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M. Ringbauer, M. Hinsche, T. Feldker, P. K. Faehrmann, J. Bermejo-Vega, C. Edmunds, L. Postler, R. Stricker, C. Marciniak, M. Meth, I. Pogorelov, R. Blatt, P. Schindler, J. Eisert, T. Monz, D. Hangleiter Verifiable measurement-based quantum random sampling with trapped ions,
Nat. Commun. 16 106 (2025-12-12),
http://dx.doi.org/10.1038/s41467-024-55342-3 doi:10.1038/s41467-024-55342-3
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 × 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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M. Dietl, M. Valentini, F. Anmasser, A. Zesar, S. Auchter, M. van Mourik, T. Monz, R. Blatt, C. Rössler, P. Schindler Test and Characterization of Multilayer Ion Traps on Fused Silica,
Advanced Quantum Technologies (2025-10-06),
Ion traps are a promising architecture to host a future quantum computer. Several challenges, such as signal-routing, power dissipation, and fabrication quality, need to be overcome to scale ion trap devices to hundreds of ions. Currently, ion traps are often fabricated on silicon substrates which result in high power dissipation. Substrates that lead to lower power dissipation are preferred. In this work, a multi-metal layer ion trap is presented on a fused silica substrate that is fabricated and tested in an industrial facility. Its design and material-stack are tailored to minimize power dissipation. Furthermore, the integrated temperature sensors are characterized and functionality down to 10 K is verified. Moreover, an automated wafer test is demonstrated to validate each trap chip prior to its integration into experimental setups. Subsequently, electric field noise and electric stray fields are characterized using a single trapped-ion as a probe, showing an improvement in trap performance over similar trap designs realized on silicon substrates.
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T. Faorlin, B. Yadin, G. Araneda, S. Nimmrichter, Y. Weiser, L. Panzl, T. Lafenthaler, R. Blatt, T. Monz, G. Cerchiari Controlling the spontaneous emission and entanglement of quantum scatterers via modulated reflection of their emitted photons,
New J. Phys. (2025-06-19),
We propose an experimental setup for manipulating the spontaneous emission (SE) of quantum scatterers, based on a spatial light modulator. We discuss this idea in the case of trapped barium ions as quantum emitters. A first novelty is the potential to entangle more than two ions through a single photon detection event with programmable adaptive optics. Additionally, this setup can be used to control the SE of single-photons emitted collectively by spatially distinguished quantum emitters.
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C. Edmunds, E. Rico, I. Arrazola, G. Brennen, M. Meth, R. Blatt, M. Ringbauer Symmetry-Protected Topological Haldane Phase on a Qudit Quantum Processor,
PRX Quantum (2025-06-11),
Symmetry-protected topological phases have fundamentally changed our understanding of quantum matter. An archetypal example of such a quantum phase of matter is the Haldane phase, containing the spin-1 Heisenberg chain. The intrinsic quantum nature of such phases, however, often makes it challenging to study them using classical means. Here, we use trapped-ion qutrits to natively engineer spin-1 chains within the Haldane phase. Using a scalable deterministic procedure to prepare the Affleck-Kennedy-Lieb-Tasaki (AKLT) state within the Haldane phase, we study the topological features of this system on a qudit quantum processor. Notably, we verify the long-range string order of the state, despite its short-range correlations, and observe spin fractionalization of the physical spin-1 particles into effective qubits at the chain edges, a defining feature of this system. The native realization of Haldane physics on a qudit quantum processor and the scalable preparation procedures open the door to the efficient exploration of a wide range of systems beyond spin-1/2.
