arXiv subjects

Martin Ringbauer

Publications and source records attributed to Martin Ringbauer.

At least 37 records · Page 2Linked to original sources

arXiv2024

Verifiable measurement-based quantum random sampling with trapped ions

Quantum computers are now on the brink of outperforming their classical counterparts. One way to demonstrate the advantage of quantum computation is through quantum random sampling performed on quantum computing devices. However, existing tools for verifying that a quantum device indeed performed the classically intractable sampling task are either impractical or not scalable to the quantum advantage regime. The verification problem thus remains an outstanding challenge. Here, we experimentally demonstrate efficiently verifiable quantum random sampling in the measurement-based model of quantum computation on a trapped-ion quantum processor. We create and sample from random cluster states, which are at the heart of measurement-based computing, up to a size of 4 x 4 qubits. By exploiting the structure of these states, we are able to recycle qubits during the computation to sample from entangled cluster states that are larger than the qubit register. We then efficiently estimate the fidelity to verify the prepared states -- in single instances and on average -- and compare our results to cross-entropy benchmarking. Finally, we study the effect of experimental noise on the certificates. Our results and techniques provide a feasible path toward a verified demonstration of a quantum advantage.

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arXiv2023

Reconstructing complex states of a 20-qubit quantum simulator

A prerequisite to the successful development of quantum computers and simulators is precise understanding of physical processes occurring therein, which can be achieved by measuring the quantum states they produce. However, the resources required for traditional quantum-state estimation scale exponentially with the system size, highlighting the need for alternative approaches. Here we demonstrate an efficient method for reconstruction of significantly entangled multi-qubit quantum states. Using a variational version of the matrix product state ansatz, we perform the tomography (in the pure-state approximation) of quantum states produced in a 20-qubit trapped-ion Ising-type quantum simulator, using the data acquired in only 27 bases with 1000 measurements in each basis. We observe superior state reconstruction quality and faster convergence compared to the methods based on neural network quantum state representations: restricted Boltzmann machines and feedforward neural networks with autoregressive architecture. Our results pave the way towards efficient experimental characterization of complex states produced by the quench dynamics of many-body quantum systems.

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arXiv2023

On the role of entanglement in qudit-based circuit compression

Gate-based universal quantum computation is formulated in terms of two types of operations: local single-qubit gates, which are typically easily implementable, and two-qubit entangling gates, whose faithful implementation remains one of the major experimental challenges since it requires controlled interactions between individual systems. To make the most of quantum hardware it is crucial to process information in the most efficient way. One promising avenue is to use higher-dimensional systems, qudits, as the fundamental units of quantum information, in order to replace a fraction of the qubit-entangling gates with qudit-local gates. Here, we show how the complexity of multi-qubit circuits can be lowered significantly by employing qudit encodings, which we quantify by considering exemplary circuits with exactly known (multi-qubit) gate complexity. We discuss general principles for circuit compression, derive upper and lower bounds on the achievable advantage, and highlight the key role played by entanglement and the available gate set. Explicit experimental schemes for photonic as well as for trapped-ion implementations are provided and demonstrate a significant expected gain in circuit performance for both platforms.

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arXiv2023

Variational quantum simulation of U(1) lattice gauge theories with qudit systems

Lattice gauge theories are fundamental to various fields, including particle physics, condensed matter, and quantum information theory. Recent progress in the control of quantum systems allows for studying Abelian lattice gauge theories in table-top experiments. However, several challenges remain, such as implementing dynamical fermions in higher spatial dimensions and magnetic field terms. Here, we map D-dimensional U(1) Abelian lattice gauge theories onto qudit systems with local interactions for arbitrary D. We propose a variational quantum simulation scheme for the qudit system with a local Hamiltonian, that can be implemented on a universal qudit quantum device as the one developed in [Nat. Phys. 18, 1053-1057 (2022)]. We describe how to implement the variational imaginary-time evolution protocol for ground state preparation as well as the variational real-time evolution protocol to simulate non-equilibrium physics on universal qudit quantum computers, supplemented with numerical simulations. Our proposal can serve as a way of simulating lattice gauge theories, particularly in higher spatial dimensions, with minimal resources, regarding both system sizes and gate count.

