arXiv subjects

Mohammad H. Amin

Publications and source records attributed to Mohammad H. Amin.

At least 19 recordsLinked to original sources

arXiv2026

Analog-Digital Quantum Computing with Quantum Annealing Processors

Quantum annealing processors typically control qubits in unison, attenuating quantum fluctuations uniformly until the applied system Hamiltonian is diagonal in the computational basis. This simplifies control requirements, allowing annealing QPUs to scale to much larger sizes than gate-based systems, but constraining the class of available operations. Here we expand the class by performing analog-digital quantum computing in a highly-multiplexed, superconducting quantum annealing processor. This involves evolution under a fixed many-body Hamiltonian that, in the weak-coupling regime, is well-described by an effective XY model, together with arbitrary-basis initialization and measurement via auxiliary qubits. Operationally, this is equivalent to implementing single-qubit gates at the beginning and end of an analog quantum evolution. We demonstrate this capability with several foundational applications: single-qubit and two-qubit coherent oscillations with varying initialization and measurement bases, a multi-qubit quantum walk with fermionic dispersion in line with theory, and Anderson localization in a disordered chain. These experiments open the door to a wide range of new possibilities in quantum computation and simulation, greatly expanding the applications of commercially available quantum annealing processors.

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arXiv2026

Blockchain with proof of quantum work

We propose a blockchain architecture in which mining requires a quantum computer. The consensus mechanism is based on proof of quantum work, a quantum-enhanced alternative to traditional proof of work that leverages quantum supremacy to make mining intractable for classical computers. We have refined the blockchain framework to incorporate the probabilistic nature of quantum mechanics, ensuring stability against sampling errors and hardware inaccuracies. To validate our approach, we implemented a prototype blockchain on four D-Wave(TM) quantum annealing processors geographically distributed within North America, demonstrating stable operation across hundreds of thousands of quantum hashing operations. Our experimental protocol follows the same approach used in the recent demonstration of quantum supremacy [King et al. Science 2025], ensuring that classical computers cannot efficiently perform the same computation task. By replacing classical machines with quantum systems for mining, it is possible to significantly reduce the energy consumption and environmental impact traditionally associated with blockchain mining while providing a quantum-safe layer of security. Beyond serving as a proof of concept for a meaningful application of quantum computing, this work highlights the potential for other near-term quantum computing applications using existing technology.

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arXiv2025

Beyond-classical computation in quantum simulation

Quantum computers hold the promise of solving certain problems that lie beyond the reach of conventional computers. However, establishing this capability, especially for impactful and meaningful problems, remains a central challenge. Here, we show that superconducting quantum annealing processors can rapidly generate samples in close agreement with solutions of the Schrödinger equation. We demonstrate area-law scaling of entanglement in the model quench dynamics of two-, three-, and infinite-dimensional spin glasses, supporting the observed stretched-exponential scaling of effort for matrix-product-state approaches. We show that several leading approximate methods based on tensor networks and neural networks cannot achieve the same accuracy as the quantum annealer within a reasonable time frame. Thus, quantum annealers can answer questions of practical importance that may remain out of reach for classical computation.

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arXiv2025

Evaluating classical simulations with a quantum processor

As simulations of quantum systems cross the limits of classical computability, both quantum and classical approaches become hard to verify. Scaling predictions are therefore based on local structure and asymptotic assumptions, typically with classical methods being used to evaluate quantum simulators where possible. Here, in contrast, we use a quantum annealing processor to produce a ground truth for evaluating classical tensor-network methods whose scaling has not yet been firmly established. Our observations run contrary to previous scaling predictions, demonstrating the need for caution when extrapolating the accuracy of classical simulations of quantum dynamics. Our results demonstrate that the virtuous cycle of competition between classical and quantum simulations can lend insight in both directions.