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M. Meth, J. Haase, J. Zhang, C. Edmunds, L. Postler, A. Steiner, A. Jena, L. Dellantonio, R. Blatt, P. Zoller, T. Monz, P. Schindler, C. A. Muschik, M. Ringbauer Simulating 2D lattice gauge theories on a qudit quantum computer,
Nature Phys. 21 576 (2025-03-25),
http://dx.doi.org/10.1038/s41567-025-02797-w doi:10.1038/s41567-025-02797-w
Particle physics describes the interplay of matter and forces through gauge theories. Yet, the intrinsic quantum nature of gauge theories makes important problems notoriously difficult for classical computational techniques. Quantum computers offer a promising way to overcome these roadblocks. We demonstrate two essential requirements on this path: first, we perform a quantum computation of the properties of the basic building block of two-dimensional lattice quantum electrodynamics, involving both gauge fields and matter. Second, we show how to refine the gauge-field discretization beyond its minimal representation, using a trapped-ion qudit quantum processor, where quantum information is encoded in several states per ion. Such qudits are ideally suited for describing gauge fields, which are naturally high dimensional, leading to reduced register size and circuit complexity. We prepare the ground state of the model using a variational quantum eigensolver and observe the effect of dynamical matter on quantized magnetic fields. By controlling the qudit dimension, we also show how to seamlessly observe the effect of different gauge-field truncations. Finally, we experimentally study the dynamics of pair creation and magnetic energy. Our results open the door for hardware-efficient quantum simulations of gauge theories with qudits in near-term quantum devices.
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Y. Weiser, T. Faorlin, L. Panzl, T. Lafenthaler, L. Dania, D. Bykov, T. Monz, R. Blatt, G. Cerchiari Backaction suppression for levitated dipolar scatterers,
Phys. Rev. A 111 13503 (2025-01-06),
URL
Levitated dipolar scatterers exhibit exceptional performance as optomechanical systems for observing quantum mechanics at the mesoscopic and atomic scales. These systems scatter photons in almost every direction, and, with generally limited light collection efficiency, only partial information about the state of the system can be extracted. In this article, we present a setup to enhance information extraction of optomechanical measurements by constraining light scattering to a specific spatial direction. The setup consists of a hollow hemispherical mirror that controls the light scattered by a dipolar scatterer at high scattering angles outside the hole's region. Control of light scattering at high angles can be used to suppress the corresponding optomechanical backaction, which results in focusing of the measurement information at low angles. This mirror is compatible with existing setups commonly employed in levitated optomechanics, including confocal lenses and optical resonators.
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T. Kraft, M. K. Joshi, W. LAM, T. Olsacher, F. Kranzl, J. Franke, L. K. Joshi, R. Blatt, A. Smerzi, D. S. França, B. Vermersch, B. Kraus, C. F. Roos, P. Zoller Bounded-Error Quantum Simulation via Hamiltonian and Lindbladian Learning,
(2025-11-28),
arXiv:2511.23392 arXiv:2511.23392
Analog Quantum Simulators offer a route to exploring strongly correlated many-body dynamics beyond classical computation, but their predictive power remains limited by the absence of quantitative error estimation. Establishing rigorous uncertainty bounds is essential for elevating such devices from qualitative demonstrations to quantitative scientific tools. Here we introduce a general framework for bounded-error quantum simulation, which provides predictions for many-body observables with experimentally quantifiable uncertainties. The approach combines Hamiltonian and Lindbladian Learning--a statistically rigorous inference of the coherent and dissipative generators governing the dynamics--with the propagation of their uncertainties into the simulated observables, yielding confidence bounds directly derived from experimental data. We demonstrate this framework on trapped-ion quantum simulators implementing long-range Ising interactions with up to 51 ions, and validate it where classical comparison is possible. We analyze error bounds on two levels. First, we learn an open-system model from experimental data collected in an initial time window of quench dynamics, simulate the corresponding master equation, and quantitatively verify consistency between theoretical predictions and measured dynamics at long times. Second, we establish error bounds directly from experimental measurements alone, without relying on classical simulation--crucial for entering regimes of quantum advantage. The learned models reproduce the experimental evolution within the predicted bounds, demonstrating quantitative reliability and internal consistency. Bounded-error quantum simulation provides a scalable foundation for trusted analog quantum computation, bridging the gap between experimental platforms and predictive many-body physics. The techniques presented here directly extend to digital quantum simulation.