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arXiv2023

Compilation of Entangling Gates for High-Dimensional Quantum Systems

Most quantum computing architectures to date natively support multi-valued logic, albeit being typically operated in a binary fashion. Multi-valued, or qudit, quantum processors have access to much richer forms of quantum entanglement, which promise to significantly boost the performance and usefulness of quantum devices. However, much of the theory as well as corresponding design methods required for exploiting such hardware remain insufficient and generalizations from qubits are not straightforward. A particular challenge is the compilation of quantum circuits into sets of native qudit gates supported by state-of-the-art quantum hardware. In this work, we address this challenge by introducing a complete workflow for compiling any two-qudit unitary into an arbitrary native gate set. Case studies demonstrate the feasibility of both, the proposed approach as well as the corresponding implementation (which is freely available at https://github.com/cda-tum/qudit-entanglement-compilation).

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arXiv2022

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 codes. 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 design 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 usage of few ancillary 'flag' qubits. We perform a logical two-qubit CNOT-gate between two instances of the seven qubit color code, and we also fault-tolerantly prepare a logical magic state. We then realize a fault-tolerant logical T-gate by injecting the magic state via teleportation from one logical qubit onto the other. We observe the hallmark feature of fault tolerance, a superior performance compared to a non-fault-tolerant implementation. In combination with recently demonstrated repeated quantum error correction cycles these results open the door to error-corrected universal quantum computation.

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arXiv2022

Native qudit entanglement in a trapped ion quantum processor

Quantum information carriers, just like most physical systems, naturally occupy high-dimensional Hilbert spaces. Instead of restricting them to a two-level subspace, these high-dimensional (qudit) quantum systems are emerging as a powerful resource for the next generation of quantum processors. Yet harnessing the potential of these systems requires efficient ways of generating the desired interaction between them. Here, we experimentally demonstrate an implementation of a native two-qudit entangling gate in a trapped-ion qudit system up to dimension $5$. This is achieved by generalizing a recently proposed light-shift gate mechanism to generate genuine qudit entanglement in a single application of the gate. The gate seamlessly adapts to the local dimension of the system with a calibration overhead that is independent of the dimension.

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arXiv2022

Adaptive Compilation of Multi-Level Quantum Operations

Quantum computers have the potential to solve some important industrial and scientific problems with greater efficiency than classical computers. While most current realizations focus on two-level qubits, the underlying physics used in most hardware is capable of extending the concepts to a multi-level logic - enabling the use of qudits, which promise higher computational power and lower error rates. Based on a strong theoretical backing and motivated by recent physical accomplishments, this also calls for methods and tools for compiling quantum circuits to those devices. To enable efficient qudit compilation, we introduce the concept of an energy coupling graph for single-qudit systems and provide an adaptive algorithm that leverages this representation for compiling arbitrary unitaries. This leads to significant improvements over the state-of-the-art compilation scheme and, additionally, provides an option to trade-off worst-case costs and run-time. The developed compiler is available via github.com/cda-tum/qudit-compilation under an open-source license.

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arXiv2022

Experimental single-setting quantum state tomography

Quantum computers solve ever more complex tasks using steadily growing system sizes. Characterizing these quantum systems is vital, yet becoming increasingly challenging. The gold-standard is quantum state tomography (QST), capable of fully reconstructing a quantum state without prior knowledge. Measurement and classical computing costs, however, increase exponentially in the system size - a bottleneck given the scale of existing and near-term quantum devices. Here, we demonstrate a scalable and practical QST approach that uses a single measurement setting, namely symmetric informationally complete (SIC) positive operator-valued measures (POVM). We implement these nonorthogonal measurements on an ion trap device by utilizing more energy levels in each ion - without ancilla qubits. More precisely, we locally map the SIC POVM to orthogonal states embedded in a higher-dimensional system, which we read out using repeated in-sequence detections, providing full tomographic information in every shot. Combining this SIC tomography with the recently developed randomized measurement toolbox ("classical shadows") proves to be a powerful combination. SIC tomography alleviates the need for choosing measurement settings at random ("derandomization"), while classical shadows enable the estimation of arbitrary polynomial functions of the density matrix orders of magnitudes faster than standard methods. The latter enables in-depth entanglement studies, which we experimentally showcase on a 5-qubit absolutely maximally entangled (AME) state. Moreover, the fact that the full tomography information is available in every shot enables online QST in real time. We demonstrate this on an 8-qubit entangled state, as well as for fast state identification. All in all, these features single out SIC-based classical shadow estimation as a highly scalable and convenient tool for quantum state characterization.