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arXiv2025

Comment on: "Dynamics of disordered quantum systems with two- and three-dimensional tensor networks" arXiv:2503.05693

In a recent preprint [1] (arXiv:2503.05693), Tindall et al. presented impressive classical simulations of quantum dynamics using tensor networks. Their methods represent a significant improvement in the classical state of the art, and in some cases show lower errors than recent simulations of quantum dynamics using a quantum annealer [2] (King et al., Science, eado6285, 2025). However, of the simulations in Ref. [2], Ref. [1] did not attempt the most complex lattice geometry, nor reproduce the largest simulations in 3D lattices, nor simulate the longest simulation times, nor simulate the low-precision ensembles in which correlations grow the fastest, nor produce the full-state and fourth-order observables produced by Ref. [2]. Thus this work should not be misinterpreted as having overturned the claim of Ref. [2]: the demonstration of quantum simulations beyond the reach of classical methods. Rather, these classical advances narrow the parameter space in which beyond-classical computation has been demonstrated. In the near future these classical methods can be combined with quantum simulations to help sharpen the boundary between classical and quantum simulability.

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arXiv2023

Quantum error mitigation in quantum annealing

Quantum Error Mitigation (QEM) presents a promising near-term approach to reduce error when estimating expectation values in quantum computing. Here, we introduce QEM techniques tailored for quantum annealing, using Zero-Noise Extrapolation (ZNE). We implement ZNE through zero-temperature extrapolation as well as energy-time rescaling. We conduct experimental investigations into the quantum critical dynamics of a transverse-field Ising spin chain, demonstrating the successful mitigation of thermal noise through both of these techniques. Moreover, we show that energy-time rescaling effectively mitigates control errors in the coherent regime where the effect of thermal noise is minimal. Our ZNE results agree with exact calculations of the coherent evolution over a range of annealing times that exceeds the coherent annealing range by almost an order of magnitude.

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arXiv2023

Quantum critical dynamics in a 5000-qubit programmable spin glass

Experiments on disordered alloys suggest that spin glasses can be brought into low-energy states faster by annealing quantum fluctuations than by conventional thermal annealing. Due to the importance of spin glasses as a paradigmatic computational testbed, reproducing this phenomenon in a programmable system has remained a central challenge in quantum optimization. Here we achieve this goal by realizing quantum critical spin-glass dynamics on thousands of qubits with a superconducting quantum annealer. We first demonstrate quantitative agreement between quantum annealing and time-evolution of the Schrödinger equation in small spin glasses. We then measure dynamics in 3D spin glasses on thousands of qubits, where simulation of many-body quantum dynamics is intractable. We extract critical exponents that clearly distinguish quantum annealing from the slower stochastic dynamics of analogous Monte Carlo algorithms, providing both theoretical and experimental support for a scaling advantage in reducing energy as a function of annealing time.

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arXiv2022

Probing flux and charge noise with macroscopic resonant tunneling

We report on measurements of flux and charge noise in an rf-SQUID flux qubit using macroscopic resonant tunneling (MRT). We measure rates of incoherent tunneling from the lowest energy state in the initial well to the ground and first excited states in the target well. The result of the measurement consists of two peaks. The first peak corresponds to tunneling to the ground state of the target well, and is dominated by flux noise. The second peak is due to tunneling to the excited state and is wider due to an intrawell relaxation process dominated by charge noise. We develop a theoretical model that allows us to extract information about flux and charge noise within one experimental setup. The model agrees very well with experimental data over a wide dynamic range and provides parameters that characterize charge and flux noise.

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arXiv2022

Multilevel resonant tunneling in the presence of flux and charge noise

Macroscopic resonant tunneling (MRT) in flux qubits is an important experimental tool for extracting information about noise produced by a qubit's surroundings. Here we present a detailed derivation of the MRT signal in the RF-SQUID flux qubit allowing for effects of flux and charge fluctuations on the interwell and intrawell transitions in the system. Taking into consideration transitions between the ground state in the initial well and excited states in the target well enable us to characterize both flux and charge noise source affecting the operation of the flux qubit. The MRT peak is formed by the dominant noise source affecting specific transition, with flux noise determining the lineshape of the ground to ground tunneling, whereas charge noise reveals itself as additional broadening of the ground to excited peak.

