Trapped-ion Quantum Research Articles

Generating target graph couplings for the quantum approximate optimization algorithm from native quantum hardware couplings

We present methods for constructing any target coupling graph using limited global controls in an Ising-like quantum spin system. Our approach is motivated by implementing the quantum approximate optimization algorithm (QAOA) on trapped-ion quantum hardware to find approximate solutions to MaxCut. We present a mathematical description of the problem and provide approximately optimal algorithmic constructions that generate arbitrary unweighted coupling graphs with $n$ nodes in $O(n)$ global entangling operations and weighted graphs with $m$ edges in $O(m)$ operations. These upper bounds are not tight in general, and we formulate a mixed-integer program to solve the graph coupling problem to optimality. We perform numeric experiments on small graphs with $n\ensuremath{\le}8$ and show that optimal sequences, which use fewer operations, can be found using mixed-integer programs. Noisy simulations of MaxCut QAOA show that our implementation is less susceptible to noise than the standard gate-based compilation.

Holographic dynamics simulations with a trapped-ion quantum computer

Quantum computers promise to efficiently simulate quantum dynamics, a classically intractable task central to fields ranging from chemistry to high-energy physics. Yet, quantum computational advantage has only been demonstrated for artificial tasks such as random circuit sampling, and hardware limitations and noise have limited experiments to qualitative studies of small-scale systems. Quantum processors capable of high-fidelity measurements and qubit reuse enable a recently proposed holographic technique that employs quantum tensor-network states, a class of states that efficiently compress quantum data, to simulate the evolution of infinitely long, entangled initial states using a small number of qubits. Here we benchmark this holographic technique in a trapped-ion quantum processor using 11 qubits to simulate the dynamics of an infinite entangled state. We observe the hallmarks of quantum chaos and light-cone propagation of correlations, and find excellent quantitative agreement with theoretical predictions for the infinite-size limit of the implemented model with minimal post-processing or error mitigation. These results show that quantum tensor-network methods, paired with state-of-the-art quantum processor capabilities, offer a viable route to practical quantum computational advantage on problems of direct interest to science and technology in the near term.

N-Body Interactions between Trapped Ion Qubits via Spin-Dependent Squeezing.

We describe a simple protocol for the single-step generation of N-body entangling interactions between trapped atomic ion qubits. We show that qubit state-dependent squeezing operations and displacement forces on the collective atomic motion can generate full N-body interactions. Similar to the Mølmer-Sørensen two-body Ising interaction at the core of most trapped ion quantum computers and simulators, the proposed operation is relatively insensitive to the state of motion. We show how this N-body gate operation allows for the single-step implementation of a family of N-bit gate operations such as the powerful N-Toffoli gate, which flips a single qubit if and only if all other N-1 qubits are in a particular state.

Design of scalable metalens array for optical addressing

Large-scale trapped-ion quantum computers hold great promise to outperform classical computers and are crucially desirable for finance, pharmaceutical industry, fundamental chemistry and other fields. Currently, a big challenge for trapped-ion quantum computers is the poor scalability mainly brought by the optical elements that are used for optical addressing. Metasurfaces provide a promising solution due to their excellent flexibility and integration ability. Here, we propose and numerically demonstrate a scalable off-axis metalens array for optical addressing working at the wavelength of 350 nm. Metalens arrays designed for x linearly polarized and left circularly polarized light respectively can focus the collimated addressing beam array into a compact focused spot array with spot spacing of 5 μm, featuring crosstalk below 0.82%.Graphical

Holographic Simulation of Correlated Electrons on a Trapped-Ion Quantum Processor

A quantum tensor network method is introduced to approximately compute the properties of interacting many-electron models, reducing the quantum memory size required to simulate complex materials and molecules and shortening the computation time.

Quantum Computing With Trapped Ions: An overview

An array of trapped atomic ions that are laser cooled and isolated in an ultrahigh-vacuum environment presents one of the most advanced physical platforms for realizing a practical quantum computer. Small-scale ion quantum computers up to tens of ions have been built and achieved the highest fidelities on elementary quantum operations and overall quantum volume (QV). This article provides an overview of the elements of trapped-ion quantum computing (TIQC), current achievements in the field, and future perspectives.

