arXiv subjects

C. Hempel

Publications and source records attributed to C. Hempel.

At least 19 recordsLinked to original sources

arXiv2024

Experimental Quantum Simulation of Chemical Dynamics

Accurate simulation of dynamical processes in molecules and reactions is among the most challenging problems in quantum chemistry. Quantum computers promise efficient chemical simulation, but the existing quantum algorithms require many logical qubits and gates, placing practical applications beyond existing technology. Here, we carry out the first quantum simulations of chemical dynamics by employing a more hardware-efficient encoding scheme that uses both qubits and bosonic degrees of freedom. Our trapped-ion device accurately simulates the dynamics of non-adiabatic chemical processes, which are among the most difficult problems in computational chemistry because they involve strong coupling between electronic and nuclear motions. We demonstrate the programmability and versatility of our approach by simulating the dynamics of three different molecules as well as open-system dynamics in the condensed phase, all with the same quantum resources. Our approach requires orders of magnitude fewer resources than equivalent qubit-only quantum simulations, demonstrating the potential of using hybrid encoding schemes to accelerate quantum simulations of complex chemical processes, which could have applications in fields ranging from energy conversion and storage to biology and drug design.

quant-ph↗

arXiv2021

Precision Characterization of the $^2$D$_{5/2}$ State and Quadratic Zeeman Coefficient in $^{171}$Yb$^+$

We report measurements of the branching fraction, hyperfine constant, and second-order Zeeman coefficient of the D$_{5/2}$ level in $^{171}$Yb$^+$ with up to two orders-of-magnitude improvement in precision compared to previously reported values. We estimate the electric quadrupole reduced matrix element of the S$_{1/2}$ $\leftrightarrow$ D$_{5/2}$ transition to be 12.5(4) $e a_0^2$. Furthermore, we determine the transition frequency of the F$_{7/2}$ $\leftrightarrow$ $^{1}$D$[3/2]_{3/2}$ at 760 nm with a $\sim$25-fold improvement in precision. These measurements provide benchmarks for quantum-many-body atomic-physics calculations and provide valuable data for efforts to improve quantum information processors based on Yb$^+$.

physics.atom-ph↗

arXiv2020

Scalable hyperfine qubit state detection via electron shelving in the ${}^2$D$_{5/2}$ and ${}^2$F$_{7/2}$ manifolds in ${}^{171}$Yb$^{+}$

Qubits encoded in hyperfine states of trapped ions are ideal for quantum computation given their long lifetimes and low sensitivity to magnetic fields, yet they suffer from off-resonant scattering during detection often limiting their measurement fidelity. In ${}^{171}$Yb$^{+}$ this is exacerbated by a low fluorescence yield, which leads to a need for complex and expensive hardware - a problematic bottleneck especially when scaling up the number of qubits. We demonstrate a detection routine based on electron shelving to address this issue in ${}^{171}$Yb$^{+}$ and achieve a 5.6$\times$ reduction in single-ion detection error on an avalanche photodiode to $1.8(2)\times10^{-3}$ in a 100 $μ$s detection period, and a 4.3$\times$ error reduction on an electron multiplying CCD camera, with $7.7(2)\times10^{-3}$ error in 400 $μ$s. We further improve the characterization of a repump transition at 760 nm to enable a more rapid reset of the auxiliary $^2$F$_{7/2}$ states populated after shelving. Finally, we examine the detection fidelity limit using the long-lived $^2$F$_{7/2}$ state, achieving a further 300$\times$ and 12$\times$ reduction in error to $6(7)\times10^{-6}$ and $6.3(3)\times10^{-4}$ in 1 ms on the respective detectors. While shelving-rate limited in our setup, we suggest various techniques to realize this detection method at speeds compatible with quantum information processing, providing a pathway to ultra-high fidelity detection in ${}^{171}$Yb$^{+}$.

quant-ph↗

arXiv2019

Dynamically corrected gates suppress spatio-temporal error correlations as measured by randomized benchmarking

