arXiv subjects

Martin Leib

Publications and source records attributed to Martin Leib.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Channel Polynomial Processing

We introduce a quantum algorithmic framework based on probabilistic mixtures of unitary channels that, similar to the framework of quantum singular value transformations, enables the application of arbitrary polynomials of hermitian operators onto arbitrary initial states. We show that our framework supports a flexible tradeoff between sample- and query complexity ranging from optimal query complexity, meaning logarithmic in the error, and exponentially scaling sample complexity to sub-polynomial query complexity in the error and polynomial sample complexity. Combined with the considerably lower quantum circuit complexity, compared to quantum singular value transformations with a linear combination of unitaries block encoding, we argue that our framework can be seamlessly scaled from NISQ to fault-tolerant quantum computing.

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arXiv2026

Rolling Stock Planning Using the Quantum Approximate Optimization Algorithm

Rolling stock planning is a complex optimization problem in railway management that involves assigning physical trains to scheduled trips while minimizing operational costs. In this work, we address a specific instance of this problem featuring 190 trips over two days, subject to constraints such as mandatory maintenance stops. We reformulate the problem as a Maximum-Weight Independent Set (MWIS) problem on a graph where nodes represent feasible train cycles. To handle the computational complexity of the large search space, we propose a hybrid divide-and-conquer algorithm. This approach iteratively selects subgraphs and solves the MWIS problem using various solvers, including exact classical methods and the Quantum Approximate Optimization Algorithm (QAOA). We evaluate the algorithm's performance by comparing these methods and analyzing the scaling with respect to subgraph size, with QAOA assessed through both classical simulation and execution on a quantum device (IQM Emerald). Our results indicate that increasing the subgraph size generally improves solution quality, demonstrating that the hybrid framework can effectively bridge the gap between polynomial-time approximate solvers and exponential-time exact methods.

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arXiv2026

Barbell Codes: qLDPC Codes for Superconducting Quantum Hardware

The major challenge on the way to fault-tolerant quantum computing comes from the insufficient quality of hardware components and the difficulty of scaling their number without further compromising fidelity. Quantum Low-Density Parity-Check (qLDPC) codes offer a promising solution by encoding logical qubits with low overhead and at a comparatively high code distance. However, it remains an open question how to scalably implement efficient qLDPC codes on fixed-connectivity quantum chips without increasing hardware complexity to enable the non-local interactions in their underlying QEC cycles. We resolve this challenge for the first time by introducing a family of qLDPC "barbell" codes accompanied by a realistic chip layout that natively supports all required two-qubit interactions. Crucially, the hardware complexity required to implement barbell codes remains constant as code distance increases. We provide a detailed investigation into the feasibility of all required hardware components and simulate a specific family of barbell codes against circuit-level noise. We find that, with a modest overhead of $<30$ data qubits per logical qubit, barbell codes can preserve information at a physical noise strength of $10^{-4}$ for several trillion QEC cycles. Simulations of logical multi-Pauli measurements, performed with circuits tailored to the chip, yield similar logical performance per QEC round, indicating that entangling gates between logical qubits in barbell codes can be realized fault-tolerantly.

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arXiv2026

A scalable quantum-enhanced greedy algorithm for maximum independent set problems

We investigate a hybrid quantum-classical algorithm for solving the Maximum Independent Set (MIS) problem on regular graphs, combining the Quantum Approximate Optimization Algorithm (QAOA) with a minimal degree classical greedy algorithm. The method leverages pre-computed QAOA angles, derived from depth-$p$ QAOA circuits on regular trees, to compute local expectation values and inform sequential greedy decisions that progressively build an independent set. This hybrid approach maintains shallow quantum circuit and avoids instance-specific parameter training, making it well-suited for implementation on current quantum hardware: we have implemented the algorithm on a 20 qubit IQM superconducting device to find independent sets in graphs with thousands of nodes. We perform tensor network simulations to evaluate the performance of the algorithm beyond the reach of current quantum hardware and compare to established classical heuristics. Our results show that even at low depth ($p=4$), the quantum-enhanced greedy method significantly outperforms purely classical greedy baselines as well as more sophisticated approximation algorithms. The modular structure of the algorithm and relatively low quantum resource requirements make it a compelling candidate for scalable, hybrid optimization in the NISQ era and beyond.

