Conditions for superdecoherence

Joris Kattemölle and Jasper van Wezel

Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, The Netherlands
QuSoft, CWI, Science Park 123, Amsterdam, The Netherlands

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Abstract

Decoherence is the main obstacle to quantum computation. The decoherence rate per qubit is typically assumed to be constant. It is known, however, that quantum registers coupling to a single reservoir can show a decoherence rate per qubit that increases linearly with the number of qubits. This effect has been referred to as superdecoherence, and has been suggested to pose a threat to the scalability of quantum computation. Here, we show that superdecoherence is absent when the spectrum of the single reservoir is continuous, rather than discrete. The reason of this absence, is that, as the number of qubits is increased, a quantum register inevitably becomes susceptible to an ever narrower bandwidth of frequencies in the reservoir. Furthermore, we show that for superdecoherence to occur in a reservoir with a discrete spectrum, one of the frequencies in the reservoir has to coincide exactly with the frequency the quantum register is most susceptible to. We thus fully resolve the conditions that determine the presence or absence of superdecoherence. We conclude that superdecoherence is easily avoidable in practical realizations of quantum computers.

In theory, quantum computers can solve problems that cannot be solved on any classical computer. Solving these problems would have far-reaching consequences in many fields, ranging from medicine to cybersecurity. It is, however, notoriously hard to build a quantum computer. This is because it is much harder to protect the fundamental building block of the quantum computer (the qubit) from noise, than it is to protect its classical counterpart (the bit) from noise. Some years ago, it was discovered that the situation might be even worse: the more qubits you add, the more each of these qubits suffers from noise, almost as if the other qubits amplify the noise. This effect is unknown to classical bits. We discovered that the more qubits you add, the more selective they become in the type of noise they are susceptible to. This is much like a fishbone radio antenna: the more vertical 'bones’ are added, the fewer different frequencies it receives. As we show, the net result is that the problem of increasing noise levels for larger systems can easily be avoided.

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