Quantum simulations on noisy hardware are often designed as if the machine were ideal, with device limitations considered only after the basis and measurement plan have been chosen. We instead use information about the physical problem and the device at an earlier stage, to decide which states and evolution times should form a compact simulation basis. Because the target problem remains unchanged, the method adapts only the representation used to solve it. Tests on many-body and molecular models show that this approach can reveal useful directions that ordinary time evolution misses, while also exposing an important limitation: some of these directions can become too similar to estimate reliably. Realistic device data further show that hardware response can change the preferred states and evolution times before execution. Across seven acquisition days, a four-qubit experiment shows a median 54\% reduction in projected-energy error from problem-informed time choices relative to uniform sampling under matched hardware conditions. These results provide a proof of principle for simulation-basis design as a practical interface between quantum algorithms and the hardware that executes them.
AI Summary
The paper asks whether physical-response models and device calibration should inform the trial states and evolution times used in projected quantum simulation, rather than only compilation and error mitigation. It combines candidate generation through conditional no-jump evolution, which changes amplitudes as well as phases, with selection based on task relevance, independence, conditioning, and preparation support. The target Hamiltonian remains unchanged.
In exact six-site Hubbard calculations at $U/t=16$ and trial dimension $m=16$, response-shaped candidates reduce projected-energy error from $0.137$ to $6.88\times10^{-4}$ relative to prescribed closed-time sampling. A matched-selector comparison retains an approximately 33-fold advantage before overlap truncation. However, at a $10^{-3}$ overlap floor, only three response modes survive versus nine closed-evolution modes, and the advantage disappears. TFIM tests show gains with locally motivated responses; molecular nitrogen tests demonstrate applicability but no uniform advantage over matched closed evolution.
Archived-device modeling changes preferred mappings and times. A separate live four-qubit TFIM experiment compares problem-informed nonuniform times with uniform sampling using matched hardware, shots, and reconstruction. Across seven acquisition days, error decreases on every day; the median error ratio is $0.464$, with paired-bootstrap 95% interval $[0.374,0.701]$.
The live experiment does not isolate a calibration-induced coordinate change or implement conditional-response preparation. Selection uses exact small-system quantities, acquisition relies on tomography, and scalable selection and estimation costs remain uncharacterized. Conditional preparation adds overhead, conditioning can erase representational gains, and tests up to 30 qubits establish execution coverage rather than projected-energy accuracy.
Some signs of AI-generated textIncrementalUnclear noveltyStrong assumptions
Written by gpt-6.1-sol from the paper's full text. Automated: it can be wrong.
Quantum simulations on noisy hardware are often designed as if the machine were ideal, with device limitations considered only after the basis and measurement plan have been chosen. We instead use information about the physical problem and the device at an earlier stage, to decide which states and evolution times should form a compact simulation basis. Because the target problem remains unchanged, the method adapts only the representation used to solve it. Tests on many-body and molecular models show that this approach can reveal useful directions that ordinary time evolution misses, while also exposing an important limitation: some of these directions can become too similar to estimate reliably. Realistic device data further show that hardware response can change the preferred states and evolution times before execution. Across seven acquisition days, a four-qubit experiment shows a median 54% reduction in projected-energy error from problem-informed time choices relative to uniform sampling under matched hardware conditions. These results provide a proof of principle for simulation-basis design as a practical interface between quantum algorithms and the hardware that executes them.
The paper asks whether physical-response models and device calibration should inform the trial states and evolution times used in projected quantum simulation, rather than only compilation and error mitigation. It combines candidate generation through conditional no-jump evolution, which changes amplitudes as well as phases, with selection based on task relevance, independence, conditioning, and preparation support. The target Hamiltonian remains unchanged.
In exact six-site Hubbard calculations at U/t=16 and trial dimension m=16, response-shaped candidates reduce projected-energy error from 0.137 to 6.88×10−4 relative to prescribed closed-time sampling. A matched-selector comparison retains an approximately 33-fold advantage before overlap truncation. However, at a 10−3 overlap floor, only three response modes survive versus nine closed-evolution modes, and the advantage disappears. TFIM tests show gains with locally motivated responses; molecular nitrogen tests demonstrate applicability but no uniform advantage over matched closed evolution.
Archived-device modeling changes preferred mappings and times. A separate live four-qubit TFIM experiment compares problem-informed nonuniform times with uniform sampling using matched hardware, shots, and reconstruction. Across seven acquisition days, error decreases on every day; the median error ratio is 0.464, with paired-bootstrap 95% interval [0.374,0.701].
