Why must Quantum Computers be reversible?

[Lovelace]

Although I've read many times that quantum computers are reversible, I am unable to find a understandable explanation as to why (this may be because I study Computer Science).
From what I've read, I assume that the answer is linked to the Second Law of Thermodynamics, but I don't know how.

Thanks

 

[Naty1]

Check out 'reversible computing' in Wiki...and then follow the link to 'Landauer's principle'.

 

[Mr_Physicist]

Try looking in "Quantum Computation and Quantum Information" by Nielsen and Chuang. First of all, reversibility is not always required, look at cluster state computation and the one-way quantum computer. My understanding is that for an ideal quantum computation, to take full advantage of all the resources you have access to, you want to start with N qubits and end with N qubits. If you don't do the computation reversibly, it essentially cost you qubits, which are coupled to your classical input and you lose out on some of the "quantumness" that makes a quantum computer worthwhile in the first place. In real life, it seems that losing out on some of those qubits is just the cost of doing business.

 

[Jon_Trevathan]

According to March 8, 2012 article in "Nature" (see citation below), the Landauer Principle has finally been experimentally verified.

According to the Nature article, Rolf Landauer in 1961 had "argued that the erasure of information is a dissipative process" and that a "minimal quantity of heat, proportional to the thermal energy and called the Landauer bound, is necessarily produced when a classical bit of information is deleted." Landauer was the first to connect the loss of
known information with a loss of free energy. "A direct consequence of this logically irreversible transformation is that the entropy of the environment increases by a finite amount"

According to an article by Michael P. Frank titled "Reversible Computing", information can never really be destroyed. Every clock cycle (that is, billions of times a second), a typical logic gate in today’s processors “overwrites” its old output with a new one. But, the information in the old output physically cannot be destroyed." ... "All this information, since it cannot be destroyed, is essentially pushed out into the environment, and the energy committed to storing this waste information (entropy) in the environment is, by definition, heat. "

The associated heat dissipation problem means that the "Landauer Principle represents one of the fundamental physical limit of irreversible computation." As noted in the Nature article, until now, the validity of the Landauer Principle "has been repeatedly questioned and its usefulness criticized (FN17–22). From a technological perspective, energy dissipation per logic operation in present-day silicon-based digital circuits is about a factor of 1,000 greater than the ultimate Landauer limit, but is predicted to quickly attain it within the next couple of decades (FN23,24)."

The cited experiment has verified that the ultimate Landauer limit is "real".
See: Antoine Bérut, et al., "Experimental verification of Landauer’s principle linking information and thermodynamics" Nature 483, 187–189 (08 March 2012)
http://www.physorg.com/news/2012-03-landauer-dissipated-memory-erased.html

 

[martinbn]

Unitary transformations are invertible.

 

[ricochet2]

A quantum computer requires an input register (I), and output register (O) and a set of extra qubits to serve as a work area (R). Suppose that a quantum calculation acts upon I and R to produce a result, which is then contained in a subset of qubits of I and R. The result could be "copied" to O by means of a set of cNot operations, but then O's state would be entangled with I and R, so, generally speaking, no meaningful result could be read from O. We would need to reverse the calculation on I and R, returning them to their initial states. Only this would leave O in a meaningful state. So the calculation would need to be reversible for this to work, i.e., it would need to be a unitary transformation.