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arXiv2025

Opportunities and challenges of quantum computing for climate modelling

Adaptation to climate change requires robust climate projections, yet the uncertainty in these projections performed by ensembles of Earth system models (ESMs) remains large. This is mainly due to uncertainties in the representation of subgrid-scale processes such as turbulence or convection that are partly alleviated at higher resolution. New developments in machine learning-based hybrid ESMs demonstrate great potential for systematically reduced errors compared to traditional ESMs. Building on the work of hybrid (physics + AI) ESMs, we here discuss the additional potential of further improving and accelerating climate models with quantum computing. We discuss how quantum computers could accelerate climate models by solving the underlying differential equations faster, how quantum machine learning could better represent subgrid-scale phenomena in ESMs even with currently available noisy intermediate-scale quantum devices, how quantum algorithms aimed at solving optimization problems could assist in tuning the many parameters in ESMs, a currently time-consuming and challenging process, and how quantum computers could aid in the analysis of climate models. We also discuss hurdles and obstacles facing current quantum computing paradigms. Strong interdisciplinary collaboration between climate scientists and quantum computing experts could help overcome these hurdles and harness the potential of quantum computing for this urgent topic.

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arXiv2024

Technology and Performance Benchmarks of IQM's 20-Qubit Quantum Computer

Quantum computing has tremendous potential to overcome some of the fundamental limitations present in classical information processing. Yet, today's technological limitations in the quality and scaling prevent exploiting its full potential. Quantum computing based on superconducting quantum processing units (QPUs) is among the most promising approaches towards practical quantum advantage. In this article the basic technological approach of IQM Quantum Computers is described covering both the QPU and the rest of the full-stack quantum computer. In particular, the focus is on a 20-qubit quantum computer featuring the Garnet QPU and its architecture, which we will scale up to 150 qubits. We also present QPU and system-level benchmarks, including a median 2-qubit gate fidelity of 99.5% and genuinely entangling all 20 qubits in a Greenberger-Horne-Zeilinger (GHZ) state.

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arXiv2024

Performance and scaling analysis of variational quantum simulation

We present an empirical analysis of the scaling of the minimal quantum circuit depth required for a variational quantum simulation (VQS) method to obtain a solution to the time evolution of a quantum system within a predefined error tolerance. In a comparison against a non-variational method based on Trotterized time evolution, we observe a better scaling of the depth requirements using the VQS approach with respect to both the size of the system and the simulated time. Results are also put into perspective by discussing the corresponding classical complexity required for VQS. Our results allow us to identify a possible advantage region for VQS over Trotterization.

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arXiv2024

Missing Puzzle Pieces in the Performance Landscape of the Quantum Approximate Optimization Algorithm

We consider the maximum cut and maximum independent set problems on random regular graphs in the infinite-size limit, and calculate the energy densities achieved by QAOA for high degrees up to $d=100$. Such an analysis is possible because the reverse causal cones of the operators in the Hamiltonian are with high probability associated with tree subgraphs, for which efficient classical contraction schemes can be developed. We combine the QAOA analysis with state-of-the-art upper bounds on optimality for both problems. This yields novel and better bounds on the approximation ratios achieved by QAOA for large problem sizes. We show that the approximation ratios achieved by QAOA improve as the graph degree increases for the maximum cut problem. However, QAOA exhibits the opposite behavior for the maximum independent set problem, i.e. the achieved approximation ratios decrease when the degree of the problem is increased. This phenomenon is explainable by the overlap gap property for large $d$, which restricts local algorithms (like QAOA) from reaching near-optimal solutions with high probability. In addition, we use the QAOA parameters determined on the tree subgraphs for small graph instances, and in that way outperform classical algorithms like Goemans-Williamson for the maximum cut problem and minimal greedy for the maximum independent set problem. In this way we circumvent the parameter optimization problem and are able to compute the expected approximation ratios.

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arXiv2024

Low-Weight High-Distance Error Correcting Fermionic Encodings

We perform an extended numerical search for practical fermion-to-qubit encodings with error correcting properties. Ideally, encodings should strike a balance between a number of the seemingly incompatible attributes, such as having a high minimum distance, low-weight fermionic logical operators, a small qubit to fermionic mode ratio and a simple qubit connectivity graph including ancilla qubits for the measurement of stabilizers. Our strategy consists of a three-step procedure in which we: first generate encodings with code distances up to $d\leq4$ by a brute-force enumeration technique; subsequently, we use these encodings as starting points and apply Clifford deformations to them which allows us to identify higher-distance codes with $d\leq7$; finally, we optimize the hardware connectivity graphs of resulting encodings in terms of the graph thickness and the number of connections per qubit. We report multiple promising high-distance encodings which significantly improve the weights of stabilizers and logical operators compared to previously reported alternatives.

