While dissipation is widely considered as being harmful for quantum coherence, it can, when properly engineered, lead to the stabilization of non-trivial pure quantum states. We proposea scheme for continuous generation and stabilization of Schr\“{o}dinger cat states in a cavity using dissipation engineering. We first generate non-classical photon states with definite parity by means of a two-photon drive and dissipation, and then stabilize these transient states against single-photon decay. The single-photon stabilization is autonomous, and is implemented through a second engineered bath, which exploits the photon number dependent frequency-splitting due to Kerr interactions in the strongly dispersive regime of circuit QED. Starting with the Hamiltonian of the baths plus cavity, we derive an effective model of only the cavity photon states along with analytic expressions for relevant physical quantities, such as the stabilization rate. The deterministic generation of such cat states is one of the key ingredients in performing universal quantum computation.
We present a new hardware-efficient paradigm for universal quantum computation which is based on encoding, protecting and manipulating quantum information in a quantum harmonic oscillator.This proposal exploits multi-photon driven dissipative processes to encode quantum information in logical bases composed of Schr\“odinger cat states. More precisely, we consider two schemes. In a first scheme, a two-photon driven dissipative process is used to stabilize a logical qubit basis of two-component Schr\“odinger cat states. While such a scheme ensures a protection of the logical qubit against the photon dephasing errors, the prominent error channel of single-photon loss induces bit-flip type errors that cannot be corrected. Therefore, we consider a second scheme based on a four-photon driven dissipative process which leads to the choice of four-component Schr\“odinger cat states as the logical qubit. Such a logical qubit can be protected against single-photon loss by continuous photon number parity measurements. Next, applying some specific Hamiltonians, we provide a set of universal quantum gates on the encoded qubits of each of the two schemes. In particular, we illustrate how these operations can be rendered fault-tolerant with respect to various decoherence channels of participating quantum systems. Finally, we also propose experimental schemes based on quantum superconducting circuits and inspired by methods used in Josephson parametric amplification, which should allow to achieve these driven dissipative processes along with the Hamiltonians ensuring the universal operations in an efficient manner.
Photons are ideal carriers for quantum information as they can have a long
coherence time and can be transmitted over long distances. These properties are
a consequence of their weakinteractions within a nearly linear medium. To
create and manipulate nonclassical states of light, however, one requires a
strong, nonlinear interaction at the single photon level. One approach to
generate suitable interactions is to couple photons to atoms, as in the strong
coupling regime of cavity QED systems. In these systems, however, one only
indirectly controls the quantum state of the light by manipulating the atoms. A
direct photon-photon interaction occurs in so-called Kerr media, which
typically induce only weak nonlinearity at the cost of significant loss. So
far, it has not been possible to reach the single-photon Kerr regime, where the
interaction strength between individual photons exceeds the loss rate. Here,
using a 3D circuit QED architecture, we engineer an artificial Kerr medium
which enters this regime and allows the observation of new quantum effects. We
realize a Gedankenexperiment proposed by Yurke and Stoler, in which the
collapse and revival of a coherent state can be observed. This time evolution
is a consequence of the quantization of the light field in the cavity and the
nonlinear interaction between individual photons. During this evolution
non-classical superpositions of coherent states, i.e. multi-component
Schroedinger cat states, are formed. We visualize this evolution by measuring
the Husimi Q-function and confirm the non-classical properties of these
transient states by Wigner tomography. The single-photon Kerr effect could be
employed in QND measurement of photons, single photon generation, autonomous
quantum feedback schemes and quantum logic operations.