Two-dimensional atom localization and formation of waveguide channels using Bragg diffraction law

Atoms of four-level atomic medium are doped in a crystal slab of silica which is immersed in a four-level atomic medium. We incorporated Bragg law in the Rabi frequencies of the driving fields and obtained absorption spectrum which exhibits atom localization inside the crystal plane and generation of waveguide channels. Varying the Bragg angle θ, leads to a number of localized peaks and craters. The number of peaks decreases as we increase the Bragg angle θ from π/8 to π/2 and the peaks disappear beyond this angle. The localization probability is independent of the Bragg angle, while the spatial resolution varies with change in Bragg angle. However, the probe detuning and amplitudes of Rabi frequencies change the localization probability. Inside the optical lattice of the silica crystal, waveguide channels and particle traps are generated which may be utilized to guide electromagnetic radiations and trap quantum particles. This work is useful for coherent control information of crystal planes, optical trapping, waveguide channels of nano crystals and data storage.

Quantum computational advantage attested by nonlocal games with the cyclic cluster state

We propose a set of Bell-type nonlocal games that can be used to prove an unconditional quantum advantage in an objective and hardware-agnostic manner. In these games, the circuit depth needed to prepare a cyclic cluster state and measure a subset of its Pauli stabilizers on a quantum computer is compared to that of classical Boolean circuits with the same, nearest-neighboring gate connectivity. Using a circuit-based trapped-ion quantum computer, we prepare and measure a six-qubit cyclic cluster state with an overall fidelity of 60.6% and 66.4%, before and after correcting for measurement-readout errors, respectively. Our experimental results indicate that while this fidelity readily passes conventional (or depth-0) Bell bounds for local hidden-variable models, it is on the cusp of demonstrating a higher probability of success than what is possible by depth-1 classical circuits. Our games offer a practical and scalable set of quantitative benchmarks for quantum computers in the pre-fault-tolerant regime as the number of qubits available increases.

Dynamical topological phase realized in a trapped-ion quantum simulator.

Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics in almost isolated systems. Here achieving precise control over quantum many-body entanglement is an essential task for quantum sensing and computation. Extensive theoretical work indicates that these capabilities can enable dynamical phases and critical phenomena that show topologically robust methods to create, protect and manipulate quantum entanglement that self-correct against large classes of errors. However, so far, experimental realizations have been confined to classical (non-entangled) symmetry-breaking orders1-5. In this work, we demonstrate an emergent dynamical symmetry-protected topological phase6, in a quasiperiodically driven array of ten 171Yb+ hyperfine qubits in Quantinuum's System Model H1 trapped-ion quantum processor7. This phase shows edge qubits that are dynamically protected from control errors, cross-talk and stray fields. Crucially, this edge protection relies purely on emergent dynamical symmetries that are absolutely stable to generic coherent perturbations. This property is special to quasiperiodically driven systems: as we demonstrate, the analogous edge states of a periodically driven qubit array are vulnerable to symmetry-breaking errors and quickly decohere. Our work paves the way for implementation of more complex dynamical topological orders8,9 that would enable error-resilient manipulation of quantum information.

Generation of High-Resolution Handwritten Digits with an Ion-Trap Quantum Computer

Generating high-quality data (e.g., images or video) is one of the most exciting and challenging frontiers in unsupervised machine learning. Utilizing quantum computers in such tasks to potentially enhance conventional machine-learning algorithms has emerged as a promising application but poses big challenges due to the limited number of qubits and the level of gate noise in available devices. In this work, we provide the first practical and experimental implementation of a quantum-classical generative algorithm capable of generating high-resolution images of handwritten digits with state-of-the-art gate-based quantum computers. In our quantum-assisted machine-learning framework, we implement a quantum-circuit-based generative model to learn and sample the prior distribution of a generative adversarial network. We introduce a multibasis technique which leverages the unique possibility of measuring quantum states in different bases, hence enhancing the expressivity of the prior distribution. We train this hybrid algorithm on an ion-trap device based on Yb+171 ion qubits to generate high-quality images and quantitatively outperform comparable classical generative adversarial networks trained on the popular MNIST dataset for handwritten digits.1 MoreReceived 26 November 2021Revised 19 April 2022Accepted 1 June 2022DOI:https://doi.org/10.1103/PhysRevX.12.031010Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasMachine learningQuantum algorithmsQuantum Information

Efficient realization of quantum primitives for Shor's algorithm using PennyLane library.

Efficient realization of quantum algorithms is among main challenges on the way towards practical quantum computing. Various libraries and frameworks for quantum software engineering have been developed. Here we present a software package containing implementations of various quantum gates and well-known quantum algorithms using PennyLane library. Additoinally, we used a simplified technique for decomposition of algorithms into a set of gates which are native for trapped-ion quantum processor and realized this technique using PennyLane library. The decomposition is used to analyze resources required for an execution of Shor's algorithm on the level of native operations of trapped-ion quantum computer. Our original contribution is the derivation of coefficients needed for implementation of the decomposition. Templates within the package include all required elements from the quantum part of Shor's algorithm, specifically, efficient modular exponentiation and quantum Fourier transform that can be realized for an arbitrary number of qubits specified by a user. All the qubit operations are decomposed into elementary gates realized in PennyLane library. Templates from the developed package can be used as qubit-operations when defining a QNode.