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arXiv2024

Small Quantum Codes from Algebraic Extensions of Generalized Bicycle Codes

Quantum error correction is rapidly seeing first experimental implementations, but there is a significant gap between asymptotically optimal error-correcting codes and codes that are experimentally feasible. Quantum LDPC codes range from the surface code, which has a vanishing encoding rate, to very promising codes with constant encoding rate and linear distance. In this work, motivated by current small-scale experimental quantum processing units, we devise small quantum codes that are inspired by a subset of quantum LDPC codes, known as generalized bicycle (GB) codes. We introduce a code construction based on algebraic manipulation of the parity-check matrix of GB codes, rather than manipulation of Tanner graphs. Our construction leads to families of quantum LDPC codes of small size, and we demonstrate numerically that their performance scales comparably to the performance of surface codes for similar sizes under a phenomenological noise model. The advantage of our code family is that they encode many logical qubits in one code, at the expense of non-local connectivity. We then explore three variants of the code construction focusing on reducing the long-range connectivity by bringing it closer to the current experimental capabilities of short-range connectivity devices.

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arXiv2023

Improved Qubit Routing for QAOA Circuits

We develop a qubit routing algorithm with polynomial classical run time for the Quantum Approximate Optimization Algorithm (QAOA). The algorithm follows a two step process. First, it obtains a near-optimal solution, based on Vizing's theorem for the edge coloring problem, consisting of subsets of the interaction gates that can be executed in parallel on a fully parallelized all-to-all connected QPU. Second, it proceeds with greedy application of SWAP gates based on their net effect on the distance of remaining interaction gates on a specific hardware connectivity graph. Our algorithm strikes a balance between optimizing for both the circuit depth and total SWAP gate count. We show that it improves upon existing state-of-the-art routing algorithms for QAOA circuits defined on $k$-regular as well as Erd\"os-Renyi problem graphs of sizes up to $N \leq 400$.

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arXiv2023

Vanishing performance of the parity-encoded quantum approximate optimization algorithm applied to spin-glass models

The parity mapping provides a geometrically local encoding of the Quantum Approximate Optimization Algorithm (QAOA), at the expense of having a quadratic qubit overhead for all-to-all connected problems. In this work, we benchmark the parity-encoded QAOA on spin-glass models. We address open questions in the scaling of this algorithm. In particular, we show that for fixed number of parity-encoded QAOA layers, the performance or the output energy, vanishes towards zero (the value achieved by random guessing) with problem size $N$ as $N^{-1/2}$. Our results suggest that the parity-encoded QAOA does not have a promising scaling compared to the standard version of QAOA. We perform tensor-network calculations to confirm our results, and comment on the concentration of optimal QAOA parameters over problem instances.

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arXiv2023

Optimal, hardware native decomposition of parameterized multi-qubit Pauli gates

We show how to efficiently decompose a parameterized multi-qubit Pauli (PMQP) gate into native parameterized two-qubit Pauli (P2QP) gates minimizing both the circuit depth and the number of P2QP gates. Given a realistic quantum computational model, we argue that the technique is optimal in terms of the number of hardware native gates and the overall depth of the decomposition. Starting from PMQP gate decompositions for the path and star hardware graph, we generalize the procedure to any generic hardware graph and provide exact expressions for the depth and number of P2QP gates of the decomposition. Furthermore, we show how to efficiently combine the decomposition of multiple PMQP gates to further reduce the depth as well as the number of P2QP gates for a combinatorial optimization problem using the Lechner-Hauke-Zoller (LHZ) mapping.

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arXiv2023

Low-depth simulations of fermionic systems on square-grid quantum hardware

We present a general strategy for mapping fermionic systems to quantum hardware with square qubit connectivity which yields low-depth quantum circuits, counted in the number of native two-qubit fSIM gates. We achieve this by leveraging novel operator decomposition and circuit compression techniques paired with specifically chosen low-depth fermion-to-qubit mappings and allow for a high degree of gate cancellations and parallelism. Our mappings retain the flexibility to simultaneously optimize for qubit counts or qubit operator weights and can be used to investigate arbitrary fermionic lattice geometries. We showcase our approach by investigating the tight-binding model, the Fermi-Hubbard model as well as the multi-orbital Hubbard-Kanamori model. We report unprecedentedly low circuit depths per single Trotter layer with up to a $70 \%$ improvement upon previous state-of-the-art. Our compression technique also results in significant reduction of two-qubit gates. We find the lowest gate-counts when applying the XYZ-formalism to the DK mapping. Additionally, we show that our decomposition and compression formalism produces favourable circuits even when no native parameterized two-qubit gates are available.

