Encoding a qubit in a trapped-ion mechanical oscillator

Abstract

The stable operation of quantum computers will rely on error-correction, in which single quantum bits of information are stored redundantly in the Hilbert space of a larger system. Such encoded qubits are commonly based on arrays of many physical qubits, but can also be realized using a single higher-dimensional quantum system, such as a harmonic oscillator [1,2]. A powerful encoding is formed from a periodically spaced superposition of position eigenstates [3][4][5]. Various proposals have been made for realizing approximations to such states, but these have thus far remained out of reach [6][7][8][9][10]. Here, we demonstrate such an encoded qubit using a superposition of displaced squeezed states of the harmonic motion of a single trapped 40 Ca + ion, controlling and measuring the oscillator through coupling to an ancilliary internal-state qubit [11]. We prepare and reconstruct logical states with an average square fidelity of 87.3 ± 0.7%, and demonstrate a universal logical single qubit gate set which we analyze using process tomography. For Pauli gates we reach process fidelities of ≈ 97%, while for continuous rotations we use gate teleportation achieving fidelities of ≈ 89%. The control demonstrated opens a route for exploring continuous variable error-correction as well as hybrid quantum information schemes using both discrete and continuous variables [12]. The code states also have direct applications in quantum sensing, allowing simultaneous measurement of small displacements in both position and momentum [13,14].

Encoding a qubit in a molecule

“…GKP codes were realized experimentally [5,6] nearly 20 years after the initial proposal [1], and full-fledged error correction for molecular qubits may still be many years away [32,Sec. V.D].…”

“…These codes are expected to perform well against realistic noise, including dissipation, which typically acts locally in phase space [2][3][4]. Construction of GKP grid states has recently been demonstrated experimentally [5,6].…”

Hybrid Rabi interactions with traveling states of light

“…Recently, a sequence of RIs between a qubit and an oscillator has been proposed to induce the deterministic Kerr, cubic or arbitrary-order nonlinear phase gates [56,57]. It was also studied for exhibition of universal phase transition properties [58][59][60], multi-photon exchange [61], stimulated emission [62], microwave-to-optical conversion [63], generation of non-Gaussian states [64][65][66], and decomposition of arbitrary unitary dynamics [67]. This power enabling synthesis of various types of nonlinearity and observation of consequent nonlinear properties is the reason why achieving RI on continuous variable platforms is important.…”

Fault-tolerant preparation of approximate GKP states

“…Given the above, it is clear that the fault-tolerant preparation of encoded GKP states is an important problem that needs to be addressed. Various proposals for preparing GKP states have been outlined [3,[8][9][10][11][12][13][14][15]. However to our knowledge, no clear definitions for fault-tolerantly preparing GKP states using qubit-cavity couplings have been proposed.…”