Probing Majorana modes via local spin dynamics

We investigate Majorana modes in a quantum spin chain with bond-dependent exchange interactions by studying its dynamics. Specifically, we consider two-time correlations for the Kitaev-Heisenberg (KH) Hamiltonian close to the so-called Kitaev critical point. Here, the model coincides with a phase boundary of two uncoupled instances of Kitaev's model for p-wave superconductors, together supporting a degenerate ground state characterized by multiple Majorana modes. In this regime, the real-time dynamics of local spins reveal a set of strong zero modes, corresponding to a set of protruding frequencies in the two-time correlation function. We derive perturbative interactions that map the KH spin chain onto the topological regime of Kitaev's fermionic model, thus opening up a bulk gap whilst retaining almost degenerate modes in the mesoscopic regime, i.e., for finite system sizes. This showcases the emergence of Majorana modes in a chain of effective dimers. Here, the binding energy within each unit cell competes with the inter-dimer coupling to generate a finite size energy gap, in analogy with local energy terms in the transverse-field Ising model. These modes give rise to long coherence times of local spins located at the system edges. By breaking the local symmetry in each dimer, one can also observe a second class of Majorana modes in terms of a beating frequency in the two-time correlations function of the edge spin. Furthermore, we develop a scenario for realizing these model predictions in ion-trap quantum simulators with collective addressing of the ions.

Low-depth amplitude estimation on a trapped-ion quantum computer

Amplitude estimation (AE) is a fundamental quantum algorithmic primitive that enables quantum computers to achieve quadratic speedups for a large class of statistical estimation problems, including Monte Carlo methods. Recent works have succeeded in somewhat reducing the necessary resources for AE by trading off some of the speedup for lower depth circuits, but high quality qubits are still needed for demonstrating such algorithms. Here, we report the results of an experimental demonstration of AE on a state-of-the-art trapped ion quantum computer. AE was used to estimate the inner product of randomly chosen four-dimensional unit vectors, and the low-depth AE algorithms were based on the maximum likelihood estimation (MLE) and the Chinese remainder theorem (CRT) techniques. Significant improvements in accuracy were observed for the MLE based approach when deeper quantum circuits were taken into account, including circuits with more than 90 two-qubit gates and depth 60, achieving a mean additive estimation error on the order of ${10}^{\ensuremath{-}2}$. The CRT based approach was found to provided accurate estimates for many of the data points but was less robust against noise on average. Last, we analyze two more AE algorithms that take into account the specifics of the hardware noise to further improve the results.

Parallel Electromagnetically Induced Transparency near Ground-State Cooling of a Trapped-Ion Crystal

We theoretically propose and experimentally demonstrate a parallel electromagnetically induced transparency (parallel EIT) cooling technique for ion crystals in the Paul trap. It breaks the stringent cooling requirements of the standard EIT cooling, thus allowing, in principle, to simultaneously cool the motional mode spectrum with an arbitrary range. Experimentally a large cooling range over 5 MHz is proved by using a single trapped ${}^{40}{\mathrm{Ca}}^{+}$ ion. We also observe simultaneous near-ground-state cooling for all motional modes of a 4-ion chain with the best average phonon number of about 0.2. For cooling a large number of modes, we only need to modulate the probe beam of the standard EIT cooling with several rf frequencies. This cooling scheme has no selectivity for the types of ions (e.g., ${}^{171}{\mathrm{Yb}}^{+}$, ${}^{40}{\mathrm{Ca}}^{+}$), therefore it would be a powerful tool for initialization of all kinds of operational trapped-ion quantum computers or simulators.

Simulation and randomized measurement of topological phase on a trapped-ion quantum computer

Simulation and randomized measurement of topological phase on a trapped-ion quantum computer

Single-qubit universal classifier implemented on an ion-trap quantum device

Quantum computers can provide solutions to certain classically intractable problems. However, current devices have limited computational resources, and an effort is made to develop useful quantum algorithms under this constraint. This work demonstrates experimentally that a single-qubit processor can host a universal classifier based on the re-uploading scheme. The quantum processor used in this work is built with an ion trap, providing highly accurate control on a one-qubit system as required by the re-uploading scheme. A set of nontrivial classification tasks are completed successfully. The training procedure is performed in two steps combining simulation and experiment. Final results are benchmarked against exact simulations of the same method and also classical algorithms, showing a competitive performance of the ion-trap quantum classifier. This work constitutes the experimental implementation of a classification algorithm based on the re-uploading scheme.