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R. Brinster, P. Tirler, S. Khandelwal, M. Meth, H. Kampermann, D. Bruss, R. Blatt, M. Ringbauer, A. Tavakoli, N. Wyderka Robust certification of non-projective measurements: theory and experiment,
(2025-11-06),
arXiv:2511.04446 arXiv:2511.04446
Determining the conditions under which positive operator-valued measures (POVMs), the most general class of quantum measurements, outperform projective measurements remains a challenging and largely unresolved problem. Of particular interest are projectively simulable POVMs, which can be realized through probabilistic mixtures of projective measurements, and therefore offer no advantage over projective schemes. Characterizing the boundary between simulable and non-simulable POVMs is, however, a difficult task, and existing tools either fail to scale efficiently, provide limited experimental feasibility or work only for specific POVMs. Here, we introduce and demonstrate a general method to certify non-simulability of a POVM by introducing a hierarchy of semidefinite programs. It provides upper bounds on the non-simulability measure of critical visibility of arbitrary POVMs which are tight in many cases and outperform previously known criteria. We experimentally certify the non-simulability of two- and three-dimensional POVMs using a trapped-ion qudit quantum processor by constructing non-simulability witnesses and introduce a modification of our framework that makes them robust against state preparation errors. Finally, we extend our results to the setting where an additional ancilla system is available.
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F. Kranzl, A. Rospars, J. Franke, M. K. Joshi, R. Blatt, C. F. Roos Spin-Locking Spectroscopy of Harmonic Motion,
(2025-10-13),
arXiv:2510.08732 arXiv:2510.08732
Characterization of noise of a quantum harmonic oscillator is important for many experimental platforms. We experimentally demonstrate motional spin-locking spectroscopy, a method that allows us to directly measure the motional noise spectrum of a quantum harmonic oscillator. We measure motional noise of a single trapped ion in a frequency range from 200 Hz to 5 kHz with a power spectral density that resolves noise over two orders of magnitude. Coherent modulations in the oscillation frequency of the oscillator can be probed with a relative frequency sensitivity at the level.
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T. Faorlin, Y. Weiser, L. Panzl, T. Lafenthaler, R. Blatt, T. Monz, G. Cerchiari, B. Yadin, S. Nimmrichter, G. Araneda Controlling the spontaneous emission of trapped ions,
(2025-01-16),
arXiv:2501.08627 arXiv:2501.08627
We propose an experimental setup for manipulating the spontaneous emission of trapped ions,
based on a spatial light modulator. Anticipated novelties include the potential to entangle more than
two ions through a single photon detection event and control the visibility for spatially distinguishable
emitters. The setup can be adapted to most of the existing ion traps commonly used in quantum
technology.
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M. K. Joshi, M. Guevara-Bertsch, F. Kranzl, R. Blatt, C. F. Roos Characterization of ion-trap-induced ac magnetic fields,
Phys. Rev. A 110 63101 (2024-12-01),
http://dx.doi.org/10.1103/PhysRevA.110.063101 doi:10.1103/PhysRevA.110.063101
The oscillating magnetic field produced by unbalanced currents in radio-frequency ion traps induces transition frequency shifts and sideband transitions that can be harmful to precision spectroscopy experiments. Here, we describe a methodology, based on two-photon spectroscopy, for determining both the strength and direction of rf-induced magnetic fields without modifying any DC magnetic bias field or changing any trap RF power. The technique is readily applicable to any trapped-ion experiment featuring narrow linewidth transitions.