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arXiv2022

Probing phases of quantum matter with an ion-trap tensor-network quantum eigensolver

Tensor-Network (TN) states are efficient parametric representations of ground states of local quantum Hamiltonians extensively used in numerical simulations. Here we encode a TN ansatz state directly into a quantum simulator, which can potentially offer an exponential advantage over purely numerical simulation. In particular, we demonstrate the optimization of a quantum-encoded TN ansatz state using a variational quantum eigensolver on an ion-trap quantum computer by preparing the ground states of the extended Su-Schrieffer-Heeger model. The generated states are characterized by estimating the topological invariants, verifying their topological order. Our TN encoding as a trapped ion circuit employs only single-site addressing optical pulses - the native operations naturally available on the platform. We reduce nearest-neighbor crosstalk by selecting different magnetic sublevels with well-separated transition frequencies to encode even and odd qubits.

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arXiv2022

Towards experimental classical verification of quantum computation

With today's quantum processors venturing into regimes beyond the capabilities of classical devices [1-3], we face the challenge to verify that these devices perform as intended, even when we cannot check their results on classical computers [4,5]. In a recent breakthrough in computer science [6-8], a protocol was developed that allows the verification of the output of a computation performed by an untrusted quantum device based only on classical resources. Here, we follow these ideas, and demonstrate in a first, proof-of-principle experiment a verification protocol using only classical means on a small trapped-ion quantum processor. We contrast this to verification protocols, which require trust and detailed hardware knowledge, as in gate-level benchmarking [9], or additional quantum resources in case we do not have access to or trust in the device to be tested [5]. While our experimental demonstration uses a simplified version [10] of Mahadev's protocol [6] we demonstrate the necessary steps for verifying fully untrusted devices. A scaled-up version of our protocol will allow for classical verification, requiring no hardware access or detailed knowledge of the tested device. Its security relies on post-quantum secure trapdoor functions within an interactive proof [11]. The conceptually straightforward, but technologically challenging scaled-up version of the interactive proofs, considered here, can be used for a variety of additional tasks such as verifying quantum advantage [8], generating [12] and certifying quantum randomness [7], or composable remote state preparation [13].

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arXiv2021

Characterizing quantum instruments: from non-demolition measurements to quantum error correction

In quantum information processing quantum operations are often processed alongside measurements which result in classical data. Due to the information gain of classical measurement outputs non-unitary dynamical processes can take place on the system, for which common quantum channel descriptions fail to describe the time evolution. Quantum measurements are correctly treated by means of so-called quantum instruments capturing both classical outputs and post-measurement quantum states. Here we present a general recipe to characterize quantum instruments alongside its experimental implementation and analysis. Thereby, the full dynamics of a quantum instrument can be captured, exhibiting details of the quantum dynamics that would be overlooked with common tomography techniques. For illustration, we apply our characterization technique to a quantum instrument used for the detection of qubit loss and leakage, which was recently implemented as a building block in a quantum error correction (QEC) experiment (Nature 585, 207-210 (2020)). Our analysis reveals unexpected and in-depth information about the failure modes of the implementation of the quantum instrument. We then numerically study the implications of these experimental failure modes on QEC performance, when the instrument is employed as a building block in QEC protocols on a logical qubit. Our results highlight the importance of careful characterization and modelling of failure modes in quantum instruments, as compared to simplistic hardware-agnostic phenomenological noise models, which fail to predict the undesired behavior of faulty quantum instruments. The presented methods and results are directly applicable to generic quantum instruments.

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arXiv2021

A universal qudit quantum processor with trapped ions

Today's quantum computers operate with a binary encoding that is the quantum analog of classical bits. Yet, the underlying quantum hardware consists of information carriers that are not necessarily binary, but typically exhibit a rich multilevel structure, which is artificially restricted to two dimensions. A wide range of applications from quantum chemistry to quantum simulation, on the other hand, would benefit from access to higher-dimensional Hilbert spaces, which conventional quantum computers can only emulate. Here we demonstrate a universal qudit quantum processor using trapped ions with a local Hilbert space dimension of up to 7. With a performance similar to qubit quantum processors, this approach enables native simulation of high-dimensional quantum systems, as well as more efficient implementation of qubit-based algorithms.

