Abstract:

Both finite memory and heat generation are problems for experimental realizations of quantum computers. A naïve erasure of a quantum memory costs work and dissipates heat into the quantum computer's environment due to Landauer's principle. We propose a protocol for erasing qubits on the go, in the middle of a quantum algorithm, hence the name online erasure. We define this protocol for instances of quantum algorithms solving the hidden subgroup problem. Making use of the entanglement between the ancillary register and the main register the online erasure procedure can be used to absorb heat from the environment, thus cooling the quantum computer on the go, while still solving the hidden subgroup problem. If we are looking at a hidden subgroup H of a group G the work cost of erasure can be negative and is lower bounded by -kT ln|G/H|. Moreover, we investigate whether the existence of an online erasure protocol implies that the quantum algorithm could have been simplified in the first place, in the sense that it could run on fewer qubits. Quantitatively, if we have open circuit access to the function oracle, an online erasure protocol erasing k ancilla qubits can be repurposed to reduce the number of main and ancilla qubits each by k.