Dynamically protected cat-qubits: a new paradigm for universal quantum computation (1312.2017v1)

Abstract: 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.

• The paper introduces two dissipative schemes using two-photon and four-photon processes to encode and protect quantum information in cat-qubits.
• The paper demonstrates universal quantum gate operations, including arbitrary rotations and entangling gates, achieved via engineered cavity couplings and the quantum Zeno effect.
• The paper proposes superconducting circuit implementations that mitigate photon dephasing and suppress single-photon loss errors for enhanced fault tolerance.

Dynamically Protected Cat-Qubits for Universal Quantum Computation

This paper presents a novel approach to realizing universal quantum computation using dynamically protected cat-qubits. It diverges from conventional multi-qubit quantum error-correcting codes by leveraging the infinite-dimensional Hilbert space of a quantum harmonic oscillator to redundantly encode quantum information while minimizing additional decay channels. The authors propose two schemes to encode, protect, and manipulate quantum information using Schrödinger cat states driven by multi-photon dissipative processes.

In the first scheme, a two-photon driven-dissipative process stabilizes a logical qubit basis comprised of two-component Schrödinger cat states. This paradigm effectively mitigates the detrimental effects of photon dephasing. However, the unavoidable single-photon loss poses a significant challenge, as it results in bit-flip errors that cannot be corrected in this framework. Consequently, the second scheme is introduced, utilizing a four-photon driven-dissipative process that stabilizes a logical qubit basis of four-component Schrödinger cat states. This design allows suppression of single-photon loss errors through continuous photon number parity measurements.

For both schemes, the authors demonstrate the feasibility of performing universal quantum gates, ensuring fault tolerance against specific decoherence channels. The toolbox for quantum gate operations includes, but is not limited to, arbitrary rotations around the Bloch sphere's $X$-axis and two-qubit entangling gates. Addressing the issue of implementing these operations fault-tolerantly, the paper highlights that fault tolerance can be achieved by using engineered coupling of storage cavity modes and relying on the quantum Zeno effect to achieve protected, universal operations.

The authors also propose experimental realizations using superconducting circuits and Josephson junctions to facilitate the desired dissipative processes and Hamiltonian dynamics necessary for universal operations. This experimental design is derived from approaches similar to those employed in Josephson parametric amplification.

The implications of this work are multifaceted. Theoretically, it provides a significant contribution toward fault-tolerant quantum computation by innovatively combining quantum harmonic oscillators with multi-photon processes. Practically, the hardware-efficient approach offers a more streamlined path to implementing protected quantum operations, potentially reducing overheads associated with traditional quantum error correction.

Speculating on future developments, this paper sets a precedent for further exploration into leveraging non-linear, multi-photon interactions within cavity quantum electrodynamics frameworks. Such endeavors might further optimize both decoherence mitigation and operational fidelity, advancing towards more scalable quantum computational systems.

The robustness of the system against single-photon errors through parity measurements and the exponentially suppressed logical phase-flip rate offers a promising pathway for achieving large-scale, fault-tolerant quantum computing devices. As experimental techniques continue to improve, the realization and operationalization of these cat-qubit systems hold significant promise for the quantum computing landscape.