arXiv subjects

Laurin E. Fischer

Publications and source records attributed to Laurin E. Fischer.

11 recordsLinked to original sources

arXiv2026

Spacetime mitigation of logical errors

Error detection can suppress noise at a lower sampling cost than probabilistic error cancellation (PEC), but leaves residual logical errors. We combine the two approaches to mitigate these errors while lowering the cost of PEC. We introduce a spacetime Pauli-Lindblad representation and use it to construct the post-selected logical noise perturbatively from physical noise and syndrome information. Individually undetected faults contribute at first order, while detected faults with canceling syndromes generate higher-order terms coupling distinct spacetime locations. To reconcile the nonlinearity of post-selection with the linearity of PEC, we formulate the combined protocol in terms of unnormalized post-selected maps, with normalization performed only after averaging. On the ibm_aachen superconducting quantum processor, Clifford experiments validate the post-selected noise model and its perturbative scaling. We then demonstrate error detection with first-order PEC for transverse-field Ising dynamics using 22 data and 27 check qubits. The combined protocol recovers the mean magnetization within statistical uncertainty through six Trotter steps and reduces the inferred sampling overhead by up to a factor of 63 relative to PEC without post-selection.

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arXiv2026

Mitigating errors in state preparation and measurement with noncomputational states

Error mitigation has enabled quantum computing applications with over one hundred qubits and deep circuits. Many error mitigation methods are noise-aware, relying on a faithful characterization of the noise channels of the hardware. However, fundamental limitations lead to unlearnable degrees of freedom of the underlying noise models when considering qubits. Here, we show how to leverage non-computational states as an additional resource to learn state-preparation errors in superconducting qubits. This allows one to fully constrain the noise models. We can thus independently and accurately mitigate state-preparation errors, gate errors and measurement errors. Our proposed method is also applicable to dynamic circuits with mid-circuit measurements. This work opens the door to improved error mitigation for measurements, both at the end of the circuit and mid-circuit.

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arXiv2026

Disambiguating Pauli noise in quantum computers

To successfully perform quantum computations, it is often necessary to first accurately characterize the noise in the underlying hardware. However, it is well known that fundamental limitations prevent the unique identification of the noise. This raises the question of whether these limitations impact the ability to predict noisy dynamics and mitigate errors. Here, we show, both theoretically and experimentally, that when learnable parameters are self-consistently characterized, the unlearnable (gauge) degrees of freedom do not impact predictions of noisy dynamics or error mitigation. We use the recently introduced framework of gate set Pauli noise learning to efficiently and self-consistently characterize and mitigate noise of a complete gate set, including state preparation, measurements, single-qubit gates and multi-qubit entangling Clifford gates. We validate our approach through experiments with up to 92 qubits and show that while the gauge choice does not affect error-mitigated observable values, optimizing it reduces sampling overhead. Our findings address an outstanding issue involving the ambiguities in characterizing and mitigating quantum noise.

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arXiv2026

Enabling large-scale digital quantum simulations with superconducting qubits

Quantum computing promises to revolutionize several scientific and technological domains through fundamentally new ways of processing information. Among its most compelling applications is digital quantum simulation, where quantum computers are used to replicate the behavior of other quantum systems. This could enable the study of problems that are otherwise intractable on classical computers, transforming fields such as quantum chemistry, condensed matter physics, and materials science. Despite this potential, realizations of practical quantum advantage for relevant problems are hindered by imperfections of current devices. This also affects quantum hardware based on superconducting circuits which is among the most advanced and scalable platforms. The envisaged long-term solution of fault-tolerant quantum computers that correct their own errors remains out of reach mainly due to the associated qubit number overhead. As a result, the field has developed strategies that combine quantum and classical resources, exploit hardware-native operations, and employ error mitigation techniques to extract meaningful results from noisy data. This doctoral thesis contributes to this broader effort by exploring methods for advancing quantum simulation across the full computational stack, including hardware-level innovations, refined techniques for noise modeling and error mitigation, and algorithmic improvements enabled by efficient measurement processing.

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arXiv2025

Large-scale implementation of quantum subspace expansion with classical shadows

Quantum subspace expansion (QSE) offers promising avenues to perform spectral calculations on quantum processors but comes with a large measurement overhead. Informationally complete (IC) measurements, such as classical shadows, were recently proposed to overcome this bottleneck. Here, we report the first large-scale implementation of QSE with IC measurements. In particular, we probe the quantum phase transition of a spin model with three-body interactions, for which we observe accurate ground state energy recovery and mitigation of local order parameters across system sizes of up to 80 qubits. We achieve this by reformulating QSE as a constrained optimization problem, obtaining rigorous statistical error estimates and avoiding numerical ill-conditioning. With over $3 \times 10^4$ measurement basis randomizations per circuit and the evaluation of $O(10^{14})$ Pauli traces, this represents one of the most significant experimental realizations of classical shadows to date.

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arXiv2024

Dynamical simulations of many-body quantum chaos on a quantum computer

Quantum circuits with local unitaries have emerged as a rich playground for the exploration of many-body quantum dynamics of discrete-time systems. While the intrinsic locality makes them particularly suited to run on current quantum processors, the task of verification at non-trivial scales is complicated for non-integrable systems. Here, we study a special class of maximally chaotic circuits known as dual unitary circuits -- exhibiting unitarity in both space and time -- that are known to have exact analytical solutions for certain correlation functions. With advances in noise learning and the implementation of novel error mitigation methods, we show that a superconducting quantum processor with 91 qubits is able to accurately simulate these correlators. We then probe dynamics beyond exact verification, by perturbing the circuits away from the dual unitary point, and compare our results to classical approximations with tensor networks. These results cement error-mitigated digital quantum simulation on pre-fault-tolerant quantum processors as a trustworthy platform for the exploration and discovery of novel emergent quantum many-body phases.