Quantum error correction provides a path to large-scale quantum computers, but is built on challenging assumptions about the characteristics of the underlying errors. In particular, the mathematical assumption of statistically independent errors in quantum logic operations is at odds with realistic environments where error sources may exhibit strong temporal and spatial correlations. We present experiments using trapped ions to demonstrate that the use of dynamically corrected gates (DCGs), generally considered for the reduction of error magnitudes, can also suppress error correlations in space and time throughout quantum circuits. We present a first-principles analysis of the manifestation of error correlations in randomized benchmarking, and validate this model through experiments performed using engineered errors. We find that standard DCGs can reduce error correlations by $\sim50\times$, while increasing the magnitude of uncorrelated errors by a factor scaling linearly with the extended DCG duration compared to a primitive gate. We then demonstrate that the correlation characteristics of intrinsic errors in our system are modified by use of DCGs, consistent with a picture in which DCGs whiten the effective error spectrum induced by external noise.

quant-ph↗

arXiv2017

Assessing the progress of trapped-ion processors towards fault-tolerant quantum computation

A quantitative assessment of the progress of small prototype quantum processors towards fault-tolerant quantum computation is a problem of current interest in experimental and theoretical quantum information science. We introduce a necessary and fair criterion for quantum error correction (QEC), which must be achieved in the development of these quantum processors before their sizes are sufficiently big to consider the well-known QEC threshold. We apply this criterion to benchmark the ongoing effort in implementing QEC with topological color codes using trapped-ion quantum processors and, more importantly, to guide the future hardware developments that shall be required in order to demonstrate beneficial QEC with small topological quantum codes. In doing so, we present a thorough description of a realistic trapped-ion toolbox for QEC, and a physically-motivated error model that goes beyond standard simplifications in the QEC literature. Our large-scale numerical analysis shows that two-species trapped-ion crystals in high-optical aperture segmented traps, with the improvements hereby described, are a very promising candidate for fault-tolerant quantum computation.

quant-ph↗

arXiv2017

Measuring and Suppressing Error Correlations in Quantum Circuits

Quantum error correction provides a path to large-scale quantum computers, but is built on challenging assumptions about the characteristics of the underlying errors. In particular, the mathematical assumption of independent errors in quantum logic operations is at odds with realistic environments where error-sources may exhibit strong temporal correlations. We present experiments enabling the identification of error correlations between operations in quantum circuits, using only projective measurements at the end of the circuit. Using a single trapped ion qubit and engineered noise with tunable temporal correlations, we identify a clear signature of error correlations between sequential gates in randomly composed quantum circuits, and extract quantitative measures linked to the underlying noise correlation length. By replacing all gates in these circuits with "virtual" dynamically corrected gates (DCGs), we demonstrate that even in the presence of strongly correlated noise the signatures of error correlations between sequential gates appear similar to standard gates exposed to uncorrelated noise. A theoretical model applied to our experiments reveals that common DCGs suppress the correlated error component by over $270\times$ with $95\%$ confidence. Using block-correlated noise, we explore the scaling of the effective error correlation length at the virtual level, and show that DCGs exhibit error correlations indistinguishable from those arising from uncorrelated noise.

quant-ph↗

arXiv2017

Experimental quantum verification in the presence of temporally correlated noise

Growth in the complexity and capabilities of quantum information hardware mandates access to practical techniques for performance verification that function under realistic laboratory conditions. Here we experimentally characterise the impact of common temporally correlated noise processes on both randomised benchmarking (RB) and gate-set tomography (GST). We study these using an analytic toolkit based on a formalism mapping noise to errors for arbitrary sequences of unitary operations. This analysis highlights the role of sequence structure in enhancing or suppressing the sensitivity of quantum verification protocols to either slowly or rapidly varying noise, which we treat in the limiting cases of quasi-DC miscalibration and white noise power spectra. We perform experiments with a single trapped $^{171}$Yb$^{+}$ ion as a qubit and inject engineered noise ($\propto σ^z$) to probe protocol performance. Experiments on RB validate predictions that the distribution of measured fidelities over sequences is described by a gamma distribution varying between approximately Gaussian for rapidly varying noise, and a broad, highly skewed distribution for the slowly varying case. Similarly we find a strong gate set dependence of GST in the presence of correlated errors, leading to significant deviations between estimated and calculated diamond distances in the presence of correlated $σ^z$ errors. Numerical simulations demonstrate that expansion of the gate set to include negative rotations can suppress these discrepancies and increase reported diamond distances by orders of magnitude for the same error processes. Similar effects do not occur for correlated $σ^x$ or $σ^y$ errors or rapidly varying noise processes, highlighting the critical interplay of selected gate set and the gauge optimisation process on the meaning of the reported diamond norm in correlated noise environments.

