Ion Trap Quantum Computer Research Articles

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 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.

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.

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.

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.

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

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.

Measurement-induced quantum phases realized in a trapped-ion quantum computer

Many-body open quantum systems balance internal dynamics against decoherence from interactions with an environment. Here, we explore this balance via random quantum circuits implemented on a trapped ion quantum computer, where the system evolution is represented by unitary gates with interspersed projective measurements. As the measurement rate is varied, a purification phase transition is predicted to emerge at a critical point akin to a fault-tolerent threshold. We probe the "pure" phase, where the system is rapidly projected to a deterministic state conditioned on the measurement outcomes, and the "mixed" or "coding" phase, where the initial state becomes partially encoded into a quantum error correcting codespace. We find convincing evidence of the two phases and show numerically that, with modest system scaling, critical properties of the transition clearly emerge.

Demonstration of fault-tolerant universal quantum gate operations.

Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error-correcting codes1,2. When manipulating the logical quantum states, it is imperative that errors caused by imperfect operations do not spread uncontrollably through the quantum register. This requires that all operations on the quantum register obey a fault-tolerant circuit design3-5, which, in general, increases the complexity of the implementation. Here we demonstrate a fault-tolerant universal set of gates on two logical qubits in a trapped-ion quantum computer. In particular, we make use of the recently introduced paradigm of flag fault tolerance, where the absence or presence of dangerous errors is heralded by the use of auxiliary flag qubits6-10. We perform a logical two-qubit controlled-NOT gate between two instances of the seven-qubit colour code11,12, and fault-tolerantly prepare a logical magic state8,13. We then realize a fault-tolerant logical T gate by injecting the magic state by teleportation from one logical qubit onto the other14. We observe the hallmark feature of fault tolerance-a superior performance compared with a non-fault-tolerant implementation. In combination with recently demonstrated repeated quantum error-correction cycles15,16, these results provide a route towards error-corrected universal quantum computation.

Fabrication of surface ion traps with integrated current carrying wires enabling high magnetic field gradients

A major challenge for quantum computers is the scalable simultaneous execution of quantum gates. One approach to address this in trapped ion quantum computers is the implementation of quantum gates based on static magnetic field gradients and global microwave fields. In this paper, we present the fabrication of surface ion traps with integrated copper current carrying wires embedded inside the substrate below the ion trap electrodes, capable of generating high magnetic field gradients. The copper layer’s measured sheet resistance of 1.12 mΩ/sq at room temperature is sufficiently low to incorporate complex designs, without excessive power dissipation at high currents causing a thermal runaway. At a temperature of 40 K the sheet resistance drops to 20.9 μΩ/sq giving a lower limit for the residual resistance ratio of 100. Continuous currents of 13 A can be applied, resulting in a simulated magnetic field gradient of 144 T m−1 at the ion position, which is 125 μm from the trap surface for the particular anti-parallel wire pair in our design.

A deterministic single ion fountain

We present an alternative approach for interconnecting trapped ion processor nodes by deterministic single ion transfer. In our experiments, we demonstrate the single ion extraction out of a linear Paul trap, into a free space trajectory, followed by recapture in the trapping potential. We recapture in the same trap, coined the ion fountain operation after a free-space travel of distance 110 mm and a time of flight of 7 μs. Our experimental realization yields a success probability of 95.1%, namely 715 out of 752 extracted ions are retrapped, cooled and observed. Based on such high success rate, we discuss the future perspective for an application towards scalable ion trap quantum computing and advanced quantum sensing.

Bounds on the recurrence probability in periodically-driven quantum systems

Periodically-driven systems are ubiquitous in science and technology. In quantum dynamics, even a small number of periodically-driven spins leads to complicated dynamics. Hence, it is of interest to understand what constraints such dynamics must satisfy. We derive a set of constraints for each number of cycles. For pure initial states, the observable being constrained is the recurrence probability. We use our constraints for detecting undesired coupling to unaccounted environments and drifts in the driving parameters. To illustrate the relevance of these results for modern quantum systems we demonstrate our findings experimentally on a trapped-ion quantum computer, and on various IBM quantum computers. Specifically, we provide two experimental examples where these constraints surpass fundamental bounds associated with known one-cycle constraints. This scheme can potentially be used to detect the effect of the environment in quantum circuits that cannot be classically simulated. Finally, we show that, in practice, testing an n-cycle constraint requires executing only O(n) cycles, which makes the evaluation of constraints associated with hundreds of cycles realistic.

Multiplexed quantum repeaters based on dual-species trapped-ion systems

Trapped ions form an advanced technology platform for quantum information processing with long qubit coherence times, high-fidelity quantum logic gates, optically active qubits, and a potential to scale up in size while preserving a high level of connectivity between qubits. These traits make them attractive not only for quantum computing but also for quantum networking. Dedicated, special-purpose trapped-ion processors in conjunction with suitable interconnecting hardware can be used to form quantum repeaters that enable high-rate quantum communications between distant trapped-ion quantum computers in a network. In this regard, hybrid traps with two distinct species of ions, where one ion species can generate ion-photon entanglement that is useful for optically interfacing with the network and the other has long memory lifetimes, useful for qubit storage, have been proposed for entanglement distribution. We consider an architecture for a repeater based on such dual-species trapped-ion systems. We propose and analyze a protocol based on spatial and temporal mode multiplexing for entanglement distribution across a line network of such repeaters. Our protocol offers enhanced rates compared to rates previously reported for such repeaters. We determine the ion resources required at the repeaters to attain the enhanced rates, and the best rates attainable when constraints are placed on the number of repeaters and the number of ions per repeater. Our results bolster the case for near-term trapped-ion systems as quantum repeaters for long-distance quantum communications.

