Quantum Device-Assisted Sampling

• Quantum device-assisted sampling is a technique that employs quantum processors to directly sample from complex probability distributions, overcoming classical limitations.
• It leverages advanced quantum circuit dynamics, entanglement, and measurement protocols to achieve exponential sampling complexity and rigorous statistical benchmarks.
• The approach finds applications in process characterization, benchmarking, generative modeling, and hybrid quantum-classical Monte Carlo methods across various quantum platforms.

Quantum device-assisted sampling encompasses a suite of methodologies in which a quantum processor directly generates samples from probability distributions that are classically hard to access or efficiently reconstruct. These approaches leverage quantum circuit dynamics, entanglement, measurement, or quantum-specific process characteristics to overcome the scaling and complexity bottlenecks of conventional sampling, finding applications in process characterization, benchmarking, generative modeling, and variational Monte Carlo. Key paradigms include influence sampling for process assessment, quantum random circuit sampling for computational hardness, measurement-based sampling protocols, quantum signal processing, device-trained neural sampling, quantum-assisted Gibbs/energy-based model sampling, and hybrid proposals for advanced Monte Carlo methods. Experimental realizations span photonic, superconducting, trapped-ion, and annealing platforms, with rigorous statistical and complexity-theoretic benchmarks substantiating both the scalability and the quantum-specific nature of these device-assisted routines.

1. Foundations and Paradigms in Quantum Device-Assisted Sampling

Quantum device-assisted sampling characterizes protocols where measurement outcomes or direct state evolution within a quantum processor generate samples from distributions not efficiently accessible classically. Formally, for an $n$-qubit quantum process $\Phi$, device-assisted schemes often utilize the quantum operation itself as an 'oracle' or generator, mediating sample production through gate application, circuit dynamics, or direct measurement. Influential paradigms include:

• Influence Sampling: Quantifies process infidelity on qubit subsets by sampling the perturbations induced by simple single-qubit test gates on randomly prepared product states, leveraging the quantum process itself as a measurement generator (Zhan et al., 8 Jun 2025).
• Random Circuit Sampling (QRS): Quantum circuits of sufficient depth and randomness produce bitstring samples whose output probability distributions are believed to be infeasible to simulate classically due to anti-concentration and gapP/#P-hard amplitude structure (Hangleiter et al., 2022).
• Measurement-Based Protocols: Sampling from specially prepared entangled resource states (e.g. cluster states) using local measurements yields distributions of high computational complexity, especially under randomness or nonadaptive measurement choices (Ringbauer et al., 2023, Miller et al., 2017).
• Quantum Signal Processing (QSP): Circumvents classical sampling bottlenecks in weighted/proportional sampling tasks by coherently encoding and extracting target distribution amplitudes through tailored polynomial transformations (Laneve, 2023).
• Quantum Annealing and Counterdiabatic Sampling: Utilizes quantum annealers and digitized counterdiabatic protocols to sample low-temperature Gibbs distributions for spin systems and general energy-based models, bypassing Markov chain slowdowns and exploiting native device parallelism (Vuffray et al., 2020, Hegade et al., 30 Oct 2025).
• Hybrid Quantum-Classical Proposals: Integrates quantum circuit outcomes (e.g., QAOA) into classical Monte Carlo frameworks via neural network surrogates or direct proposal distributions to accelerate convergence and diminish mixing times in complex many-body sampling (Nakano et al., 2 Jun 2025, Chang et al., 28 Feb 2025).

2. Influence Sampling: Quantum Process Characterization at Scale

Influence sampling harnesses the quantum process as a device-side sampler to efficiently assess the influence of $\Phi$ on arbitrary qubit subsets, circumventing the resource demands of full process tomography (Zhan et al., 8 Jun 2025). The procedure employs up to three single-qubit gates ($U_1=I$, $U_2=H$, $U_3=R_x(\pi/2)$) applied in parallel, followed by the unknown process $\Phi$ and subsequent measurement of all qubits. Sampling over random bit-string preparations and the chosen gate yields a set $T_l$ of 'influenced' qubits. Aggregating outcomes over $M \sim 10^5$ queries enables empirical estimation of influence quantities $\mathrm{Inf}_S[\Phi]$, extracting rigorous bounds on process infidelity and enabling noisy-qubit identification, junta testing, and crosstalk detection.

This protocol's sampling complexity is $O(1/\delta^2)$ for error threshold $\delta$, independent of the number of qubits $n$. Experimental demonstrations span photonic platforms (4-qubit processes with fidelity $\approx 98\%$) and time-multiplexed circuits for up to 24 qubits, establishing scalability and applicability to large-scale device assessment and model learning, with substantial preprocessing utility for tomographic tasks and benchmarking (Zhan et al., 8 Jun 2025).

3. Quantum Random Circuit Sampling and Effective Sampling Width

Quantum random circuit sampling is the prevailing mechanism for demonstrating quantum advantage on pre-fault-tolerant hardware (Hangleiter et al., 2022). The essential computational hardness arises from the circuit-induced output distributions, which anti-concentrate (exhibiting nearly uniform probabilities upon measurement) but display small second moments, enforcing sample complexity exponential in $n$ for device-independent verification (Hangleiter et al., 2018).