The live experiment does not isolate a calibration-induced coordinate change or implement conditional-response preparation. Selection uses exact small-system quantities, acquisition relies on tomography, and scalable selection and estimation costs remain uncharacterized. Conditional preparation adds overhead, conditioning can erase representational gains, and tests up to 30 qubits establish execution coverage rather than projected-energy accuracy.
Classical simulation of Noisy Intermediate Scale Quantum computers is a crucial task for testing the expected performance of real hardware. The standard approach, based on solving Schrödinger and Lindblad equations, is demanding when scaling the number of qubits in terms of both execution time and memory. In this article, attempts in defining compact models for the simulation of quantum hardware are proposed, ensuring results close to those obtained with standard formalism. Molecular Nuclear Magnetic Resonance quantum hardware is the target technology, where three non-ideality phenomena—common to other quantum technologies—are taken into account: decoherence, off-resonance qubit evolution, and undesired qubit-qubit residual interaction. A model for each non-ideality phenomenon is embedded into a MATLAB simulation infrastructure of noisy quantum computers. The accuracy of the models is tested on a benchmark of quantum circuits, in the expected operating ranges of quantum hardware. The corresponding outcomes are compared with those obtained via numeric integration of the Schrödinger equation and the Qiskit’s QASMSimulator. The achieved results give evidence that this work is a step forward towards the definition of compact models able to provide fast results close to those obtained with the traditional physical simulation strategies, thus paving the way for their integration into a classical simulator of quantum computers.
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. Access to a computational space that incorporates quantum effects, such as superposition and entanglement, enables the derivation of promising quantum algorithms for important tasks, including preparing the ground state of a quantum system or predicting its evolution over time. Successfully tackling these tasks promises insights into significant theoretical and technological questions, such as superconductivity and the design of new materials. The aim of quantum algorithms is to use a series of quantum operations in a quantum circuit to solve a problem beyond the reach of classical computers. However, the noise and limited scale of current quantum computers restricts these circuits to moderate sizes and depths. As a result, many prominent algorithms are currently infeasible to run for problem sizes of practical interest. In response, recent research focused on variational quantum algorithms, which allow the selection of circuits that act within a quantum device's capabilities. Yet, these algorithms can require the execution of a large number of circuits, leading to prohibitively long computation times. This doctoral thesis develops two main techniques to reduce these quantum computational resource requirements, with the goal of scaling up application sizes on current quantum processors. The first approach is based on stochastic approximations of computationally costly quantities, such as quantum circuit gradients or the quantum geometric tensor (QGT). The second method takes a different perspective on the QGT, leading to a potentially more efficient description of time evolution on current quantum computers. Both techniques rely on maintaining available information and only computing necessary corrections, instead of re-computing possibly redundant data. The main focus of application for our algorithms is the simulation of quantum systems, broadly defined as including the preparation of ground and thermal states, and the real- and imaginary-time propagation of a system. The developed subroutines, however, can further be utilized in the fields of optimization or machine learning. Our algorithms are benchmarked on a range of representative models, such as Ising or Heisenberg spin models, both in numerical simulations and experiments on the hardware. In combination with error mitigation techniques, the latter is scaled up to 27 qubits; into a regime that variational quantum algorithms are challenging to scale to on noisy quantum computers without our algorithms.
As quantum devices continue to improve in scale and precision, a central challenge is how to effectively utilize noisy hardware for meaningful computation. Most existing approaches aim to recover noiseless circuit outputs from noisy ones through error mitigation or correction. Here, we show that noisy quantum devices can be directly leveraged as computational resources to enhance the classical simulation of quantum circuits. We introduce the Noisy-device-enhanced Classical Simulation (NDE-CS) protocol, which improves stabilizer-based classical Monte Carlo simulation methods by incorporating data obtained from noisy quantum hardware. Specifically, NDE-CS uses noisy executions of a target circuit together with noisy Clifford circuits to learn how the target circuit can be expressed in terms of Clifford circuits under realistic noise. The same learned relation can then be reused in the noiseless Clifford limit, enabling accurate estimation of ideal expectation values with substantially reduced sampling cost. Numerical simulations on Trotterized Ising circuits demonstrate that NDE-CS achieves orders-of-magnitude reductions in sampling cost compared to the underlying purely classical Monte Carlo approaches from which it is derived, while maintaining the same accuracy. We also compare NDE-CS with Sparse Pauli Dynamics (SPD), a powerful classical framework capable of simulating quantum circuits at previously inaccessible scales, and provide an example where the cost of SPD scales exponentially with system size, while NDE-CS scales much more favorably. These results establish NDE-CS as a scalable hybrid simulation approach for quantum circuits, where noise can be harnessed as a computational asset.