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arXiv2022

Co-Design quantum simulation of nanoscale NMR

Quantum computers have the potential to efficiently simulate the dynamics of nanoscale NMR systems. In this work we demonstrate that a noisy intermediate-scale quantum computer can be used to simulate and predict nanoscale NMR resonances. In order to minimize the required gate fidelities, we propose a superconducting application-specific Co-Design quantum processor that reduces the number of SWAP gates by over 90 % for chips with more than 20 qubits. The processor consists of transmon qubits capacitively coupled via tunable couplers to a central co-planar waveguide resonator with a quantum circuit refrigerator (QCR) for fast resonator reset. The QCR implements the non-unitary quantum operations required to simulate nuclear hyperpolarization scenarios.

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arXiv2021

TensorFlow Quantum: A Software Framework for Quantum Machine Learning

We introduce TensorFlow Quantum (TFQ), an open source library for the rapid prototyping of hybrid quantum-classical models for classical or quantum data. This framework offers high-level abstractions for the design and training of both discriminative and generative quantum models under TensorFlow and supports high-performance quantum circuit simulators. We provide an overview of the software architecture and building blocks through several examples and review the theory of hybrid quantum-classical neural networks. We illustrate TFQ functionalities via several basic applications including supervised learning for quantum classification, quantum control, simulating noisy quantum circuits, and quantum approximate optimization. Moreover, we demonstrate how one can apply TFQ to tackle advanced quantum learning tasks including meta-learning, layerwise learning, Hamiltonian learning, sampling thermal states, variational quantum eigensolvers, classification of quantum phase transitions, generative adversarial networks, and reinforcement learning. We hope this framework provides the necessary tools for the quantum computing and machine learning research communities to explore models of both natural and artificial quantum systems, and ultimately discover new quantum algorithms which could potentially yield a quantum advantage.

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arXiv2021

Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor

We demonstrate the application of the Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems with the quantum approximate optimization algorithm (QAOA). Like past QAOA experiments, we study performance for problems defined on the (planar) connectivity graph of our hardware; however, we also apply the QAOA to the Sherrington-Kirkpatrick model and MaxCut, both high dimensional graph problems for which the QAOA requires significant compilation. Experimental scans of the QAOA energy landscape show good agreement with theory across even the largest instances studied (23 qubits) and we are able to perform variational optimization successfully. For problems defined on our hardware graph we obtain an approximation ratio that is independent of problem size and observe, for the first time, that performance increases with circuit depth. For problems requiring compilation, performance decreases with problem size but still provides an advantage over random guessing for circuits involving several thousand gates. This behavior highlights the challenge of using near-term quantum computers to optimize problems on graphs differing from hardware connectivity. As these graphs are more representative of real world instances, our results advocate for more emphasis on such problems in the developing tradition of using the QAOA as a holistic, device-level benchmark of quantum processors.

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arXiv2020

Quantum algorithms with local particle number conservation: noise effects and error correction

Quantum circuits with local particle number conservation (LPNC) restrict the quantum computation to a subspace of the Hilbert space of the qubit register. In a noiseless or fault-tolerant quantum computation, such quantities are preserved. In the presence of noise, however, the evolution's symmetry could be broken and non-valid states could be sampled at the end of the computation. On the other hand, the restriction to a subspace in the ideal case suggest the possibility of more resource efficient error mitigation techniques for circuits preserving symmetries that are not possible for general circuits. Here, we analyze the probability of staying in such symmetry-preserved subspaces under noise, providing an exact formula for local depolarizing noise. We apply our findings to benchmark, under depolarizing noise, the symmetry robustness of XY-QAOA, which has local particle number conserving symmetries, and is a special case of the Quantum Alternating Operator Ansatz. We also analyze the influence of the choice of encoding the problem on the symmetry robustness of the algorithm and discuss a simple adaption of the bit flip code to correct for symmetry-breaking errors with reduced resources.

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