Toward systematic architectural design of near-term trapped ion quantum computers

Trapped ions (TIs) are a leading candidate for building Noisy Intermediate-Scale Quantum (NISQ) hardware. TI qubits have fundamental advantages over other technologies, featuring high qubit quality, coherence time, and qubit connectivity. However, current TI systems are small in size and typically use a single trap architecture, which has fundamental scalability limitations. To progress toward the next major milestone of 50--100 qubit TI devices, a modular architecture termed the Quantum Charge Coupled Device (QCCD) has been proposed. In a QCCD-based TI device, small traps are connected through ion shuttling. While the basic hardware components for such devices have been demonstrated, building a 50--100 qubit system is challenging because of a wide range of design possibilities for trap sizing, communication topology, and gate implementations and the need to match diverse application resource requirements. Toward realizing QCCD-based TI systems with 50--100 qubits, we perform an extensive application-driven architectural study evaluating the key design choices of trap sizing, communication topology, and operation implementation methods. To enable our study, we built a design toolflow, which takes a QCCD architecture's parameters as input, along with a set of applications and realistic hardware performance models. Our toolflow maps the applications onto the target device and simulates their execution to compute metrics such as application run time, reliability, and device noise rates. Using six applications and several hardware design points, we show that trap sizing and communication topology choices can impact application reliability by up to three orders of magnitude. Microarchitectural gate implementation choices influence reliability by another order of magnitude. From these studies, we provide concrete recommendations to tune these choices to achieve highly reliable and performant application executions. With industry and academic efforts underway to build TI devices with 50-100 qubits, our insights have the potential to influence QC hardware in the near future and accelerate the progress toward practical QC systems.

Design of an Integrated Bell-State Analyzer on a Thin-Film Lithium Niobate Platform

Trapped ions are excellent candidates for quantum computing and quantum networks because of their long coherence times, ability to generate entangled photons as well as high fidelity single- and two-qubit gates. To scale up trapped ion quantum computing, we need a Bell-state analyzer on a reconfigurable platform that can herald high fidelity entanglement between ions. In this work, we design a photonic Bell-state analyzer on a reconfigurable thin film lithium niobate platform for polarization-encoded qubits. We optimize the device to achieve high fidelity entanglement between two trapped ions and find >99% fidelity. The proposed device can scale up trapped ion quantum computing as well as other optically active spin qubits, such as color centers in diamond, quantum dots, and rare-earth ions.

Efficient quantum programming using EASE gates on a trapped-ion quantum computer

Parallel operations in conventional computing have proven to be an essential tool for efficient and practical computation, and the story is not different for quantum computing. Indeed, there exists a large body of works that study advantages of parallel implementations of quantum gates for efficient quantum circuit implementations. Here, we focus on the recently invented efficient, arbitrary, simultaneously entangling (EASE) gates, available on a trapped-ion quantum computer. Leveraging its flexibility in selecting arbitrary pairs of qubits to be coupled with any degrees of entanglement, all in parallel, we show an n-qubit Clifford circuit can be implemented using 6log(n) EASE gates, an n-qubit multiply-controlled NOT gate can be implemented using 3n/2 EASE gates, and an n-qubit permutation can be implemented using six EASE gates. We discuss their implications to near-term quantum chemistry simulations and the state of the art pattern matching algorithm. Given Clifford + multiply-controlled NOT gates form a universal gate set for quantum computing, our results imply efficient quantum computation by EASE gates, in general.

Approximate unitary 3-designs from transvection Markov chains

Unitary k-designs are probabilistic ensembles of unitary matrices whose first k statistical moments match that of the full unitary group endowed with the Haar measure. In prior work, we showed that the automorphism group of classical \({\mathbb {Z}}_4\)-linear Kerdock codes maps to a unitary 2-design, which established a new classical-quantum connection via graph states. In this paper, we construct a Markov process that mixes this Kerdock 2-design with symplectic transvections, and show that this process produces an \(\epsilon \)-approximate unitary 3-design. We construct a graph whose vertices are Pauli matrices, and two vertices are connected by directed edges if and only if they commute. A unitary ensemble that is transitive on vertices, edges, and non-edges of this Pauli graph is an exact 3-design, and the stationary distribution of our process possesses this property. With respect to the symmetries of Kerdock codes, the Pauli graph has two types of edges; the Kerdock 2-design mixes edges of the same type, and the transvections mix the types. More precisely, on m qubits, the process samples \(O(\log (N^5/\epsilon ))\) random transvections, where \(N = 2^m\), followed by a random Kerdock 2-design element and a random Pauli matrix. Hence, the simplicity of the protocol might make it attractive for several applications. From a hardware perspective, 2-qubit transvections exactly map to the Mølmer–Sørensen gates that form the native 2-qubit operations for trapped-ion quantum computers. Thus, it might be possible to extend our work to construct an approximate 3-design that only involves such 2-qubit transvections.