Abstract Design space exploration (DSE) plays an important role in optimising quantum circuit execution by systematically evaluating different configurations of compilation strategies and hardware settings. In this paper, we conduct a comprehensive investigation into the impact of various layout methods, qubit routing techniques, and optimisation levels, as well as device-specific properties such as different variants and strengths of noise and imperfections, the topological structure of qubits, connectivity densities, and back-end sizes. By spanning through these dimensions, we aim to understand the interplay between compilation choices and hardware characteristics. A key question driving our exploration is whether the optimal selection of device parameters, mapping techniques, comprising of initial layout strategies and routing heuristics can mitigate device induced errors beyond standard error mitigation approaches. Our results show that carefully selecting software strategies (e.g., mapping and routing algorithms) and tailoring hardware characteristics (such as minimising noise and leveraging topology and connectivity density) significantly improve the fidelity of circuit execution outcomes, and thus the expected correctness or success probability of the computational result. We provide estimates based on key metrics such as circuit depth, gate count and expected fidelity. Our results highlight the importance of hardware–software co-design, particularly as quantum systems scale to larger dimensions, and along the way towards fully error corrected quantum systems: Our study is based on computationally noisy simulations, but considers various implementations of quantum error correction (QEC) using the same approach as for other algorithms. The observed sensitivity of circuit fidelity to noise and connectivity suggests that co-design principles will be equally critical when integrating QEC in future systems. Our exploration provides practical guidelines for co-optimising physical mapping, qubit routing, and hardware configurations in realistic quantum computing scenarios.
Design space exploration (DSE) plays an important role in optimising quantum circuit execution by systematically evaluating different configurations of compilation strategies and hardware settings. In this work, we study the impact of layout methods, qubit routing techniques, compiler optimization levels, and hardware-specific properties, including noise characteristics, topological structures, connectivity densities, and device sizes. By traversing these dimensions, we aim to understand how compilation choices interact with hardware features. A central question in our study is whether carefully selected device parameters and mapping strategies, including initial layouts and routing heuristics, can mitigate hardware-induced errors beyond standard error mitigation methods. Our results show that choosing the right software strategies (e.g., layout and routing) and tailoring hardware properties (e.g., reducing noise or leveraging connectivity) significantly enhances the fidelity of quantum circuit executions. We provide performance estimates using metrics such as circuit depth, gate count, and expected fidelity. These findings highlight the value of hardware-software co-design, especially as quantum systems scale and move toward error-corrected computing. Our simulations, though noisy, include quantum error correction (QEC) scenarios, revealing similar sensitivities to layout and connectivity. This suggests that co-design principles will be vital for integrating QEC in future devices. Overall, we offer practical guidance for co-optimizing mapping, routing, and hardware configuration in real-world quantum computing.
While quantum computers promise to solve classically intractable problems, identifying the point at which fault-tolerant quantum computation outperforms the best classical algorithms for practical applications remains an outstanding challenge. Here we establish a concrete quantum-classical crossover for quantum many-body dynamics under realistic hardware conditions. We introduce a scalable fault-tolerant framework that combines coherent observable estimation with a space-time-efficient implementation of non-Clifford rotations, suppressing the residual logical errors that limit existing partially fault-tolerant approaches. A benchmark against state-of-the-art tensor-network and variational Monte Carlo algorithms reveals a concrete crossover for mixed-field Ising dynamics at modest system sizes. For a physical error rate of p=10−3, fault-tolerant simulation requires approximately 2 hours and 3.7×105 physical qubits for a 100-site 1D system, whereas tensor network approaches would require about 100 years. For 2D models, where rapid entanglement growth limits the classical evolution time, we project quantum runtimes within minutes. A physical error rate of p=10−4 leads to at least an order of magnitude reduction in qubit count (3.1×104 physical qubits) and runtime (minutes for 1D and seconds for 2D). The reduction in quantum runtime arises from our improved rotation-state injection and co-design of quantum error correction and observable-estimation protocols, which jointly suppress logical-error accumulation and reduce sampling overhead. Our results establish a scalable route towards practical quantum advantage and identify quantitative engineering targets for future fault-tolerant architectures.