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arXiv2020

Entangling logical qubits with lattice surgery

Future quantum computers will require quantum error correction for faithful operation. The correction capabilities come with an overhead for performing fault-tolerant logical operations on the encoded qubits. One of the most resource efficient ways to implement logical operations is lattice surgery, where groups of physical qubits, arranged on lattices, can be merged and split to realize entangling gates and teleport logical information. Here, we report on the experimental realization of lattice surgery between two topologically encoded qubits in a 10-qubit ion trap quantum information processor. In particular, we demonstrate entanglement between two logical qubits and we implement logical state teleportation.

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arXiv2020

Deterministic correction of qubit loss

The loss of qubits - the elementary carriers of quantum information - poses one of the fundamental obstacles towards large-scale and fault-tolerant quantum information processors. In this work, we experimentally demonstrate a complete toolbox and the implementation of a full cycle of qubit loss detection and correction on a minimal instance of a topological surface code. This includes a quantum non-demolition measurement of a qubit loss event that conditionally triggers a restoration procedure, mapping the logical qubit onto a new encoding on the remaining qubits. The demonstrated methods, implemented here in a trapped-ion quantum processor, are applicable to other quantum computing architectures and codes, including leading 2D and 3D topological quantum error correcting codes. These tools complement previously demonstrated techniques to correct computational errors, and in combination constitute essential building blocks for complete and scalable quantum error correction.

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arXiv2019

Assisted Macroscopic Quantumness

It is commonly expected that quantum theory is universal, in that it describes the world at all scales. Yet, quantum effects at the macroscopic scale continue to elude our experimental observation. This fact is commonly attributed to decoherence processes affecting systems of sufficiently large number of constituent subsystems leading to an effective macro-scale beyond which a quantum description of the whole system becomes superfluous. Here, we show both theoretically and experimentally that the existence of such a scale is unjustifiable from an information-theoretic perspective. We introduce a variant of the Wigner's friend experiment in which a multiparticle quantum system is observed by the friend. The friend undergoes rapid decoherence through her interactions with the environment. In the usual version of this thought experiment, decoherence removes the need for Wigner to treat her as a quantum system. However, for our variant we prove theoretically and observe experimentally that there exist partitions of the subsystems in which the friend is entangled with one of the particles in assistance with the other particle, as observed by Wigner. Importantly, we show that the friend is indispensable for the entanglement to be observed. Hence Wigner is compelled to treat the friend as part of a larger quantum system. By analyzing our scenario in the context of a quantum key distribution protocol, we show that a semi-classical description of the experiment is suboptimal for security analysis, highlighting the significance of the quantum description of the friend.

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arXiv2019

Experimental test of local observer-independence

The scientific method relies on facts, established through repeated measurements and agreed upon universally, independently of who observed them. In quantum mechanics, the objectivity of observations is not so clear, most dramatically exposed in Eugene Wigner's eponymous thought experiment where two observers can experience seemingly different realities. The question whether these realities can be reconciled in an observer-independent way has long remained inaccessible to empirical investigation, until recent no-go-theorems constructed an extended Wigner's friend scenario with four observers that allows us to put it to the test. In a state-of-the-art 6-photon experiment, we realise this extended Wigner's friend scenario, experimentally violating the associated Bell-type inequality by 5 standard deviations. If one holds fast to the assumptions of locality and free-choice, this result implies that quantum theory should be interpreted in an observer-dependent way.

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arXiv2019

Measurement Device Independent Verification of Quantum Channels

The capability to reliably transmit and store quantum information is an essential building block for future quantum networks and processors. Gauging the ability of a communication link or quantum memory to preserve quantum correlations is therefore vital for their technological application. Here, we experimentally demonstrate a measurement-device-independent protocol for certifying that an unknown channel acts as an entanglement-preserving channel. Our results show that, even under realistic experimental conditions, including imperfect single-photon sources and the various kinds of noise---in the channel or in detection---where other verification means would fail or become inefficient, the present verification protocol is still capable of affirming the quantum behaviour in a faithful manner without requiring any trust on the measurement device.

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