused by fluctuations in the local magnetic field.

Figure 13 Quantum Error Correction [view large image]

There is a fundamental obstacle before quantum computers can become a practical reality: decoherence, which is the loss of the very quantum property (superposition) that such computers would rely on. Decoherence stems from the tiniest stray interactions with the ambient environment, and thus most quantum computer designs seek to isolate the sensitive working elements from their surroundings. It is found that even perfect isolation would not keep dechoherence at bay. A process called spontaneous symmetry breaking will ruin the delicate state required for quantum computing. In the case of one proposed device based on superconducting qubits, it is predicted that this new source of decoherence would degrade the qubits after just a few seconds. However, quantum error correction may come to the rescue once the coherence time is long enough. By running on batches of qubits that each last for only a second, a quantum computer as a whole can continue working indefinitely.