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An algorithm is proposed which transfers the quantum information of a wavefunction (analogue signal) into a register of qubits (digital signal) such that$n$ qubits describe the amplitudes and phases of $2^n$ points of a sufficientlysmooth wave function. We assume that the continuous degree of freedom couplesto one or more qubits of a quantum register via a Jaynes Cummings Hamiltonianand that we have universal quantum computation capabilities on the register aswell as the possibility to perform bang-bang control on the qubits. Thetransfer of information is mainly based on the application of the quantumphase-estimation algorithm in both directions. Here, the running time increasesexponentially with the number of qubits. We pose it as an open question whichinteractions would allow polynomial running time. One example would beinteractions which enable exact squeezing operations

Quantum analog-to-digital and digital-to-analog conversion