How can quantum decoherence be managed?

Decoherence can be viewed as the loss of information from a system into the environment (often modeled as a heat bath), since every system is loosely coupled with the energetic state of its surroundings.

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Decoherence represents a challenge for the practical realization of quantum computers, since such machines are expected to rely heavily on the undisturbed evolution of quantum coherences. Simply put, they require that coherent states be preserved and that decoherence is managed, in order to actually perform quantum computation.

(emphasis mine)

So I am wondering how can this loss of information be managed? Does this mean that it should be prevented completely, or is it necessary for quantum computing to actually allow some information loss in order to compute?

• As far as I understand, decoherence is unavoidable, i.e. no matter what there will always be some loss of information. Beyond that, I don't know of anything specific that could be turned into an answer. – Kiro Mar 28 '18 at 7:35

The quantum circuit model describes a quantum computer as a closed quantum system and assumes that there is a system which executes the circuit but is completely isolated from the rest of the universe. In the real world, however, there are no known mechanisms for truly isolating a quantum system from its environment. Real quantum systems are open quantum systems. Open quantum systems couple to their environment and destroy the quantum information in the system through decoherence. When examining the simple evolution of a single quantum system this system-environment coupling appears to cause errors on the quantum system’s evolution (which wouldn't be unitary in this case).

A coin has two states, and makes a good bit but a poor qubit because it cannot remain in superposition of head and tail for very long as it is a classical object. A single nuclear spin can be a very good qubit, because superposition of being aligned with or against an external magnetic field can last for a long time, even days. But it can be difficult to build a quantum computer from nuclear spins because their coupling is so small that it is hard to measure the orientation of a single nuclei. The observation that the constraints are opposing in general: a quantum computer has to be well isolated in order to retain its quantum properties, but at the same time its qubits have to be accessible so that they can be manipulated to perform computation and read out the results. A realistic implementation must strike a balance between these constraints.

The first step towards solving the decoherence problem was taken in 1995 when Shor and Steane independently discovered a quantum analogue of classical error correcting codes. Shor discovered that by encoding quantum information, this information could become more resistant to interaction with its environment. Following this discovery a rigorous theory of quantum error correction was developed. Many different quantum error correcting codes were discovered and this further led to a theory of fault-tolerant quantum computation. Fully fault-tolerant quantum computation describes methods for dealing with system-environment coupling as well as dealing with faulty control of the quantum computer.

Of particular significance was the discovery of the threshold theorem for fault-tolerant quantum computation. The threshold theorem states that if the decoherence interactions are of a certain form and are weaker than the controlling interactions by a certain ratio, quantum computation to any desired precision can be achieved. The threshold theorem for fault-tolerance thus declares a final solution to the question of whether there are theoretical limits to the construction of robust quantum computers.

Yes, currently the loss of information is being managed by means of quantum error correction protocols.

Ideally, quantum decoherence and eventual loss of information should be prevented. However, in real-world scenarios, it is hard to completely isolate quantum systems from their environment.

Technically, quantum decoherence is something necessary for the overall operation of the quantum computing system, in order to bring the quantum computing system to equilibrium state to initiate or perform another computing operation. Having said that loss of information due to quantum decoherence during an computing operation is not an ideal thing.

• The first paragraph is not consistent with the third one. It is also quite vague, can you be more specific about what you are referring to here? – glS Mar 28 '18 at 8:58
• @gIS: Quantum decoherence leads to relaxation and eventual return to the equilibrium state. I was referring to relaxation to equilibrium state in the third paragraph. – RussellB Mar 28 '18 at 9:50
• then it would be useful to have that included in the answer, possibly with examples of quantum algorithms that exploit this kind of relaxation – glS Mar 28 '18 at 10:36
• @glS. Thanks for pointing out. I was referring to the NMR T1 relaxation stuff and which would not go well with the answer. I am removing now. – RussellB Mar 28 '18 at 10:45