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L. Postler, F. Butt, I. Pogorelov, C. Marciniak, S. Heußen, R. Blatt, P. Schindler, M. Rispler, M. Müller, T. Monz Demonstration of fault-tolerant Steane quantum error correction,
PRX Quantum 5 030326-19 (2024-08-07),
http://dx.doi.org/10.1103/PRXQuantum.5.030326 doi:10.1103/PRXQuantum.5.030326
Encoding information redundantly using quantum error-correcting (QEC) codes allows one to overcome the inherent sensitivity to noise in quantum computers to ultimately achieve large-scale quantum computation. The Steane QEC method involves preparing an auxiliary logical qubit of the same QEC code used for the data<br />
register. The data and auxiliary registers are then coupled with a logical CNOT gate, enabling a measurement of the auxiliary register to reveal the error syndrome. This study presents the implementation of multiple rounds<br />
of fault-tolerant Steane QEC on a trapped-ion quantum computer. Various QEC codes are employed, and the<br />
results are compared to a previous experimental approach utilizing flag qubits. Our experimental findings show improved logical fidelities for Steane QEC. This establishes experimental Steane QEC as a competitive paradigm for fault-tolerant quantum computing.
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L. K. Joshi, J. Franke, A. Rath, F. Ares, S. Murciano, F. Kranzl, R. Blatt, P. Zoller, B. Vermersch, P. Calabrese, C. F. Roos, M. K. Joshi Observing the quantum Mpemba effect in quantum simulations,
PRL 133 10402 (2024-07-01),
http://dx.doi.org/10.1103/PhysRevLett.133.010402 doi:10.1103/PhysRevLett.133.010402
The non-equilibrium physics of many-body quantum systems harbors various unconventional phenomena. In this study, we experimentally investigate one of the most puzzling of these phenomena— the quantum Mpemba effect, where a tilted ferromagnet restores its symmetry more rapidly when it is farther from the symmetric state compared to when it is closer. We present the first experimental evidence of the occurrence of this effect in a trapped-ion quantum simulator. The symmetry breaking and restoration are monitored through entanglement asymmetry, probed via randomized measurements, and post-processed using the classical shadows technique. Our findings are further substantiated by measuring the Frobenius distance between the experimental state and the stationary thermal symmetric theoretical state, offering direct evidence of subsystem thermalization.
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H. Hainzer, D. Kiesenhofer, T. Ollikainen, M. Bock, F. Kranzl, M. K. Joshi, G. Yoeli, R. Blatt, T. Gefen, C. F. Roos Correlation Spectroscopy with Multiqubit-Enhanced Phase Estimation,
Phys. Rev. X 14 24 (2024-02-29),
http://dx.doi.org/10.1103/PhysRevX.14.011033 doi:10.1103/PhysRevX.14.011033
Ramsey interferometry is a widely used tool for precisely measuring transition frequencies between two energy levels of a quantum system, with applications in time keeping, precision spectroscopy, quantum optics, and quantum information. Often, the coherence time of the quantum system surpasses the one of the<br />
oscillator probing the system, thereby limiting the interrogation time and associated spectral resolution.<br />
Correlation spectroscopy overcomes this limitation by probing two quantum systems with the same noisy<br />
oscillator for a measurement of their transition frequency difference; this technique has enabled very<br />
precise comparisons of atomic clocks. Here, we extend correlation spectroscopy to the case of multiple<br />
quantum systems undergoing strong correlated dephasing. We model Ramsey correlation spectroscopy<br />
with N particles as a multiparameter phase estimation problem and demonstrate that multiparticle correlations can assist in reducing the measurement uncertainties even in the absence of entanglement. We<br />
derive precision limits and optimal sensing techniques for this problem and compare the performance of<br />
probe states and measurement with and without entanglement. Using one- and two-dimensional ion<br />
Coulomb crystals with up to 91 qubits, we experimentally demonstrate the advantage of measuring multiparticle correlations for reducing phase uncertainties and apply correlation spectroscopy to measure ion-ion distances, transition frequency shifts, laser-ion detunings, and path-length fluctuations. Our method can be straightforwardly implemented in experimental setups with globally coherent qubit control and<br />
qubit-resolved single-shot readout and is, thus, applicable to other physical systems such as neutral atoms in tweezer arrays.