quant-ph↗

arXiv2016

Efficient tomography of a quantum many-body system

Quantum state tomography (QST) is the gold standard technique for obtaining an estimate for the state of small quantum systems in the laboratory. Its application to systems with more than a few constituents (e.g. particles) soon becomes impractical as the effort required grows exponentially in the number of constituents. Developing more efficient techniques is particularly pressing as precisely-controllable quantum systems that are well beyond the reach of QST are emerging in laboratories. Motivated by this, there is a considerable ongoing effort to develop new characterisation tools for quantum many-body systems. Here we demonstrate Matrix Product State (MPS) tomography, which is theoretically proven to allow the states of a broad class of quantum systems to be accurately estimated with an effort that increases efficiently with constituent number. We first prove that this broad class includes the out-of-equilbrium states produced by 1D systems with finite-range interactions, up to any fixed point in time. We then use the technique to reconstruct the dynamical state of a trapped-ion quantum simulator comprising up to 14 entangled spins (qubits): a size far beyond the reach of QST. Our results reveal the dynamical growth of entanglement and description complexity as correlations spread out during a quench: a necessary condition for future beyond-classical performance. MPS tomography should find widespread use to study large quantum many-body systems and to benchmark and verify quantum simulators and computers.

quant-ph↗

arXiv2016

Direct observation of dynamical quantum phase transitions in an interacting many-body system

Dynamical quantum phase transitions (DQPTs) extend the concept of phase transitions and thus universality to the non-equilibrium regime. In this letter, we investigate DQPTs in a string of ions simulating interacting transverse-field Ising models. We observe non-equilibrium dynamics induced by a quantum quench and show for strings of up to 10 ions the direct detection of DQPTs by measuring a quantity that becomes non-analytic in time in the thermodynamic limit. Moreover, we provide a link between DQPTs and the dynamics of other relevant quantities such as the magnetization, and we establish a connection between DQPTs and entanglement production.

quant-ph↗

arXiv2016

EIT ground-state cooling of long ion strings

Electromagnetically-induced-transparency (EIT) cooling is a ground-state cooling technique for trapped particles. EIT offers a broader cooling range in frequency space compared to more established methods. In this work, we experimentally investigate EIT cooling in strings of trapped atomic ions. In strings of up to 18 ions, we demonstrate simultaneous ground state cooling of all radial modes in under 1 ms. This is a particularly important capability in view of emerging quantum simulation experiments with large numbers of trapped ions. Our analysis of the EIT cooling dynamics is based on a novel technique enabling single-shot measurements of phonon numbers, by rapid adiabatic passage on a vibrational sideband of a narrow transition.

quant-ph↗

arXiv2015

Spectroscopy of interacting quasiparticles in trapped ions

The static and dynamic properties of many-body quantum systems are often well described by collective excitations, known as quasiparticles. Engineered quantum systems offer the opportunity to study such emergent phenomena in a precisely controlled and otherwise inaccessible way. We present a spectroscopic technique to study artificial quantum matter and use it for characterizing quasiparticles in a many-body system of trapped atomic ions. Our approach is to excite combinations of the system's fundamental quasiparticle eigenmodes, given by delocalised spin waves. By observing the dynamical response to superpositions of such eigenmodes, we extract the system dispersion relation, magnetic order, and even detect signatures of quasiparticle interactions. Our technique is not limited to trapped ions, and it is suitable for verifying quantum simulators by tuning them into regimes where the collective excitations have a simple form.

quant-ph↗

arXiv2014

Entanglement-enhanced detection of single-photon scattering events

The ability to detect the interaction of light and matter at the single-particle level is becoming increasingly important for many areas of science and technology. The absorption or emission of a photon on a narrow transition of a trapped ion can be detected with near unit probability, thereby enabling the realization of ultra-precise ion clocks and quantum information processing applications. Extending this sensitivity to broad transitions is challenging due to the difficulty of detecting the rapid photon scattering events in this case. Here, we demonstrate a technique to detect the scattering of a single photon on a broad optical transition with high sensitivity. Our approach is to use an entangled state to amplify the tiny momentum kick an ion receives upon scattering a photon. The method should find applications in spectroscopy of atomic and molecular ions and quantum information processing.

