Dynamically protected cat-qubits: a new paradigm for universal quantum computation

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 multiphoton driven dissipative processes to encode quantum information in logical bases composed of Schrödinger 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 Schrödinger 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 bitflip 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 Schrödinger 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 Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. amplification, which should allow one to achieve these driven dissipative processes along with the Hamiltonians ensuring the universal operations in an efficient manner.Keywords: quantum superconducting circuits, circuit quantum electrodynamics, quantum error correction, quantum reservoir engineering, universal quantum computation n n n and therefore the measurement of the photon number parity can indicate the occurrence of a photon loss event. While the parity measurements keep track of the photon loss events, the deterministic relaxation of the energy, replacing α by α κ − e / t 2 , remains inevitable. To overcome this relaxation of energy, we need to intervene before the coherent states start to overlap in a significant manner to re-pump energy into the codeword. New J. Phys. 16 (2014) 045014 M Mirrahimi et al New J. Phys. 16 (2014) 045014 M Mirrahimi et al New J. Phys. 16 (2014) 045014 M Mirrahimi et al 7 / aa . Extension to four-photon driven dissipative processSimilarly to the case of the two-photon process, we need to achieve an effective Hamiltonian of the form New J. Phys. 16 (2014) 045014 M Mirrahimi et al 21

Interferometric quantum cascade systems

“…gineering system-bath coupling in quantum optical systems, which in turn may help in dissipatively preparing quantum many-body states of matter [20][21][22] with important consequences in the analysis of non-equilibrium condensed matter physics problems [23][24][25][26] and quantum information [10,[27][28][29][30]. Aim of the present work is to derive a mathematical framework that incorporate these phenomena in a consistent way.…”

Nondegenerate parametric oscillations in a tunable superconducting resonator

“…The JPO regime is established at parametric pump amplitudes above a critical value (threshold), where an instability of the resonator ground state is developed, and it is stabilized by the Kerr nonlinearity. The JPO can be used for vacuum squeezing and photonic entanglement [13,14], photonic qubit operation [15], and catstate engineering [16][17][18]. The JPO has also been employed for high-fidelity readout of superconducting qubits [19,20].…”

Quantum plasmonic excitation in graphene and loss-insensitive propagation

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