Norbert M. Linke

The unification of quantum mechanics and general relativity remains one of the major open problems of theoretical physics. The Anti-de Sitter/Conformal Field Theory (AdS/CFT) correspondence provides a valuable theoretical framework for this effort via a holographic duality between a theory of quantum gravity in asymptotically AdS spacetime and a conformal quantum field theory on the lower-dimensional boundary. Here, we implement a toy model of this duality called the HaPPY code, a quantum error-correcting code in the form of a tensor network with hyperbolic entanglement patterns, on a trapped-ion quantum computer. We present the first experimental confirmation of the Faulkner-Lewkowycz-Maldacena formula in this model - a key test of the holographic correspondence. We then enrich it with non-stabilizerness, or magic, and observe entropic precursors expected of emergent gravity. Finally, we present and measure a code construction whose entropic behavior is reminiscent of a highly quantum wormhole. Our experiments illustrate how quantum computers can serve as testbeds for modeling the emergence of spacetime.

Large-language-model (LLM) agents can write and run experimental control code. This allows laboratory work to be conducted autonomously. However, this autonomy raises a safety problem that prior work has not addressed. Unchecked code can damage the apparatus, and there is no formal, per-operation boundary between human authorization/supervision, and agent decisions. We present a control system that places an LLM agent in the loop of a trapped-ion experiment while enforcing such a boundary. The agent controls the existing Advanced Real-Time Infrastructure for Quantum physics (ARTIQ) stack through tools provided by a Model Context Protocol (MCP) server. No tool call reaches the hardware unless it carries an authorization token bound to its exact contents. Tokens are issued in one of two ways: automatically, by running the agent's proposed script in an isolated hardware simulation (dax.sim) and checking every operation against preset per-device bounds, or manually by a human operator for sensitive actions. Within this boundary the agent develops its own experiments, rather than only calling pre-built routines. We deploy the system on a co-trapped $^{40}$Ca$^{+}$/$^{40}$CaOH$^{+}$ crystal, where the agent autonomously builds a full calibration stack and, with targeted operator guidance, closes a cross-instrument magnetic-field-stabilization loop. On a separate, independent $^{171}$Yb$^{+}$ platform, we confirm interface-level portability. We systematically test token-authorization mechanism with adversarial scripts that attempt to bypass it, mapping the precise boundary of its protection and prioritizing where to strengthen it next. Analyzing where the agent still requires human guidance, we find that its limits lie in metacognitive control, namely recognizing when a problem must be re-framed, rather than in domain knowledge.

Parallel processing of information plays a critical role in accelerating computation. This includes quantum computers, where parallel processing of quantum information will play a critical role in practical quantum advantage. Here, we demonstrate a new type of parallel entangling gates in a trapped-ion quantum computer, that simultaneously provides efficient gate-pulse synthesis and calibration, as well as graph-pattern-agnostic implementation. We demonstrate the resulting reduced execution time in three well-known algorithms, exhibiting disjoint gates, a star graph and a ring graph respectively. For disjoint qubit pairs the execution time of our parallel gates is comparable to that of a single-pair entangling gate resulting in an approximately linear speed up. For all graph patterns our parallel gate fidelities are comparable to the fidelity of a single-pair entangling gate. These advantages motivate architectures featuring multiple medium length ion chains in future quantum computing devices.

Nonlocal games provide application-level benchmarks for quantum hardware whose classical performance bounds are information-theoretic, holding against all classical strategies regardless of computational resources. We implement a 14-vertex graph coloring game, the smallest graph exhibiting a quantum-classical separation for this game type, on four trapped-ion quantum processors across three institutions. One system achieved a win rate that surpasses the classical bound with statistical significance, marking the first violation of a classical bound in a graph coloring nonlocal game on quantum hardware. The remaining systems achieved win rates comparable to the best superconducting processors evaluated on the same game, further illustrating the potential of nonlocal games as cross-architecture quantum benchmarks.