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R. Stricker, J. Carrasco, M. Ringbauer, L. Postler, M. Meth, C. Edmunds, P. Schindler, R. Blatt, P. Zoller, B. Kraus, T. Monz Towards experimental classical verification of quantum computation,
Quantum Sci. Technol. 9 (2024-02-26),
http://dx.doi.org/10.1088/2058-9565/ad2986 doi:10.1088/2058-9565/ad2986
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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D. Miller, K. Levi, L. Postler, A. Steiner, L. Bittel, G. A. White, Y. Tang, E. J. Kuehnke, A. A. Mele, S. Khatri, L. Leone, J. Carrasco, C. Marciniak, I. Pogorelov, M. Guevara-Bertsch, R. Freund, R. Blatt, P. Schindler, T. Monz, M. Ringbauer, J. Eisert Experimental measurement and a physical interpretation of quantum shadow enumerators,
(2024-08-29),
http://dx.doi.org/10.48550/arXiv.2408.16914 doi:10.48550/arXiv.2408.16914
Throughout its history, the theory of quantum error correction has heavily benefited from translating classical concepts into the quantum setting. In particular, classical notions of weight enumerators, which relate to the performance of an error-correcting code, and MacWilliams' identity, which helps to compute enumerators, have been generalized to the quantum case. In this work, we establish a distinct relationship between the theoretical machinery of quantum weight enumerators and a seemingly unrelated physics experiment: we prove that Rains' quantum shadow enumerators - a powerful mathematical tool - arise as probabilities of observing fixed numbers of triplets in a Bell sampling experiment. This insight allows us to develop here a rigorous framework for the direct measurement of quantum weight enumerators, thus enabling experimental and theoretical studies of the entanglement structure of any quantum error-correcting code or state under investigation. On top of that, we derive concrete sample complexity bounds and physically-motivated robustness guarantees against unavoidable experimental imperfections. Finally, we experimentally demonstrate the possibility of directly measuring weight enumerators on a trapped-ion quantum computer. Our experimental findings are in good agreement with theoretical predictions and illuminate how entanglement theory and quantum error correction can cross-fertilize each other once Bell sampling experiments are combined with the theoretical machinery of quantum weight enumerators.
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C. Edmunds, E. Rico, I. Arrazola, G. Brennen, M. Meth, R. Blatt, M. Ringbauer Constructing the spin-1 Haldane phase on a qudit quantum processor,
(2024-08-08),
http://dx.doi.org/10.48550/arXiv.2408.04702 doi:10.48550/arXiv.2408.04702
Symmetry-protected topological phases have fundamentally changed our understanding of quantum matter. An archetypal example of such a quantum phase of matter is the Haldane phase, containing the spin-1 Heisenberg chain. The intrinsic quantum nature of such phases, however, often makes it challenging to study them using classical means. Here, we use trapped-ion qutrits to natively engineer spin-1 chains within the Haldane phase. Using a scalable, deterministic procedure to prepare the Affleck-Kennedy-Lieb-Tasaki (AKLT) state within the Haldane phase, we study the topological features of this system on a qudit quantum processor. Notably, we verify the long-range string order of the state, despite its short-range correlations, and observe spin fractionalization of the physical spin-1 particles into effective qubits at the chain edges, a defining feature of this system. The native realization of Haldane physics on a qudit quantum processor and the scalable preparation procedures open the door to the efficient exploration of a wide range of systems beyond spin-1/2.