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arXiv2022

Error measurements for a quantum annealer using the one-dimensional Ising model with twisted boundaries

A finite length ferromagnetic chain with opposite spin polarisation imposed at its two ends is one of the simplest frustrated spin models. In the clean classical limit the domain wall inserted on account of the boundary conditions resides with equal probability on any one of the bonds, and the degeneracy is precisely equal to the number of bonds. If quantum mechanics is introduced via a transverse field, the domain wall will behave as a particle in a box, and prefer to be nearer the middle of the chain rather than the ends. A simple characteristic of a real quantum annealer is therefore which of these limits obtains in practice. Here we have used the ferromagnetic chain with antiparallel boundary spins to test a real flux qubit quantum annealer and discover that contrary to both expectations, the domain walls found are non-uniformly distributed on account of effective random longitudinal fields present notwithstanding tuning carried out to zero out such fields when the couplings between qubits are nominally zero. We present a simple derivation of the form of the distribution function for the domain walls, and show also how the effect we have discovered can be used to determine the strength of the effective random fields (noise) characterising the annealer. The noise measured in this fashion is smaller than what is seen during the single qubit tuning process, but nonetheless qualitatively affects the outcome of the simulation performed by the annealer.

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arXiv2022

Coherent quantum annealing in a programmable 2000-qubit Ising chain

Quantum simulation has emerged as a valuable arena for demonstrating and understanding the capabilities of near-term quantum computers. Quantum annealing has been used successfully in simulating a range of open quantum systems, both at equilibrium and out of equilibrium. However, in all previous experiments, annealing has been too slow to simulate a closed quantum system coherently, due to the onset of thermal effects from the environment. Here we demonstrate coherent evolution through a quantum phase transition in the paradigmatic setting of the 1D transverse-field Ising chain, using up to 2000 superconducting flux qubits in a programmable quantum annealer. In large systems we observe the quantum Kibble-Zurek mechanism with theoretically predicted kink statistics, as well as characteristic positive kink-kink correlations, independent of system temperature. In small chains, excitation statistics validate the picture of a Landau-Zener transition at a minimum gap. In both cases, results are in quantitative agreement with analytical solutions to the closed-system quantum model. For slower anneals we observe anti-Kibble-Zurek scaling in a crossover to the open quantum regime. These experiments demonstrate that large-scale quantum annealers can be operated coherently, paving the way to exploiting coherent dynamics in quantum optimization, machine learning, and simulation tasks.

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arXiv2021

Diversity metric for evaluation of quantum annealing

Solving discrete NP-hard problems is an important part of scientific discoveries and operations research as well as many commercial applications. A commonly used metric to compare meta-heuristic solvers is the time required to obtain an optimal solution, known as time to solution. However, for some applications it is desirable to have a set of high-quality and diverse solutions, instead of a single optimal one. For these applications, time to solution may not be informative of the performance of a solver, and another metric would be necessary. In particular, it is not known how well quantum solvers sample the configuration space in comparison to their classical counterparts. Here, we apply a recently introduced collective distance measure in solution space to quantify diversity by Mohseni et. al. and, based on that, we employ time-to-diversity as a metric for evaluation of meta-heuristics solvers. We use this measure to compare the performance of the D-Wave quantum annealing processor with a few classical heuristic solvers on a set of synthetic problems and show that D-Wave quantum annealing processor is indeed a competitive heuristic, and on many instances outperforms state-of-the-art classical solvers, while it remains on par on other instances. This suggests that a portfolio solver that combines quantum and classical solutions may win over all solvers.

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arXiv2021

Architectural considerations in the design of a third-generation superconducting quantum annealing processor

Early generations of superconducting quantum annealing processors have provided a valuable platform for studying the performance of a scalable quantum computing technology. These studies have directly informed our approach to the design of the next-generation processor. Our design priorities for this generation include an increase in per-qubit connectivity, a problem Hamiltonian energy scale similar to previous generations, reduced Hamiltonian specification errors, and an increase in the processor scale that also leaves programming and readout times fixed or reduced. Here we discuss the specific innovations that resulted in a processor architecture that satisfies these design priorities.

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arXiv2021

Quantum annealing simulation of out-of-equilibrium magnetization in a spin-chain compound

Geometrically frustrated spin-chain compounds such as Ca3Co2O6 exhibit extremely slow relaxation under a changing magnetic field. Consequently, both low-temperature laboratory experiments and Monte Carlo simulations have shown peculiar out-of-equilibrium magnetization curves, which arise from trapping in metastable configurations. In this work we simulate this phenomenon in a superconducting quantum annealing processor, allowing us to probe the impact of quantum fluctuations on both equilibrium and dynamics of the system. Increasing the quantum fluctuations with a transverse field reduces the impact of metastable traps in out-of-equilibrium samples, and aids the development of three-sublattice ferrimagnetic (up-up-down) long-range order. At equilibrium we identify a finite-temperature shoulder in the 1/3-to-saturated phase transition, promoted by quantum fluctuations but with entropic origin. This work demonstrates the viability of dynamical as well as equilibrium studies of frustrated magnetism using large-scale programmable quantum systems, and is therefore an important step toward programmable simulation of dynamics in materials using quantum hardware.