Monolithic three-dimensional (3D) Paul traps combine the high-precision microfabrication of two-dimensional (2D) chip traps with the deep trapping potentials and low heating rates characteristic of macroscopic 3D Paul traps, which are typically machined by traditional means and mechanically assembled. However, achieving low motional heating rates and optical access with a high numerical aperture (NA) while maintaining the high radio-frequency (RF) voltages required for trapping heavy ionic species, such as Yb$^{+}$ and Ba$^{+}$, remains a significant technical challenge. In this work, we present a fused-silica, monolithic segmented 3D Paul trap with an ion-electrode distance of 250 $μ$m, and stable operation at high RF voltages. We benchmark the performance of the trap using Yb$^{+}$ ions, demonstrating axially homogeneous trapping potentials spanning over 200 $μ$m about the axial center of the trap, high multi-directional optical access (up to 0.7 NA), and radial motional heating as low as $\dot{\bar n}=1.1 \pm 0.1 $ quanta/s at radial trap frequencies about 3 MHz near room temperature. Furthermore, we observe a motional Ramsey coherence time, ${T}_{2}$, of about 95 ms for the radial center-of-mass mode. We demonstrate the generation of a two-qubit Bell state with a parity contrast of ${99.3}^{+0.7} _{-1.5}$% with state preparation and measurement correction. These results establish fused-silica monolithic 3D Paul traps as a scalable, modular platform for quantum simulation, computation, metrology, and networking with heavy ionic species.

Autonomous quantum machines (AQMs) execute tasks without requiring time-dependent external control. Motivations for AQMs include the restrictions imposed by classical control on quantum machines' coherence times and geometries. Most AQM work is theoretical and abstract; yet an experiment recently demonstrated AQMs' usefulness in qubit reset, crucial to quantum computing. To further reduce quantum computing's classical control, we propose realizations of (fully and partially) quantum-autonomous gates on three platforms: Rydberg atoms, trapped ions, and superconducting qubits. First, we show that a Rydberg-blockade interaction or an ultrafast transition can quantum-autonomously effect entangling gates on Rydberg atoms. One can perform $Z$ or entangling gates on trapped ions mostly quantum-autonomously, by sculpting a linear Paul trap or leveraging a ring trap. Passive lasers control these gates, as well as the Rydberg-atom gates, quantum-autonomously. Finally, circuit quantum electrodynamics can enable quantum-autonomous $Z$ and $XY$ gates on superconducting qubits. The gates can serve as building blocks for (fully or partially) quantum-autonomous circuits, which may reduce classical-control burdens.

Simulating out-of-equilibrium dynamics of quantum field theories in nature is challenging with classical methods, but is a promising application for quantum computers. Unfortunately, simulating interacting bosonic fields involves a high boson-to-qubit encoding overhead. Furthermore, when mapping to qubits, the infinite-dimensional Hilbert space of bosons is necessarily truncated, with truncation errors that grow with energy and time. A qubit-based quantum computer, augmented with an active bosonic register, and with qubit, bosonic, and mixed qubit-boson quantum gates, offers a more powerful platform for simulating bosonic theories. We demonstrate this capability experimentally in a hybrid analog-digital trapped-ion quantum computer, where qubits are encoded in the internal states of the ions, and the bosons in the ions' motional states. Specifically, we simulate nonequilibrium dynamics of a (1+1)-dimensional Yukawa model, a simplified model of interacting nucleons and pions, and measure fermion- and boson-occupation-state probabilities. These dynamics populate high bosonic-field excitations starting from an empty state, and the experimental results capture well such high-occupation states. This simulation approaches the regime where classical methods become challenging, bypasses the need for a large qubit overhead, and removes truncation errors. Our results, therefore, open the way to achieving demonstrable quantum advantage in qubit-boson quantum computing.

We implement a quantum generalization of a neural network on trapped-ion and IBM superconducting quantum computers to classify MNIST images, a common benchmark in computer vision. The network feedforward involves qubit rotations whose angles depend on the results of measurements in the previous layer. The network is trained via simulation, but inference is performed experimentally on quantum hardware. The classical-to-quantum correspondence is controlled by an interpolation parameter, $a$, which is zero in the classical limit. Increasing $a$ introduces quantum uncertainty into the measurements, which is shown to improve network performance at moderate values of the interpolation parameter. We then focus on particular images that fail to be classified by a classical neural network but are detected correctly in the quantum network. For such borderline cases, we observe strong deviations from the simulated behavior. We attribute this to physical noise, which causes the output to fluctuate between nearby minima of the classification energy landscape. Such strong sensitivity to physical noise is absent for clear images. We further benchmark physical noise by inserting additional single-qubit and two-qubit gate pairs into the neural network circuits. Our work provides a springboard toward more complex quantum neural networks on current devices: while the approach is rooted in standard classical machine learning, scaling up such networks may prove classically non-simulable and could offer a route to near-term quantum advantage.