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M. Valentini, M. van Mourik, F. Butt, J. Wahl, M. Dietl, M. Pfeifer, F. Anmasser, Y. Colombe, C. Rössler, P. Holz, R. Blatt, M. Müller, T. Monz, P. Schindler Demonstration of two-dimensional connectivity for a scalable error-corrected ion-trap quantum processor architecture,
(2024-06-04),
arXiv:2406.02406 arXiv:2406.02406
A major hurdle for building a large-scale quantum computer is to scale up the number of qubits while maintaining connectivity between them. In trapped-ion devices, this connectivity can be provided by physically moving subregisters consisting of a few ions across the processor. The topology of the connectivity is given by the layout of the ion trap where one-dimensional and two-dimensional arrangements are possible. Here, we focus on an architecture based on a rectangular two-dimensional lattice, where each lattice site contains a subregister with a linear string of ions. We refer to this architecture as the Quantum Spring Array (QSA). Subregisters placed in neighboring lattice sites can be coupled by bringing the respective ion strings close to each other while avoiding merging them into a single trapping potential. Control of the separation of subregisters along one axis of the lattice, known as the axial direction, uses quasi-static voltages, while the second axis, the radial, requires control of radio frequency signals. In this work, we investigate key elements of the 2D lattice quantum computation architecture along both axes: We show that the coupling rate between neighboring lattice sites increases with the number of ions per site and the motion of the coupled system can be resilient to noise. The coherence of the coupling is assessed, and an entangled state of qubits in separate trapping regions along the radial axis is demonstrated. Moreover, we demonstrate control over radio frequency signals to adjust radial separation between strings, and thus tune their coupling rate. We further map the 2D lattice architecture to code primitives for fault-tolerant quantum error correction, providing a step towards a quantum processor architecture that is optimized for large-scale fault-tolerant operation.
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Y. Weiser, T. Faorlin, L. Panzl, T. Lafenthaler, L. Dania, D. S. Bykov, T. Monz, R. Blatt, G. Cerchiari Back action suppression for levitated dipolar scatterers,
(2024-02-07),
arXiv:2402.04802 arXiv:2402.04802
Levitated dipolar scatterers exhibit exceptional performance as optomechanical systems for observing quantum mechanics at the mesoscopic scale. However, their tendency to scatter light in almost any direction poses experimental challenges, in particular limiting light collection efficiencies and, consequently, the information extractable from the system. In this article, we present a setup designed to enhance the information gleaned from optomechanical measurements by constraining the back action to a specific spatial direction. This approach facilitates achieving Heisenberg-limited detection at any given numerical aperture. The setup consists of a hollow hemispherical mirror that controls the light scattered by the dipolar emitter, particularly at high scattering angles, thereby focusing the obtained information. This mirror is compatible with existing setups commonly employed in levitated optomechanics, including confocal lenses and optical resonators.
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M. K. Kurmapu, V. V. Tiunova, E. S. Tiunov, M. Ringbauer, C. Maier, R. Blatt, T. Monz, A. K. Fedorov, A. I. Lvovsky Reconstructing Complex States of a 20-Qubit Quantum Simulator,
PRX Quantum 4 40345 (2023-12-20),
http://dx.doi.org/10.1103/PRXQuantum.4.040345 doi:10.1103/PRXQuantum.4.040345
A prerequisite to the successful development of quantum computers and simulators is precise understanding of the physical processes occurring therein, which can be achieved by measuring the quantum states that 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 multiqubit 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 feed-forward neural networks with autoregressive architecture. Our results pave the way toward efficient experimental characterization of complex states produced by the quench dynamics of many-body quantum systems.
