A method of measuring self-Kerr in a physical
quantum system configured to host a bosonic code
qubit, comprises the following operations: 1) providing a physical
quantum system configured to host a bosonic code
qubit, said physical
quantum system comprising (i) a
quantum circuit comprising oscillators hosting a buffer or readout mode and a memory mode, and a non-
linear element coupling the buffer or readout mode to the memory mode, and (ii) a
control circuit configured to apply one or more control signals to the
quantum circuit to stabilize the bosonic code
qubit in the memory mode and further configured to receive measurement signals from at least the buffer or readout mode, 2) define a coherent state (α) for the memory mode, and, for each of a plurality of coherent state amplitudes and each of a plurality of durations (t), a. prepare, using the
control circuit, said coherent state (α) in the memory having one of said plurality of coherent state amplitudes, b. wait for a period of time having one of said duration (t), c. apply, using the
control circuit, one or more control signals to said
quantum circuit such that the quantum circuit is in a resonant regime | i * ω a - ω b | = j * |ω cs | if said one or more control signals comprise an AC component having an
angular frequency |ω cs | or | i * ω a - ω b | = 0 if said one or more control signals comprise only DC components, resulting in an interaction, mediated via said non-
linear element, in said physical
quantum system which results in a Hamiltonian having a leading term of the general formula Hi,(j,0) α ξ(j,0) (α†)i b + h.c...., where α is the
annihilation operator of said memory mode, i is an integer superior or equal to 1, ω a is the
angular frequency of the memory mode whilst the quantum circuit is in the resonant regime, j is an integer superior or equal to 1, b is the
annihilation operator of the buffer or readout mode, ω b is the
angular frequency of the buffer or readout mode whilst the quantum circuit is in the resonant regime, and ξ(j,0) is the strength of said interaction, and d. simultaneously to operation 2)c., using the control circuit, receiving measurement signals comprising at least the mode phase and / or mode amplitude of the buffer or readout mode, 3) derive an effective detuning or a decayed mode amplitude for each coherent state amplitude, by fitting of the measurements of operation 2)d. which are associated with said each coherent state amplitude, 4) derive at least one of self-Kerr coefficients, stark-shift detuning, and memory
dephasing rate from the plurality of effective detunings or decayed mode amplitudes of operation 3) by fitting of a function of the
absolute magnitude squares of coherent state amplitude in said memory mode.