Quantum games, like quantum algorithms, exploit quantum entanglement to establish strong correlations between strategic player actions. This paper introduces quantum game-theoretic models applied to trading and demonstrates their implementation on an ion-trap quantum computer. The results showcase a quantum advantage, previously known only theoretically, realized as higher-paying market Nash equilibria. This advantage could help uncover alpha in trading strategies, defined as excess returns compared to established benchmarks. These findings suggest that quantum computing could significantly influence the development of financial strategies.

The calibration of quantum measurements is limited by the ability to accurately prepare quantum states under unknown device errors. We develop an accurate calibration protocol for the measurement apparatus of a quantum computer that is `blind' to the state preparation. Blind calibration quantifies and corrects measurement errors from simple tomographic data on a noisy quantum state. Importantly, it calibrates multiple error mechanisms in a single experiment, eliminating the need for bespoke, separate calibration experiments. Using a trapped-ion quantum computer, we systematically demonstrate the accuracy of the method. We use blind calibration to estimate the native calibration parameters of the experimental system. The recovered calibrations are consistent with directly measured values and perform similarly in predicting the state properties.

The quantum chromodynamics (QCD) phase diagram, which reveals the state of strongly interacting matter at different temperatures and densities, is key to answering open questions in physics, ranging from the behavior of particles in neutron stars to the conditions of the early universe. However, classical simulations of QCD face significant computational barriers, such as the sign problem at finite matter densities. Quantum computing offers a promising solution to overcome these challenges. Here, we take an important step toward exploring the QCD phase diagram with quantum devices by preparing thermal states in one-dimensional non-Abelian gauge theories. We experimentally simulate the thermal states of SU(2) and SU(3) gauge theories at finite densities on a trapped-ion quantum computer using a variational method. This is achieved by introducing two features: Firstly, we add motional ancillae to the existing qubit register to efficiently prepare thermal probability distributions. Secondly, we introduce charge-singlet measurements to enforce color-neutrality constraints. This work marks the first lattice gauge theory quantum simulation of QCD at finite density and temperature for two and three colors, laying the foundation to explore QCD phenomena on quantum platforms.

Parallel operations are important for both near-term quantum computers and larger-scale fault-tolerant machines because they reduce execution time and qubit idling. We propose and implement a pairwise-parallel gate scheme on a trapped-ion quantum computer. The gates are driven simultaneously on different sets of orthogonal motional modes of a trapped-ion chain. We demonstrate the utility of this scheme by creating a GHZ state in one step using parallel gates with one overlapping qubit. We also show its advantage for circuits by implementing a digital quantum simulation of the dynamics of an interacting spin system, the transverse-field Ising model. This method effectively extends the available gate depth by up to two times with no overhead apart from additional initial cooling when no overlapping qubit is involved. This is because using a set of extra modes as additional quantum degrees of freedom is nearly equivalent to halving the trap heating rate, doubling the laser and qubit coherence time, and extending the controller memory depth by up to a factor of two. This scheme can be easily applied to different trapped-ion qubits and gate schemes, broadly enhancing the capabilities of trapped-ion quantum computers.

As quantum computers and simulators begin to produce results that cannot be verified classically, it becomes imperative to develop a variety of tools to detect and diagnose experimental errors on these devices. While state or process tomography is a natural way to characterize sources of experimental error, the intense measurement requirements make these strategies infeasible in all but the smallest of quantum systems. In this work, we formulate signatures of unitary evolution based on specific properties of periodically driven quantum systems. The absence of these signatures indicates a break either in the unitarity or periodicity condition on the evolution. We experimentally detect incoherent error on a trapped-ion quantum computer using these signatures. Our method is based on repeated measurements of a single observable, making this a low-cost evaluation of error with measurement requirements that scales according to the character of the dynamics, rather than the system size.