Recent advances in holographic random circuit sampling (HRCS) exploit both circuit depth and temporal resources, recycling qubit registers via repeated interactions, mid-circuit measurements, and resets. This protocol amplifies the effective sample space size from $N_A$ physical qubits to $N_{\rm eff} = N_A + t N_B$ measured bits after $t$ rounds, where each bath register induces new output bits per round (Zhang et al., 7 Nov 2025). Empirical realization on 20-qubit IBM devices yielded effective sampling over $N_{\rm eff}=200$ logical qubits, verified with a linear XEB fidelity of $0.0593$, and upholds anticoncentration properties. Scalability is predicated on hardware support for mid-circuit measurement and reset operations, making HRCS a route to exponential sampling complexity without expanding physical qubit resources.

4. Measurement-Based Sampling and Verification

Measurement-based quantum computation and sampling leverage entangled resource (cluster) states and nonadaptive, often randomized, single-qubit measurements (Ringbauer et al., 2023, Miller et al., 2017). In this model, the resource state is typically a stabilizer (or cubic IQP state), and measurement outcomes encode samples from complex output distributions, obtained in constant-depth protocols and with independence from adaptive control schemes. Verification of the sampling task is tractable under efficient direct fidelity estimation or stabilizer measurements, achieving sample complexity $O(1/\epsilon^2)$ independent of system size.

Miller et al. demonstrated that nonadaptive, local measurement architectures enable unified sampling and verification: switching measurement bases on output qubits allows direct application of stabilizer-based fidelity lower bounds, which correspond to TVD distance bounds on the sampled distribution. Under average-case hardness conjectures, these MBQC protocols deliver sampling and verification tasks that match in physical requirements and can be implemented without the need for quantum error correction (Miller et al., 2017).

5. Device-Assisted Sampling for Statistical and Generative Modeling

Quantum devices offer generative sampling capabilities for statistical physics and machine learning models, particularly in Gibbs, Boltzmann, or joint probability density contexts (Wild et al., 2020, Hegade et al., 30 Oct 2025, Ingelmann et al., 17 Jun 2025). Quantum algorithms map classical Markov chains to parent Hamiltonians whose ground states are coherent encodings of the target distributions, leveraging adiabatic evolution or counterdiabatic driving to prepare such ground states efficiently. Quantum-assisted tracer dispersion utilizes parameterized circuits to encode high-dimensional joint PDFs in amplitude distributions and performs one-shot inference for Lagrangian transport models, with direct sampling for velocity components facilitating advanced Monte Carlo and CFD parameterizations in turbulent flows (Ingelmann et al., 17 Jun 2025).

Digitized counterdiabatic quantum sampling (DCQS) further improves sampling from low-temperature Boltzmann distributions by iteratively steering device dynamics toward deeper minima and aggregating outputs at multiple effective temperatures through classical reweighting. Benchmarks on spin-glass and Ising models up to 156 qubits demonstrate dramatic sample and runtime savings compared to classical methods like Metropolis–Hastings and parallel tempering (Hegade et al., 30 Oct 2025).

6. Hybrid and Quantum-Trained Sampling Proposals

Recent hybrid protocols integrate quantum device outcomes and classical learning to address mixing-time bottlenecks in MCMC, VMC, and related sampling tasks (Nakano et al., 2 Jun 2025, Chang et al., 28 Feb 2025). Neural-network-assisted Monte Carlo sampling employs a generative neural sampler trained on output distributions of short-depth QAOA circuits, offering classical surrogates that maintain high spectral gaps and rapid decorrelation without prior symmetry constraints or continuous quantum queries. In variational Monte Carlo for quantum many-body systems, quantum-assisted proposals via time-evolution under problem Hamiltonians yield transitions between high-probability configurations irrespective of their Hamming separation. This produces order-of-magnitude gains in spectral gap (up to exponential advantage in some regimes), reduced autocorrelation times, and enhanced estimator accuracy for both classical and molecular models (e.g. Fermi–Hubbard, H$_n$) (Chang et al., 28 Feb 2025). Notably, the quantum proposal runtime scales polynomially with system size, qualifying these protocols for genuine asymptotic speedup.

7. Device-Independence, Verification, and Complexity-Theoretic Barriers

The inherent flatness and anti-concentration of quantum process-induced sampling distributions rigidly enforce exponential sample complexity for any device-independent classical certification strategy (Hangleiter et al., 2018, Hangleiter, 2020). Exact or approximate identity testing against the ideal distribution is intractable without additional quantum-side trust assumptions, cryptographic anchoring, or interactive protocols. Efficient certification is regained via measurement-device-dependent methods: direct fidelity estimation, stabilizer witnesses, and local measurement protocols all yield rigorous TVD bounds or fidelity estimates with sample complexity $O(1/\epsilon^2)$. Complexity-theoretic analysis situates quantum device-assisted sampling in the regime where stockmeier counting, anti-concentration, gapP hardness, and the quantum sign problem demarcate the computational boundary between BPP and the intractable quantum regime (Hangleiter, 2020).

In summary, quantum device-assisted sampling offers a multifaceted framework for scalable, hardware-efficient generation of samples from complex distributions, with rigorous computational hardness guarantees, verifiable protocols, and diverse applications across process characterization, benchmarking, statistical modeling, and quantum-enhanced Monte Carlo techniques.