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M. K. Joshi, C. Kokail, R. van Bijnen, F. Kranzl, T. Zache, R. Blatt, C. F. Roos, P. Zoller Exploring Large-Scale Entanglement in Quantum Simulation,
Nature 624 539 (2023-11-29),
http://dx.doi.org/10.1038/s41586-023-06768-0 doi:10.1038/s41586-023-06768-0
Entanglement is a distinguishing feature of quantum many-body systems, and uncovering the entanglement structure for large particle numbers in quantum simulation experiments is a fundamental challenge in quantum information science. Here we perform experimental investigations of entanglement based on the entanglement Hamiltonian, as an effective description of the reduced density operator for large subsystems. We prepare ground and excited states of a 1D XXZ Heisenberg chain on a 51-ion programmable quantum simulator and perform sample-efficient `learning' of the entanglement Hamiltonian for subsystems of up to 20 lattice sites. Our experiments provide compelling evidence for a local structure of the entanglement Hamiltonian. This observation marks the first instance of confirming the fundamental predictions of quantum field theory by Bisognano and Wichmann, adapted to lattice models that represent correlated quantum matter. The reduced state takes the form of a Gibbs ensemble, with a spatially-varying temperature profile as a signature of entanglement. Our results also show the transition from area to volume-law scaling of Von Neumann entanglement entropies from ground to excited states. As we venture towards achieving quantum advantage, we anticipate that our findings and methods have wide-ranging applicability to revealing and understanding entanglement in many-body problems with local interactions including higher spatial dimensions.
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F. Kranzl, S. Birnkammer, M. K. Joshi, A. Bastianello, R. Blatt, M. Knap, C. F. Roos Observation of magnon bound states in the long-range, anisotropic Heisenberg model,
Phys. Rev. X 13 031017-12 (2023-08-11),
http://dx.doi.org/10.1103/PhysRevX.13.031017 doi:10.1103/PhysRevX.13.031017
Over the recent years coherent, time-periodic modulation has been established as a versatile tool for realizing novel Hamiltonians. Using this approach, known as Floquet engineering, we experimentally realize a long-ranged, anisotropic Heisenberg model with tunable interactions in a trapped ion quantum simulator. We demonstrate that the spectrum of the model contains not only single magnon excitations but also composite magnon bound states. For the long-range interactions with the experimentally realized power-law exponent, the group velocity of magnons is unbounded. Nonetheless, for sufficiently strong interactions we observe bound states of these unconventional magnons which possess a non-diverging group velocity. By measuring the configurational mutual information between two disjoint intervals, we demonstrate the implications of the bound state formation on the entanglement dynamics of the system. Our observations provide key insights into the peculiar role of composite excitations in the non-equilibrium dynamics of quantum many-body systems.
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M. Ringbauer, M. Hinsche, T. Feldker, P. K. Faehrmann, J. Bermejo-Vega, C. Edmunds, L. Postler, R. Stricker, C. Marciniak, M. Meth, I. Pogorelov, R. Blatt, P. Schindler, J. Eisert, T. Monz, D. Hangleiter Verifiable measurement-based quantum random sampling with trapped ions,
Nat. Commun. 16 9 (2023-07-26),
arXiv:2307.14424 arXiv:2307.14424
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 random cluster states, which are at the heart of measurement-based computing, up to a size of 4 x 4 qubits. Moreover, 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
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F. Kranzl, A. Lasek, M. K. Joshi, A. Kalev, R. Blatt, C. F. Roos, N. Yunger Halpern Experimental observation of thermalization with noncommuting charges,
PRX Quantum 4 20318 (2023-04-28),
http://dx.doi.org/10.1103/PRXQuantum.4.020318 doi:10.1103/PRXQuantum.4.020318
Quantum simulators have recently enabled experimental observations of the internal thermalization of quantum many-body systems. Often, the global energy and particle number are conserved and the system is prepared with a well-defined particle number—in a microcanonical subspace. However, quantum evolution can also conserve quantities, or charges, that fail to commute with each other. Noncommuting charges have recently emerged as a subfield at the intersection of quantum thermodynamics and quantum information. Until now, this subfield has remained theoretical. We initiate the experimental testing of its predictions, with a trapped-ion simulator. We prepare 6–21 spins in an approximate microcanonical subspace, a generalization of the microcanonical subspace for accommodating noncommuting charges, which cannot necessarily have well-defined nontrivial values simultaneously. We simulate a Heisenberg evolution using laser-induced entangling interactions and collective spin rotations. The noncommuting charges are the three spin components. We find that small subsystems equilibrate to near a recently predicted non-Abelian thermal state. This work bridges quantum many-body simulators to the quantum thermodynamics of noncommuting charges, the predictions of which can now be tested.