Two-qubit gate performance is vital for scaling up ion-trap quantum computing. Optimized quantum control is needed to achieve reductions in gate-time and gate error-rate. We describe two-qubit gates with addressed Raman beams within a linear trapped-ion chain by a quantum master equation (QME). The QME incorporates the single-ion two-photon effective Rabi frequency, Autler-Townes and vibrational Bloch-Siegert energy shifts, off-resonant transitions, Raman and Rayleigh scattering, laser-power fluctuations, motional heating, cross-Kerr phonon coupling, laser spillover, asymmetric addressing beams and an imperfect initial motional ground state, with no fitting parameters. Whereas state-of-the-art methods are oblivious to these effects in the gate design procedure. We employ global optimization to design pulse sequences for achieving a robust rapid two-qubit gate for seven trapped $^{171}$Yb$^{+}$ ions by optimizing over numerically integrated QME solutions. Here, robust means resilient against slow drift of motional frequencies, and rapid means gate execution where the effective Rabi frequency is comparable to the detuning of the laser from the ion's bare electronic transition. Our robust quantum control delivers rapid high-quality two-qubit gates in long ion chains, enabling scalable quantum computing with trapped ions.

Two-qubit gates are a fundamental constituent of a quantum computer and typically its most challenging operation. In a trapped-ion quantum computer, this is typically implemented with laser beams which are modulated in amplitude, frequency, phase, or a combination of these. The required modulation becomes increasingly more complex as the quantum computer becomes larger, complicating the control hardware design. Here, we develop a simple method to essentially remove the pulse-modulation complexity by engineering the normal modes of the ion chain. We experimentally demonstrate the required mode engineering in a three ion chain. This opens up the possibility to trade off complexity between the design of the trapping fields and the optical control system, which will help scale the ion trap quantum computing platform.

Deformed oscillators allow for a generalization of the standard fermions and bosons, namely, for the description of para-particles. Such particles, while indiscernible in nature, can represent good candidates for descriptions of physical phenomena like topological phases of matter. Here, we report the digital quantum simulation of para-particle oscillators by mapping para-particle states to the state of a qubit register, which allow us to identify the para-particle oscillator Hamiltonian as an $XY$ model, and further digitize the system onto a universal set of gates. In both instances, the gate depth grows polynomially with the number of qubits used. To establish the validity of our results, we experimentally simulate the dynamics of para-fermions and para-bosons, demonstrating full control of para-particle oscillators on a quantum computer. Furthermore, we compare the overall performance of the digital simulation of dynamics of the driven para-Fermi oscillator to a recent analog quantum simulation result.

Combinatorial optimization problems on graphs have broad applications in science and engineering. The Quantum Approximate Optimization Algorithm (QAOA) is a method to solve these problems on a quantum computer by applying multiple rounds of variational circuits. However, there exist several challenges limiting the real-world applications of QAOA. In this paper, we demonstrate on a trapped-ion quantum computer that QAOA results improve with the number of rounds for multiple problems on several arbitrary graphs. We also demonstrate an advanced mixing Hamiltonian that allows sampling of all optimal solutions with predetermined weights. Our results are a step towards applying quantum algorithms to real-world problems.

Tracking the dynamics of physical systems in real time is a prime application of digital quantum computers. Using a trapped-ion system with up to six qubits, we simulate the real-time dynamics of a lattice gauge theory in 1+1 dimensions, i.e., the lattice Schwinger model, and demonstrate non-perturbative effects such as pair creation for times much longer than previously accessible. We study the gate requirement of two formulations of the model using the Suzuki-Trotter product formula, as well as the trade-off between errors from the ordering of the Hamiltonian terms, the Trotter step size, and experimental imperfections. To mitigate experimental errors, a recent symmetry-protection protocol for suppressing coherent errors and a symmetry-inspired post-selection scheme are applied. This work demonstrates the integrated theoretical, algorithmic, and experimental approach that is essential for efficient simulation of lattice gauge theories and other complex physical systems.

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.