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arXiv2020

Improving nonstoquastic quantum annealing with spin-reversal transformations

Nonstoquastic Hamiltonians are hard to simulate due to the sign problem in quantum Monte Carlo simulation. It is however unclear whether nonstoquasticity can lead to advantage in quantum annealing. Here we show that YY-interaction between the qubits makes the adiabatic path during quantum annealing, and therefore the performance, dependent on spin-reversal transformations. With the right choice of spin-reversal transformation, a nonstoquastic Hamiltonian with YY-interaction can outperform stoquastic Hamiltonians with similar parameters. We introduce an optimization protocol to determine the optimal transformation and discuss the effect of suboptimality.

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arXiv2019

A Path Towards Quantum Advantage in Training Deep Generative Models with Quantum Annealers

The development of quantum-classical hybrid (QCH) algorithms is critical to achieve state-of-the-art computational models. A QCH variational autoencoder (QVAE) was introduced in Ref. [1] by some of the authors of this paper. QVAE consists of a classical auto-encoding structure realized by traditional deep neural networks to perform inference to, and generation from, a discrete latent space. The latent generative process is formalized as thermal sampling from either a quantum or classical Boltzmann machine (QBM or BM). This setup allows quantum-assisted training of deep generative models by physically simulating the generative process with quantum annealers. In this paper, we have successfully employed D-Wave quantum annealers as Boltzmann samplers to perform quantum-assisted, end-to-end training of QVAE. The hybrid structure of QVAE allows us to deploy current-generation quantum annealers in QCH generative models to achieve competitive performance on datasets such as MNIST. The results presented in this paper suggest that commercially available quantum annealers can be deployed, in conjunction with well-crafted classical deep neutral networks, to achieve competitive results in unsupervised and semisupervised tasks on large-scale datasets. We also provide evidence that our setup is able to exploit large latent-space (Q)BMs, which develop slowly mixing modes. This expressive latent space results in slow and inefficient classical sampling, and paves the way to achieve quantum advantage with quantum annealing in realistic sampling applications.

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arXiv2019

Scaling advantage in quantum simulation of geometrically frustrated magnets

The promise of quantum computing lies in harnessing programmable quantum devices for practical applications such as efficient simulation of quantum materials and condensed matter systems. One important task is the simulation of geometrically frustrated magnets in which topological phenomena can emerge from competition between quantum and thermal fluctuations. Here we report on experimental observations of relaxation in such simulations, measured on up to 1440 qubits with microsecond resolution. By initializing the system in a state with topological obstruction, we observe quantum annealing (QA) relaxation timescales in excess of one microsecond. Measurements indicate a dynamical advantage in the quantum simulation over the classical approach of path-integral Monte Carlo (PIMC) fixed-Hamiltonian relaxation with multiqubit cluster updates. The advantage increases with both system size and inverse temperature, exceeding a million-fold speedup over a CPU. This is an important piece of experimental evidence that in general, PIMC does not mimic QA dynamics for stoquastic Hamiltonians. The observed scaling advantage, for simulation of frustrated magnetism in quantum condensed matter, demonstrates that near-term quantum devices can be used to accelerate computational tasks of practical relevance.

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arXiv2019

PixelVAE++: Improved PixelVAE with Discrete Prior

Constructing powerful generative models for natural images is a challenging task. PixelCNN models capture details and local information in images very well but have limited receptive field. Variational autoencoders with a factorial decoder can capture global information easily, but they often fail to reconstruct details faithfully. PixelVAE combines the best features of the two models and constructs a generative model that is able to learn local and global structures. Here we introduce PixelVAE++, a VAE with three types of latent variables and a PixelCNN++ for the decoder. We introduce a novel architecture that reuses a part of the decoder as an encoder. We achieve the state of the art performance on binary data sets such as MNIST and Omniglot and achieve the state of the art performance on CIFAR-10 among latent variable models while keeping the latent variables informative.

cs.CV↗