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arXiv2024

Hardware-Tailored Diagonalization Circuits

A central building block of many quantum algorithms is the diagonalization of Pauli operators. Although it is always possible to construct a quantum circuit that simultaneously diagonalizes a given set of commuting Pauli operators, only resource-efficient circuits can be executed reliably on near-term quantum computers. Generic diagonalization circuits, in contrast, often lead to an unaffordable Swap gate overhead on quantum devices with limited hardware connectivity. A common alternative is to exclude two-qubit gates altogether. However, this comes at the severe cost of restricting the class of diagonalizable sets of Pauli operators to tensor product bases (TPBs). In this article, we introduce a theoretical framework for constructing hardware-tailored (HT) diagonalization circuits. Our framework establishes a systematic and highly flexible procedure for tailoring diagonalization circuits with ultra-low gate counts. We highlight promising use cases of our framework and - as a proof-of-principle application - we devise an efficient algorithm for grouping the Pauli operators of a given Hamiltonian into jointly-HT-diagonalizable sets. For several classes of Hamiltonians, we observe that our approach requires fewer measurements than conventional TPB approaches. Finally, we experimentally demonstrate that HT circuits can improve the efficiency of estimating expectation values with cloud-based quantum computers.

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arXiv2024

Dual frame optimization for informationally complete quantum measurements

Randomized measurement protocols such as classical shadows represent powerful resources for quantum technologies, with applications ranging from quantum state characterization and process tomography to machine learning and error mitigation. Recently, the notion of measurement dual frames, in which classical shadows are generalized to dual operators of POVM effects, resurfaced in the literature. This brought attention to additional degrees of freedom in the post-processing stage of randomized measurements that are often neglected by established techniques. In this work, we leverage dual frames to construct improved observable estimators from informationally complete measurement samples. We introduce novel classes of parametrized frame superoperators and optimization-free dual frames based on empirical frequencies, which offer advantages over their canonical counterparts while retaining computational efficiency. Remarkably, this comes at almost no quantum or classical cost, thus rendering dual frame optimization a valuable addition to the randomized measurement toolbox.

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arXiv2023

Pulse variational quantum eigensolver on cross-resonance based hardware

State-of-the-art noisy digital quantum computers can only execute short-depth quantum circuits. Variational algorithms are a promising route to unlock the potential of noisy quantum computers since the depth of the corresponding circuits can be kept well below hardware-imposed limits. Typically, the variational parameters correspond to virtual $R_Z$ gate angles, implemented by phase changes of calibrated pulses. By encoding the variational parameters directly as hardware pulse amplitudes and durations we succeed in further shortening the pulse schedule and overall circuit duration. This decreases the impact of qubit decoherence and gate noise. As a demonstration, we apply our pulse-based variational algorithm to the calculation of the ground state of different hydrogen-based molecules (H$_2$, H$_3$ and H$_4$) using IBM cross-resonance-based hardware. We observe a reduction in schedule duration of up to $5\times$ compared to CNOT-based Ansätze, while also reducing the measured energy. In particular, we observe a sizable improvement of the minimal energy configuration of H$_3$ compared to a CNOT-based variational form. Finally, we discuss possible future developments including error mitigation schemes and schedule optimizations, which will enable further improvements of our approach paving the way towards the simulation of larger systems on noisy quantum devices.

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arXiv2023

Universal qudit gate synthesis for transmons

Gate-based quantum computers typically encode and process information in two-dimensional units called qubits. Using $d$-dimensional qudits instead may offer intrinsic advantages, including more efficient circuit synthesis, problem-tailored encodings and embedded error correction. In this work, we design a superconducting qudit-based quantum processor wherein the logical space of transmon qubits is extended to higher-excited levels. We propose a universal gate set featuring a two-qudit cross-resonance entangling gate, for which we predict fidelities beyond $99\%$ in the $d=4$ case of ququarts with realistic experimental parameters. Furthermore, we present a decomposition routine that compiles general qudit unitaries into these elementary gates, requiring fewer entangling gates than qubit alternatives. As proof-of-concept applications, we numerically demonstrate the synthesis of ${\rm SU}(16)$ gates for noisy quantum hardware and an embedded error correction sequence that encodes a qubit memory in a transmon ququart to protect against pure dephasing noise. We conclude that universal qudit control -- a valuable extension to the operational toolbox of superconducting quantum information processing -- is within reach of current transmon-based architectures and has applications to near-term and long-term hardware.

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arXiv2022

Ancilla-free implementation of generalized measurements for qubits embedded in a qudit space

Informationally complete (IC) positive operator-valued measures (POVMs) are generalized quantum measurements that offer advantages over the standard computational basis readout of qubits. For instance, IC-POVMs enable efficient extraction of operator expectation values, a crucial step in many quantum algorithms. POVM measurements are typically implemented by coupling one additional ancilla qubit to each logical qubit, thus imposing high demands on the device size and connectivity. Here, we show how to implement a general class of IC-POVMs without ancilla qubits. We exploit the higher-dimensional Hilbert space of a qudit in which qubits are often encoded. POVMs can then be realized by coupling each qubit to two of the available qudit states, followed by a projective measurement. We develop the required control pulse sequences and numerically establish their feasibility for superconducting transmon qubits through pulse-level simulations. Finally, we present an experimental demonstration of a qudit-space POVM measurement on IBM Quantum hardware. This paves the way to making POVM measurements broadly available to quantum computing applications.

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