Para-particles are fascinating because they are neither bosons nor fermions. While unlikely to be found in nature, they might represent accurate descriptions of physical phenomena like topological phases of matter. We report the quantum simulation of para-particle oscillators by tailoring the native couplings of two orthogonal motional modes of a trapped ion. Our system reproduces the dynamics of para-bosons and para-fermions of even order very accurately. These results represent the first experimental analogy of para-particle dynamics in any physical system and demonstrate full control of para-particle oscillators.

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 $O(\sqrt{n})$ cycles, which makes the evaluation of constraints associated with hundreds of cycles realistic.

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.

Quantum field theories are the cornerstones of modern physics, providing relativistic and quantum mechanical descriptions of physical systems at the most fundamental level. Simulating real-time dynamics within these theories remains elusive in classical computing. This provides a unique opportunity for quantum simulators, which hold the promise of revolutionizing our simulation capabilities. Trapped-ion systems are successful quantum-simulator platforms for quantum many-body physics and can operate in digital, or gate-based, and analog modes. Inspired by the progress in proposing and realizing quantum simulations of a number of relativistic quantum field theories using trapped-ion systems, and by the hybrid analog-digital proposals for simulating interacting boson-fermion models, we propose hybrid analog-digital quantum simulations of selected quantum field theories, taking recent developments to the next level. On one hand, the semi-digital nature of this proposal offers more flexibility in engineering generic model interactions compared with a fully-analog approach. On the other hand, encoding the bosonic fields onto the phonon degrees of freedom of the trapped-ion system allows a more efficient usage of simulator resources, and a more natural implementation of intrinsic quantum operations in such platforms. This opens up new ways for simulating complex dynamics of e.g., Abelian and non-Abelian gauge theories, by combining the benefits of digital and analog schemes.

Fault-tolerant quantum error correction (QEC) is crucial for unlocking the true power of quantum computers. QEC codes use multiple physical qubits to encode a logical qubit, which is protected against errors at the physical qubit level. Here we use a trapped ion system to experimentally prepare $m$-qubit GHZ states and sample the measurement results to construct $m\times m$ logical states of the $[[m^2,1,m]]$ Shor code, up to $m=7$. The synthetic logical fidelity shows how deeper encoding can compensate for additional gate errors in state preparation for larger logical states. However, the optimal code size depends on the physical error rate and we find that $m=5$ has the best performance in our system. We further realize the direct logical encoding of the $[[9,1,3]]$ Shor code on nine qubits in a thirteen-ion chain for comparison, with $98.8(1)\%$ and $98.5(1)\%$ fidelity for state $\left\vert\pm\right\rangle_L$, respectively.

We present a method to extract the phase shift of a scattering process using the real-time evolution in the early and intermediate stages of the collision in order to estimate the time delay of a wave packet. This procedure is convenient when using noisy quantum computers for which the asymptotic out-state behavior is unreachable. We demonstrate that the challenging Fourier transforms involved in the state preparation and measurements can be implemented in $1+1$ dimensions with current trapped ion devices and IBM quantum computers. We compare quantum computation of the time delays obtained in the one-particle quantum mechanics limit and the scalable quantum field theory formulation with accurate numerical results. We discuss the finite volume effects in the Wigner formula connecting time delays to phase shifts. The results reported involve two- and four-qubit calculations, and we discuss the possibility of larger scale computations in the near future.

By leveraging shared entanglement between a pair of qubits, one can teleport a quantum state from one particle to another. Recent advances have uncovered an intrinsically many-body generalization of quantum teleportation, with an elegant and surprising connection to gravity. In particular, the teleportation of quantum information relies on many-body dynamics, which originate from strongly-interacting systems that are holographically dual to gravity; from the gravitational perspective, such quantum teleportation can be understood as the transmission of information through a traversable wormhole. Here, we propose and analyze a new mechanism for many-body quantum teleportation -- dubbed peaked-size teleportation. Intriguingly, peaked-size teleportation utilizes precisely the same type of quantum circuit as traversable wormhole teleportation, yet has a completely distinct microscopic origin: it relies upon the spreading of local operators under generic thermalizing dynamics and not gravitational physics. We demonstrate the ubiquity of peaked-size teleportation, both analytically and numerically, across a diverse landscape of physical systems, including random unitary circuits, the Sachdev-Ye-Kitaev model (at high temperatures), one-dimensional spin chains and a bulk theory of gravity with stringy corrections. Our results pave the way towards using many-body quantum teleportation as a powerful experimental tool for: (i) characterizing the size distributions of operators in strongly-correlated systems and (ii) distinguishing between generic and intrinsically gravitational scrambling dynamics. To this end, we provide a detailed experimental blueprint for realizing many-body quantum teleportation in both trapped ions and Rydberg atom arrays; effects of decoherence and experimental imperfections are analyzed.