Optimization and implementation of a surface-electrode ion trap junction

We describe the design of a surface-electrode ion trap junction, which is a key element for large-scale ion trap arrays. A bi-objective optimization method is used for designing the electrodes, which maintains the total pseudo-potential curvature while minimizing the axial pseudo-potential gradient along the ion transport path. To facilitate the laser beam delivery for parallel operations in multiple trap zones, we implemented integrated optics on each arm of this X-junction trap. The layout of the trap chip for commercial foundry fabrication is presented. This work suggests routes to improving ion trap junction performance in scalable implementations. Together with integrated optical addressing, this contributes to modular trapped-ion quantum computing in interconnected two-dimensional arrays.

Tensor-network discriminator architecture for classification of quantum data on quantum computers

We demonstrate the use of matrix product state (MPS) models for discriminating quantum data on quantum computers using holographic algorithms, focusing on classifying a translationally invariant quantum state based on $L$ qubits of quantum data extracted from it. We detail a process in which data from single-shot experimental measurements are used to optimize an isometric tensor network, the tensors are compiled into unitary quantum operations using greedy compilation heuristics, parameter optimization on the resulting quantum circuit model removes the post-selection requirements of the isometric tensor model, and the resulting quantum model is inferenced on either product state or entangled quantum data. We demonstrate our training and inference architecture on a synthetic dataset of six-site single-shot measurements from the bulk of a one-dimensional transverse field Ising model (TFIM) deep in its antiferromagnetic and paramagnetic phases. We experimentally evaluate models on Quantinuum's H1-2 trapped ion quantum computer using entangled input data modeled as translationally invariant, bond dimension 4 MPSs across the known quantum phase transition of the TFIM. Using linear regression on the experimental data near the transition point, we find predictions for the critical transverse field of $h=0.962$ and $0.994$ for tensor network discriminators of bond dimension $\chi=2$ and $\chi=4$, respectively. These predictions compare favorably with the known transition location of $h=1$ despite training on data far from the transition point. Our techniques identify families of short-depth variational quantum circuits in a data-driven and hardware-aware fashion and robust classical techniques to precondition the model parameters, and can be adapted beyond machine learning to myriad applications of tensor networks on quantum computers, such as quantum simulation and error correction.

Observation of supersymmetry and its spontaneous breaking in a trapped ion quantum simulator

Supersymmetry (SUSY) helps solve the hierarchy problem in high-energy physics and provides a natural groundwork for unifying gravity with other fundamental interactions. While being one of the most promising frameworks for theories beyond the Standard Model, its direct experimental evidence in nature still remains to be discovered. Here we report experimental realization of a supersymmetric quantum mechanics (SUSY QM) model, a reduction of the SUSY quantum field theory for studying its fundamental properties, using a trapped ion quantum simulator. We demonstrate the energy degeneracy caused by SUSY in this model and the spontaneous SUSY breaking. By a partial quantum state tomography of the spin-phonon coupled system, we explicitly measure the supercharge of the degenerate ground states, which are superpositions of the bosonic and the fermionic states. Our work demonstrates the trapped-ion quantum simulator as an economic yet powerful platform to study versatile physics in a single well-controlled system.

Verification of Information Thermodynamics in a Trapped Ion System.

Information thermodynamics has developed rapidly over past years, and the trapped ions, as a controllable quantum system, have demonstrated feasibility to experimentally verify the theoretical predictions in the information thermodynamics. Here, we address some representative theories of information thermodynamics, such as the quantum Landauer principle, information equality based on the two-point measurement, information-theoretical bound of irreversibility, and speed limit restrained by the entropy production of system, and review their experimental demonstration in the trapped ion system. In these schemes, the typical physical processes, such as the entropy flow, energy transfer, and information flow, build the connection between thermodynamic processes and information variation. We then elucidate the concrete quantum control strategies to simulate these processes by using quantum operators and the decay paths in the trapped-ion system. Based on them, some significantly dynamical processes in the trapped ion system to realize the newly proposed information-thermodynamic models is reviewed. Although only some latest experimental results of information thermodynamics with a single trapped-ion quantum system are reviewed here, we expect to find more exploration in the future with more ions involved in the experimental systems.