High-fidelity feedback-assisted parity measurement in circuit QED

Abstract

We analyze a two qubit parity measurement based on dispersive read-out in circuit quantum electrodynamics. The back-action on the qubits has two qualitatively different contributions. One is an unavoidable dephasing in one of the parity subspaces, arising during the transient time of switching on the measurement. The other part is a stochastic rotation of the phase in the same subspace, which persists during the whole measurement. The latter can be determined from the full measurement record, using the method of state estimation. Our main result is that the outcome of this phase determination process is independent of the initial state in the state estimation procedure. The procedure can thus be used in a measurement situation, where the initial state is unknown. We discuss how this feed-back method can be used to achieve a high fidelity parity measurement for realistic values of the cavity-qubit coupling strength. Finally, we discuss the robustness of the feed-back procedure towards errors in the measurement record.

Generation and stabilization of a three-qubit entangledWstate in circuit QED via quantum feedback control

“…5(d), the fidelity is still above 0.9 for η as low as 0.2 for the case of χ = −0.11κ and qubits' decay rates γ j = γ = 4 × 10 −3 κ. The value of η < 1 implies appearance of an additional nonunraveling dephasing term in the quantum trajectory (stochastic master) equation [44]. However, this term causes dephasing only among |111 , |W + , |W − , and |000 for the initial qubits' states chosen in our simulations.…”

“…Then, following the calculations in Refs. [38] and [50], we obtain an effective master equation for the qubits' degrees of freedom alone conditioned on continuous homodyne detection as [38,44,50] …”

“…One possible way to resolve this problem is to employ the technique of quantum feedback control [39][40][41][42][43][44][45]. There have been proposals of using quantum feedback control to stabilize and generate two-qubit Bell states in circuit QED [42,43,46].…”

Three-qubit direct dispersive parity measurement with tunable coupling qubits

“…The added overhead of the required ancilla qubits is another deficiency of this paradigm. For this reason the quest for alternative ways of performing stabilizer measurements has become an active area of research [6][7][8][9][10][11][12][13][14][15].…”

Characterization of hidden modes in networks of superconducting qubits

“…Measurement-induced-dephasing is a well known phenomenon [12][13][14][15][16] that has been characterized in experimental systems using tunable couplings between the qubit and its environment 17 and has served as a mechanism for measuring thermal noise [18][19][20] . Various efforts have been made to avoid populating resonators in qubit gates that depend on the qubit-resonator coupling 21,22 , to reduce qubit dephasing through measurement feedback [23][24][25] or tunable coupling to the readout resonator 26 . However, we can also take advantage of this phenomenon to determine the frequency of bus resonators and the strength of bus-qubit coupling.…”