Quantum computing is currently limited by the cost of two-qubit entangling operations. In order to scale up quantum processors and achieve a quantum advantage, it is crucial to economize on the power requirement of two-qubit gates, make them robust to drift in experimental parameters, and shorten the gate times. In this paper, we present two methods, one exact and one approximate, to construct optimal pulses for entangling gates on a pair of ions within a trapped ion chain, one of the leading quantum computing architectures. Our methods are direct, non-iterative, and linear, and can construct gate-steering pulses requiring less power than the standard method by more than an order of magnitude in some parameter regimes. The power savings may generally be traded for reduced gate time and greater qubit connectivity. Additionally, our methods provide increased robustness to mode drift. We illustrate these trade-offs on a trapped-ion quantum computer.

The quantum walk formalism is a widely used and highly successful framework for modeling quantum systems, such as simulations of the Dirac equation, different dynamics in both the low and high energy regime, and for developing a wide range of quantum algorithms. Here we present the circuit-based implementation of a discrete-time quantum walk in position space on a five-qubit trapped-ion quantum processor. We encode the space of walker positions in particular multi-qubit states and program the system to operate with different quantum walk parameters, experimentally realizing a Dirac cellular automaton with tunable mass parameter. The quantum walk circuits and position state mapping scale favorably to a larger model and physical systems, allowing the implementation of any algorithm based on discrete-time quantum walks algorithm and the dynamics associated with the discretized version of the Dirac equation.

We introduce an approach to improve the accuracy and reduce the sample complexity of near term quantum-classical algorithms. We construct a simpler initial parameterized quantum state, or ansatz, based on the past causal cone of each observable, generally yielding fewer qubits and gates. We implement this protocol on a trapped ion quantum computer and demonstrate improvement in accuracy and time-to-solution at an arbitrary point in the variational search space. We report a $\sim 27\%$ improvement in the accuracy of the calculation of the deuteron binding energy and $\sim 40\%$ improvement in the accuracy of the quantum approximate optimization of the MAXCUT problem applied to the dragon graph $T_{3,2}$. When the time-to-solution is prioritized over accuracy, the former requires $\sim 71\%$ fewer measurements and the latter requires $\sim 78\%$ fewer measurements.

Ion trap systems are a leading platform for large scale quantum computers. Trapped ion qubit crystals are fully-connected and reconfigurable, owing to their long range Coulomb interaction that can be modulated with external optical forces. However, the spectral crowding of collective motional modes could pose a challenge to the control of such interactions for large numbers of qubits. Here, we show that high-fidelity quantum gate operations are still possible with very large trapped ion crystals, simplifying the scaling of ion trap quantum computers. To this end, we present analytical work that determines how parallel entangling gates produce a crosstalk error that falls off as the inverse cube of the distance between the pairs. We also show experimental work demonstrating entangling gates on a fully-connected chain of seventeen $^{171}{\rm{Yb}}^{+}$ ions with fidelities as high as $97(1)\%$.

We report results for simulating an effective field theory to compute the binding energy of the deuteron nucleus using a hybrid algorithm on a trapped-ion quantum computer. Two increasingly complex unitary coupled-cluster ansaetze have been used to compute the binding energy to within a few percent for successively more complex Hamiltonians. By increasing the complexity of the Hamiltonian, allowing more terms in the effective field theory expansion and calculating their expectation values, we present a benchmark for quantum computers based on their ability to scalably calculate the effective field theory with increasing accuracy. Our result of $E_4=-2.220 \pm 0.179$MeV may be compared with the exact Deuteron ground-state energy $-2.224$MeV. We also demonstrate an error mitigation technique using Richardson extrapolation on ion traps for the first time. The error mitigation circuit represents a record for deepest quantum circuit on a trapped-ion quantum computer.