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P. Hrmo, B. Wilhelm, L. Gerster, M. van Mourik, M. Huber, R. Blatt, P. Schindler, T. Monz, M. Ringbauer Native qudit entanglement in a trapped ion quantum processor,
Nat. Commun. 14 doi.org/10.1038/s41467-023-37375-223-37375-2 (2023-04-19),
URL
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 up to dimension 5 in a trapped-ion system. 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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J. Franke, S. M. Muleady, C. R. Kaubrügger, F. Kranzl, R. Blatt, A. M. Rey, M. K. Joshi, C. F. Roos Quantum-enhanced sensing on optical transitions through finite-range interactions,
Nature 621 740 (2023-03-27),
http://dx.doi.org/10.1038/s41586-023-06472-z doi:10.1038/s41586-023-06472-z
The control over quantum states in atomic systems has led to the most precise optical atomic clocks to date. Their sensitivity is currently bounded by the standard quantum limit, a fundamental floor set by quantum mechanics for uncorrelated particles, which can nevertheless be overcome when operated with entangled particles. Yet demonstrating a quantum advantage in real world sensors is extremely challenging and remains to be achieved aside from two remarkable examples, LIGO and more recently HAYSTAC. Here we illustrate a pathway for harnessing scalable entanglement in an optical transition using 1D chains of up to 51 ions with state-dependent interactions that decay as a power-law function of the ion separation. We show our sensor can be made to behave as a one-axis-twisting (OAT) model, an iconic fully connected model known to generate scalable squeezing. The collective nature of the state manifests itself in the preservation of the total transverse magnetization, the reduced growth of finite momentum spin-wave excitations, the generation of spin squeezing comparable to OAT (a Wineland parameter of −3.9±0.3 dB for only N = 12 ions) and the development of non-Gaussian states in the form of atomic multi-headed cat states in the Q-distribution. The simplicity of our protocol enables scalability to large arrays with minimal overhead, opening the door to advances in timekeeping as well as new methods for preserving coherence in quantum simulation and computation. We demonstrate this in a Ramsey-type interferometer, where we reduce the measurement uncertainty by −3.2±0.5 dB below the standard quantum limit for N = 51 ions.
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L. O. Conlon, Tobias Vogl, C. Marciniak, Ivan Pogorelov, Simun K. Yung, Falk Eilenberger, D. W. Berry, F. S. Santana, Rainer Blatt, Thomas Monz, Ping Koy Lam, S. M. Assad Approaching optimal entangling collective measurements on quantum computing platforms,
Nature Phys. 1-7 (2023-01-12),
http://dx.doi.org/10.1038/s41567-022-01875-7 doi:10.1038/s41567-022-01875-7
Entanglement is a fundamental feature of quantum mechanics and holds great promise for enhancing metrology and communications. Much of the focus of quantum metrology so far has been on generating highly entangled quantum states that offer better sensitivity, per resource, than what can be achieved classically. However, to reach the ultimate limits in multi-parameter quantum metrology and quantum information processing tasks, collective measurements, which generate entanglement between multiple copies of the quantum state, are necessary. Here, we experimentally demonstrate theoretically optimal single- and two-copy collective measurements for simultaneously estimating two non-commuting qubit rotations. This allows us to implement quantum-enhanced sensing, for which the metrological gain persists for high levels of decoherence, and to draw fundamental insights about the interpretation of the uncertainty principle. We implement our optimal measurements on superconducting, trapped-ion and photonic systems, providing an indication of how future quantum-enhanced sensing networks may look.