Encoding and controlling a GKP logical qubit in a trapped-ion oscillator

Christa Flühmann, T. L. Nguyen, Matteo Marinelli +3 more

Vassili G. Matsos, Christophe H. Valahu, Maverick J. Millican +4 more

Abstract Conventional approaches towards creating a large-scale, fault-tolerant quantum computer require an error correction scheme that uses multiple physical qubits to encode one logical qubit of protected quantum information. A key limiting factor in realizing error-corrected quantum information processing is the large ratio of physical-to-logical qubits required by many error correction codes, outstripping the size of near-term devices. The Gottesman–Kitaev–Preskill (GKP) code offers hardware efficiency at the cost of increased encoding complexity by encoding a logical qubit into a single quantum harmonic oscillator. Building on earlier demonstrations of GKP-encoded operations, we realize an entangling gate on GKP logical qubits. Our experiments use an optimal control strategy that deterministically implements a universal set of energy-preserving logical gates on finite-energy GKP states encoded in the mechanical motions of a trapped ion. We also directly generate a GKP Bell state starting from vacuum. Our approach is compatible with existing hardware architectures, demonstrating the potential for optimal control techniques with advanced encoding schemes to accelerate the path towards large-scale fault-tolerant quantum information processing.

Haruki Aoki, Kazufumi Tanji, Shohei Kiryu +2 more

Distributing entanglement directly between error-corrected logical qubits is an important capability for scalable quantum networks. We propose a heralded protocol for generating remote entanglement between Gottesman--Kitaev--Preskill qubits encoded in the motional modes of spatially separated trapped ions, using the internal electronic states to interface the motional qubits with emitted photons. We derive the protocol for single-rail and polarization photonic encodings and evaluate the effects of finite GKP squeezing, photon loss, photon recoil, motional heating, and motional dephasing on the decoded logical state. Moreover, we numerically analysed the fidelity of distributed logical Bell-pair fidelity. We find that one can achieve more than 95% of fidelity in the realistic situation. The protocol combines motional-control and photonic-networking operations that have already been demonstrated in trapped-ion experiments.

Laird Egan, Marko Cetina, Michael Goldman +5 more

Vassili G. Matsos, Christophe H. Valahu, Maverick J. Millican +4 more

The realisation of a universal quantum computer at scale promises to deliver a paradigm shift in information processing, providing the capability to solve problems that are intractable with conventional computers. A key limiting factor of realising fault-tolerant quantum information processing (QIP) is the large ratio of physical-to-logical qubits that outstrip device sizes available in the near future. An alternative approach proposed by Gottesman, Kitaev, and Preskill (GKP) encodes a single logical qubit into a single harmonic oscillator, alleviating this hardware overhead in exchange for a more complex encoding. Owing to this complexity, current experiments with GKP codes have been limited to single-qubit encodings and operations. Here, we report on the experimental demonstration of a universal gate set for the GKP code, which includes single-qubit gates and -- for the first time -- a two-qubit entangling gate between logical code words. Our scheme deterministically implements energy-preserving quantum gates on finite-energy GKP states encoded in the mechanical motion of a trapped ion. This is achieved by a novel optimal control strategy that dynamically modulates an interaction between the ion's spin and motion. We demonstrate single-qubit gates with a logical process fidelity as high as 0.960 and a two-qubit entangling gate with a logical process fidelity of 0.680. We also directly create a GKP Bell state from the oscillators' ground states in a single step with a logical state fidelity of 0.842. The overall scheme is compatible with existing hardware architectures, highlighting the opportunity to leverage optimal control strategies as a key accelerant towards fault tolerance.

Christopher J. Ballance