Abstract Continuous-variable (CV) encoding allows information to be processed compactly and efficiently on quantum processors. Recently developed techniques such as controlled beam-splitter operations and the near deterministic phonon subtractions make trapped ion systems attractive for exploring CV quantum computing. Here we propose a probabilistic scheme based on the boson sculpting technique for generating multipartite highly entangled states of motional modes of trapped ion systems. We also investigate the effects of decoherence on the fidelity of the generated state by performing numerical simulations with realistic noise parameters. Our work is a step towards generating multipartite CV entanglement.
Abstract Continuous-variable (CV) encoding allows information to be processed compactly and efficiently on quantum processors. Recently developed techniques such as controlled beam-splitter operations and the near deterministic phonon subtractions make trapped ion systems attractive for exploring CV quantum computing. Here we propose a probabilistic scheme based on the boson sculpting technique for generating multipartite highly entangled states of motional modes of trapped ion systems. We also investigate the effects of decoherence on the fidelity of the generated state by performing numerical simulations with realistic noise parameters. Our work is a step towards generating multipartite CV entanglement.
Abstract Continuous-variable quantum computing (CVQC) uses quantum states with continuous degrees of freedom, such as the quadratures of bosonic modes, to encode information, promising efficient solutions to complex problems. Trapped-ion systems provide a robust platform with long coherence times and precise qubit control, enabling the manipulation of quantum information through its motional and electronic degrees of freedom. In this theoretical work, we quantitatively analyze the fidelity of a Kerr operation in a single trapped-ion system, calibrating the interaction time using a motional-state Rabi frequency correction. Through numerical simulations, we validate Gaussian and non-Gaussian CVQC operations, achieving fidelities exceeding 99% in all cases, including non-Gaussian operations. Furthermore, we demonstrate two key applications: first, the implementation of a continuous-variable quantum neural network for regression problems, which exhibits low error rates; and second, its application to state preparation tasks, achieving a fidelity of 90% for the given example. These results open new opportunities to execute quantum computing algorithms on continuous variables with trapped ions, such as quantum machine learning algorithms.
The full characterization of a continuous-variable quantum system is a challenging problem. For the trapped-ion system, a number of methods of measuring the quantum states have been developed, including the measurement of the Q quasiprobability function and the density-matrix elements in the Fock basis, but these approaches are often slow and difficult to scale to multimode states. Here, we demonstrate a novel and powerful scheme for measuring a continuous-variable quantum state that uses the direct single-shot measurement of the joint parity of the phonon states of a trapped ion. We drive a spin-dependent bichromatic beam-splitter interaction that coherently exchanges phonons between different harmonic oscillator modes of the ion. This interaction encodes the joint-parity information into the relative phase between the two spin states, enabling measurement of the combined phonon-number parity across multiple modes in a single shot. Leveraging this capability, we directly measure multimode Wigner quasiprobability distributions to perform quantum state tomography of an entangled coherent state, and calculate various quantum informational quantities with a model-based estimation of the density matrix. We further show that the single-shot joint-parity measurement can be used to detect parity-flip errors in real time. By postselecting the parity-measurement outcomes, we experimentally demonstrate the partial recovery of coherence, effectively implementing an error-mitigation technique. Lastly, we identify the various sources of error affecting the fidelity of the spin-dependent beam-splitter operation and study the feasibility of high-fidelity operations. The interaction studied in this work can be extended to more than two modes, and is highly relevant to continuous-variable quantum computing and quantum metrology.
Using discrete and continuous variable subsystems, hybrid approaches to quantum information could enable more quantum computational power for the same physical resources. Here, we propose a hybrid scheme that can be used to generate the necessary Gaussian and non-Gaussian operations for universal continuous variable quantum computing in trapped ions. This scheme utilizes two linear spin-motion interactions to generate a broad set of nonlinear effective spin-motion interactions including one- and two-mode squeezing, beam splitter, and trisqueezing operations in trapped ion systems. We discuss possible experimental implementations using laser-based and laser-free approaches.
The usually employed methods of using spin states of atomic-like systems for quantum information encoding [1,2] suffer from scalability issues. For example, it becomes very challenging to control a large number of trapped atomic ions each representing a physical qubit. The alternative approach would be to exploit the large Hilbert space provided by a near-harmonic trapping potential and encode the information in the oscillator states [3,4]. We use sideband-resolved addressing of motional states in a single trapped171Yb+ion to demonstrate a conditional beam splitter gate. The conditional beam splitter (CBS) Hamiltonian |e〉〈e|(a†b + ab†) swaps the quantum states of two motional modes of a trapped ion, conditioned on the ion's internal state. It thus can be viewed as a SWAP gate and we uilize it to demonstrate SWAP tests, implement single shot parity measurements, and generate maximally entangled NOON states of motion (see Figure 1).
Continuous-variable quantum computing utilizes continuous parameters of a quantum system to encode information, promising efficient solutions to complex problems. Trapped-ion systems provide a robust platform with long coherence times and precise qubit control, enabling the manipulation of quantum information through its motional and electronic degrees of freedom. In this work, quantum operations that can be generated in trapped-ion systems are employed to investigate applications aimed at state preparation in continuous-variable quantum systems.
To be useful, quantum computers will be required to successfully correct errors occurring at the hardware level. Bosonic codes provide a hardware-efficient option for error correction, but fault-tolerance further requires that the available gate interactions be compatible with the code. A promising bosonic code is the Gottesman-Kitaev-Preskill (GKP) code, for which a linear beamsplitter-like coupling between two bosonic modes is fault-tolerant, making this a key primitive for building larger systems. Here, using two motional modes of a trapped ion, we demonstrate the generation of entangled states of GKP qubits by interfering two qunaught states, which have a grid structure but carry no logical information, on a beamsplitter. We generate all four Bell states with an average fidelity of 69%, and subsequently demonstrate an extension of the entangled state lifetime through the use of quantum error correction. These results complete the set of Gaussian operations required for quantum computing with GKP codes and enable explorations of multi-mode bosonic encodings as well as fundamental tests of information channels.