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

By Mazyar Mirrahimi, Zaki Leghtas, Victor V. Albert, S. Touzard, Robert J. Schoelkopf, Liang Jiang, Michel H. Devoret. 2013

705 citations recorded by the source corpus.

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 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 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 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 amplification, which should allow one to achieve these driven dissipative processes along with the Hamiltonians ensuring the universal operations in an efficient manner.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/eee25fa68388167a7b9cd1b732256487bd0afe21

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Citations in the corpus

Engineered dissipation for quantum information science (2022, background): “Similarly, bosonic Cat codes 22,106,112,126–129 are robust to single photon loss by encoding logical qubits in Schrödinger cat states—superpositions of two or more coherent states.”
Harnessing the Power of the Second Quantum Revolution (2020, methodology): “The Ramsey interferometric technique, which they developed to observe the “birth and death of photon” in a cavity [151], is now a method for syndrome extraction on an error-correcting “cat code” [152], which was the ﬁrst to demonstrate “break-even” in correcting native errors [70].”
New class of quantum error-correcting codes for a bosonic mode (2016, methodology): “The four-legged cat code [18] protects against single-photon losses and thus is similar to the class of binomial codes with L 1⁄4 1, of which the simplest case is Eq.”
Quantum computing with neutral atoms (2020, background): “Such realizations have also been proposed with superconducting qubits that are used as resources (ancilla) to perform photonic gates in the microwave frequency range [98, 99, 100].”
Quantum error correction for quantum memories (2013, neutral): “Leghtas et al. (2013) and Mirrahimi et al. (2013) proposed the interaction of super-conducting qubits coupled to 2D or 3D microwave cavities (circuit QED) to be used for encoding, correction, and decoding of such cat states while Sun et al. (2014) showed how this was done in an experiment.”
Quantum information processing with superconducting circuits: a review (2016, background): “However, the super ior coherence times of 3D resonators have recently been exploited by the Yale group to design a 3D architecture [142, 143] which encodes quantum information in the Hilbert space of a 3D array of 3D superconducting cavi ties and employs the Josephson junction only to perform oper”
Hybrid discrete- and continuous-variable quantum information (2014, methodology): “More-over, by extending the cat qubit to include four diﬀerent coherent state phases, the qubit becomes more robust against losses [111, 112]; and a universal set of gates can be realized by tailoring a speciﬁc Hamiltonian using circuit QED [113].”
Blueprint for a Scalable Photonic Fault-Tolerant Quantum Computer (2020, background): “Examples of bosonic codes include GKP [20], dual-rail [3, 54], cat [55, 56], hypercat [57, 58], binomial [59], and general rotation-symmetric codes [60].”
Geometry and Response of Lindbladians (2015, background): “As an example of the above DFS simplification, consider the bosonic Lindbladian [61,71,139,140] with one jump operator F 1⁄4 a(2) − α(2) and rate κ 1⁄4 1, where α ∈ R, 1⁄2a; a† 1⁄4 I and n≡ a†a.”
Circuit quantum electrodynamics (2020, background): “…of quantum optics and circuit QED include cat codes (Cochrane et al., 1999; Gilchrist et al., 2004; Grimm et al., 2019; Lescanne et al., 2019b; Mirrahimi et al., 2014; Ofek et al., 2016; Puri et al., 2017; Ralph et al., 2003), the related binomial codes (Hu et al., 2019; Michael et al.,…”
Performance and structure of single-mode bosonic codes (2017, methodology): “1)—consist of superpositions of coherent states which are evenly distributed around a circle in phase space [13,15,27].”