quant-ph↗

arXiv2014

Observation of entanglement propagation in a quantum many-body system

The key to explaining a wide range of quantum phenomena is understanding how entanglement propagates around many-body systems. Furthermore, the controlled distribution of entanglement is of fundamental importance for quantum communication and computation. In many situations, quasiparticles are the carriers of information around a quantum system and are expected to distribute entanglement in a fashion determined by the system interactions. Here we report on the observation of magnon quasiparticle dynamics in a one-dimensional many-body quantum system of trapped ions representing an Ising spin model. Using the ability to tune the effective interaction range, and to prepare and measure the quantum state at the individual particle level, we observe new quasiparticle phenomena. For the first time, we reveal the entanglement distributed by quasiparticles around a many-body system. Second, for long-range interactions we observe the divergence of quasiparticle velocity and breakdown of the light-cone picture that is valid for short-range interactions. Our results will allow experimental studies of a wide range of phenomena, such as quantum transport, thermalisation, localisation and entanglement growth, and represent a first step towards a new quantum-optical regime with on-demand quasiparticles with tunable non-linear interactions.

quant-ph↗

arXiv2013

Experimental violation of multipartite Bell inequalities with trapped ions

We report on the experimental violation of multipartite Bell inequalities by entangled states of trapped ions. First we consider resource states for measurement-based quantum computation of between 3 and 7 ions and show that all strongly violate a Bell-type inequality for graph states, where the criterion for violation is a sufficiently high fidelity. Second we analyze GHZ states of up to 14 ions generated in a previous experiment using stronger Mermin-Klyshko inequalities, and show that in this case the violation of local realism increases exponentially with system size. These experiments represent a violation of multipartite Bell-type inequalities of deterministically prepared entangled states. In addition, the detection loophole is closed.

quant-ph↗

arXiv2013

Measurement-based quantum computation with trapped ions

Measurement-based quantum computation (MBQC) represents a powerful and flexible framework for quantum information processing, based on the notion of entangled quantum states as computational resources. The most prominent application is the one-way quantum computer, with the cluster state as its universal resource. Here we demonstrate the principles of MBQC using deterministically generated graph states of up to 7 qubits, in a system of trapped atomic ions. Firstly we implement a universal set of operations for quantum computing. Secondly we demonstrate a family of measurement-based quantum error correction codes, and show their improved performance as the code length is increased. We show that all our graph states violate a multipartite Bell inequality and are therefore capable of information processing tasks that cannot be described by a local hidden variable model. The methods presented can directly be scaled up to generate graph states of several tens of qubits.

quant-ph↗

arXiv2013

Generation of quantum discord between ionic qubits via noisy processes

Quantum systems in mixed states can be unentangled and yet still correlated in a way that is not possible for classical systems. These correlations can be quantified by the quantum discord and might provide a resource for certain mixed-state quantum information processing tasks. Here we report on the generation of discordant states of two trapped atomic ions via Markovian decoherence processes. While entanglement is strictly non-increasing under such operations, discord can be generated in various forms. Firstly we show that, starting from two classically correlated qubits, it is possible to generate discord by applying decoherence to just one of them. Secondly, even when starting with completely uncorrelated systems, we show that discord can be generated via classically correlated decoherence processes. Finally, the Werner states are created. The generated states can be used as a resource state for quantum information transmission and could be readily extended to more ions.

quant-ph↗

arXiv2012

Guiding of Rydberg atoms in a high-gradient magnetic guide

We study the guiding of $^{87}$Rb 59D$_{5/2}$ Rydberg atoms in a linear, high-gradient, two-wire magnetic guide. Time delayed microwave ionization and ion detection are used to probe the Rydberg atom motion. We observe guiding of Rydberg atoms over a period of 5 ms following excitation. The decay time of the guided atom signal is about five times that of the initial state. We attribute the lifetime increase to an initial phase of $l$-changing collisions and thermally induced Rydberg-Rydberg transitions. Detailed simulations of Rydberg atom guiding reproduce most experimental observations and offer insight into the internal-state evolution.

physics.atom-ph↗

arXiv2011

Universal digital quantum simulation with trapped ions

A digital quantum simulator is an envisioned quantum device that can be pro- grammed to efficiently simulate any other local system. We demonstrate and investigate the digital approach to quantum simulation in a system of trapped ions. Using sequences of up to 100 gates and 6 qubits, the full time dynamics of a range of spin systems are digitally simulated. Interactions beyond those naturally present in our simulator are accurately reproduced and quantitative bounds are provided for the overall simulation quality. Our results demon- strate the key principles of digital quantum simulation and provide evidence that the level of control required for a full-scale device is within reach.

quant-ph↗