Quantum scrambling is the dispersal of local information into many-body quantum entanglements and correlations distributed throughout the entire system. This concept underlies the dynamics of thermalization in closed quantum systems, and more recently has emerged as a powerful tool for characterizing chaos in black holes. However, the direct experimental measurement of quantum scrambling is difficult, owing to the exponential complexity of ergodic many-body entangled states. One way to characterize quantum scrambling is to measure an out-of-time-ordered correlation function (OTOC); however, since scrambling leads to their decay, OTOCs do not generally discriminate between quantum scrambling and ordinary decoherence. Here, we implement a quantum circuit that provides a positive test for the scrambling features of a given unitary process. This approach conditionally teleports a quantum state through the circuit, providing an unambiguous litmus test for scrambling while projecting potential circuit errors into an ancillary observable. We engineer quantum scrambling processes through a tunable 3-qubit unitary operation as part of a 7-qubit circuit on an ion trap quantum computer. Measured teleportation fidelities are typically $\sim80\%$, and enable us to experimentally bound the scrambling-induced decay of the corresponding OTOC measurement.

We reduce measurement errors in a quantum computer using machine learning techniques. We exploit a simple yet versatile neural network to classify multi-qubit quantum states, which is trained using experimental data. This flexible approach allows the incorporation of any number of features of the data with minimal modifications to the underlying network architecture. We experimentally illustrate this approach in the readout of trapped-ion qubits using additional spatial and temporal features in the data. Using this neural network classifier, we efficiently treat qubit readout crosstalk, resulting in a 30\% improvement in detection error over the conventional threshold method. Our approach does not depend on the specific details of the system and can be readily generalized to other quantum computing platforms.

We demonstrate a Bayesian quantum game on an ion trap quantum computer with five qubits. The players share an entangled pair of qubits and perform rotations on their qubit as the strategy choice. Two five-qubit circuits are sufficient to run all 16 possible strategy choice sets in a game with four possible strategies. The data are then parsed into player types randomly in order to combine them classically into a Bayesian framework. We exhaustively compute the possible strategies of the game so that the experimental data can be used to solve for the Nash equilibria of the game directly. Then we compare the payoff at the Nash equilibria and location of phase-change-like transitions obtained from the experimental data to the theory, and study how it changes as a function of the amount of entanglement.

The efficient simulation of correlated quantum systems is the most promising near-term application of quantum computers. Here, we present a measurement of the second Renyi entropy of the ground state of the two-site Fermi-Hubbard model on a $5$-qubit programmable quantum computer based on trapped ions. Our work illustrates the extraction of a non-linear characteristic of a quantum state using a controlled-swap gate acting on two copies of the state. This scalable measurement of entanglement on a universal quantum computer will, with more qubits, provide insights into many-body quantum systems that are impossible to simulate on classical computers.

In an ion trap quantum computer, collective motional modes are used to entangle two or more qubits in order to execute multi-qubit logical gates. Any residual entanglement between the internal and motional states of the ions results in loss of fidelity, especially when there are many spectator ions in the crystal. We propose using a frequency-modulated (FM) driving force to minimize such errors. In simulation, we obtained an optimized FM two-qubit gate that can suppress errors to less than 0.01\% and is robust against frequency drifts over $\pm$1 kHz. Experimentally, we have obtained a two-qubit gate fidelity of $98.3(4)\%$, a state-of-the-art result for two-qubit gates with 5 ions.

Using a segmented ion trap with mK laser-cooled ions we have realised a novel single ion source which can deterministically deliver a wide range of ion species, isotopes or ionic molecules [Schnitzler et al., Phys. Rev. Lett. 102, 070501 (2009)]. Experimental data is discussed in detail and compared with numerical simulations of ion trajectories. For the novel ion source we investigate numerically the influence of various extraction parameters on fluctuations in velocity and position of the beam. We present specialized ion optics and show from numerical simulations that nm resolution is achievable. The Paul trap, which is used as a single ion source, together with the presented ion optics, constitutes a promising candidate for a deterministic ion implantation method for applications in solid state quantum computing or classical nano-electronic devices.