arXiv subjects

Ryan Babbush

Publications and source records attributed to Ryan Babbush.

At least 19 recordsLinked to original sources

arXiv2026

Machine learning quantum data to accelerate quantum Monte Carlo

Simulating strongly correlated electrons in molecules and materials remains a central goal for quantum computing. A promising strategy uses quantum processors to prepare trial wavefunctions that guide classical quantum Monte Carlo (QMC). However, the enormous computational cost of repeatedly processing quantum measurements has severely limited the practical scalability of this approach. Here, we overcome this bottleneck by compressing quantum measurement data into machine-learning models that efficiently provide the wavefunction overlaps needed by QMC. This accelerates quantum-classical QMC by orders of magnitude, enabling chemically accurate simulations on up to 40 qubits, more than doubling the scale of previous hardware demonstrations with comparable accuracy. We demonstrate our approach on hydrogen chains and strongly correlated iron-sulfur clusters using measurements from Google's Willow processor. By enabling efficient reuse of quantum-state information on the classical coprocessor, our framework addresses a fundamental bottleneck in hybrid quantum algorithms that will persist even into the fault-tolerant era.

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arXiv2026

Basis-set error bounds for first-quantised quantum simulation of chemistry

In quantum simulation of electronic structure it is often expected that the estimate of the ground energy converges to the continuum basis limit at a rate of $\mathcal O(N^{-1})$ for a basis of size $N$. This has been found in analytical and numerical studies, but without a rigorous treatment of the error in the quantities considered in quantum algorithms. Here we show the $\mathcal O(N^{-1})$ scaling of the error for a wide range of cases needed for quantum simulation of chemistry. We show the error in the ground energy scales as $\mathcal O(N^{-1})$ for plane-wave as well as spatial grid bases. For the spatial grid we consider both a periodic system and a non-periodic system with open boundaries. For time evolution, our bound on the error in the state itself is weaker than $\mathcal O(N^{-1})$, but we show that the error in observables scales as $\widetilde{\mathcal O}(N^{-1})$ in important cases. In particular, we may consider a smoothed observable that describes the position of particles. We show that this error scales as $\mathcal O(N^{-5/3}+tN^{-1})$ for time $t$, again both for plane-wave and spatial grid bases. For the non-periodic grid case we use a condition that the true evolution would not result in significant leakage past the boundaries, which introduces basis error unrelated to the resolution of the discretisation. We also show the error in the kinetic energy of a particle scales as $\mathcal O((t+\log N)/N)$ for the plane-wave and grid bases. Together, these results show that $\mathcal O(N^{-1})$ scaling of the error holds for many of the relevant cases for quantum algorithms (with a trivial log factor for kinetic energy).

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arXiv2026

The Compendium of Super-Quadratic Computational Quantum Advantages

This compendium presents a structured collection of computational problems with credible prospects for realizing meaningful quantum advantage, focused on describing problem characteristics rather than specific algorithms. It is intended for non-quantum researchers and practitioners with strong computational backgrounds, particularly domain experts, seeking to assess the relevance of quantum methods to real-world problems. The compendium focuses on enumerating core problems for which there is good evidence that a quantum computer can realize more than a quadratic speedup in offline non-relativized time-complexity (e.g., as opposed to in oracular settings, streaming models, or communication advantages). Entries characterize the structural constraints that real-world instances must satisfy to realize those advantages in practice. The intention is to provide a reference that can be leveraged to connect quantum algorithms to practical use cases.

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arXiv2026

Leveraging verifiable structure in quantum circuits to find more efficient compilations with agentic AI

We discuss an effective paradigm of utilizing AI agents to better compile quantum circuits when one can constrain bottleneck subroutines to have some form of classically verifiable structure. For example, when critical subroutines are composed exclusively of reversible classical logic, phasing operations, and measurement based uncomputation, one can efficiently simulate execution for classical inputs. This property facilitates efficient certification of approximate circuit synthesis via a form of fuzz testing, provided suitable assumptions on the input distribution. While this pattern was recently exploited to improve quantum cryptanalysis circuits, here we highlight the flexibility of the broader approach by discussing three important applications. (1) The computation of $1/\sqrt{x}$ that bottlenecks real space simulations of the Coulomb operator such as those important for modeling inertial confinement fusion reactors. (2) The decoding of Reed-Solomon codes which bottlenecks the decoded quantum interferometry algorithm when used to approximately solve the optimal polynomial intersection problem. And (3) the quantum look-up tables and controlled application of Givens rotations that bottleneck the most performant quantum algorithms for simulating chemistry in second quantization. We discuss reference implementations of these algorithms and how they can be constrained and verified in the interest of seeding a Kaggle competition designed to accelerate AI-based research into the optimization of their compilation.

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arXiv2026

Exponential quantum advantage in processing massive classical data

Broadly applicable quantum advantage, particularly in classical data processing and machine learning, has been a fundamental open problem. In this work, we prove that a small quantum computer of polylogarithmic size can perform large-scale classification and dimension reduction on massive classical data by processing samples on the fly, whereas any classical machine achieving the same prediction performance requires exponentially larger size. Furthermore, classical machines that are exponentially larger yet below the required size need superpolynomially more samples and time. We provide evidence for these quantum advantages in real-world applications, including single-cell RNA sequencing and movie review sentiment analysis, demonstrating four to six orders of magnitude reduction in size with fewer than 60 logical qubits. These quantum advantages are enabled by quantum oracle sketching, an algorithm for accessing the classical world in quantum superposition using only random classical data samples. Combined with classical shadows, our algorithm circumvents the data loading and readout bottleneck to construct succinct classical models from massive classical data, a task provably impossible for any classical machine that is not exponentially larger than the quantum machine. These quantum advantages persist even when classical machines are granted unlimited time or if BPP = BQP, and rely only on the correctness of quantum mechanics. Together, our results establish machine learning on classical data as a broad and natural domain of quantum advantage and a fundamental test of quantum mechanics at the complexity frontier.

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arXiv2026

Quantum Advantage in Topological Data Analysis via Mayer Homology

Prior work has explored quantum algorithms for topological data analysis (TDA), revealing the possibility of exponential quantum speedups in estimating the ratios of Betti numbers to the dimension of the combinatorial Laplacian. However, this quantity is only non-vanishing and efficient-to-quantumly-estimate when Betti numbers are exponentially large, a case for which concrete examples are rarely known. Furthermore, certain randomized classical algorithms are sometimes efficient in this regime. Thus, the prospect of achieving quantum advantage in conventional TDA appears fairly narrow. Here, we address these challenges to the quantum advantage in TDA by developing quantum algorithms for Mayer homology, which generalize simplicial homology to $N$-nilpotent boundary operators ($\partial^N =0$) and have recently been successfully applied to real-world TDA contexts. We introduce an efficient quantum algorithm for estimating Mayer Betti numbers and their persistent counterparts. We then prove that for high-order simplices, Mayer Betti numbers are often exponentially large in the dense regime, which ameliorates the normalization bottleneck of conventional quantum TDA. In the same regime, we argue that existing dequantization algorithms developed for conventional TDA, when applied to Mayer homology, generally lose theoretical guaranties, facing certain structural barriers that prevent their practical utilities. We also provide logical resource estimates revealing that a quantum computer with roughly a few hundred qubits and sixty million Toffoli gates could solve Mayer homology problems beyond the capabilities of known classical approaches. Finally, we discuss real-world applications of Mayer homology in genomics, supersymmetry, drug discovery, and neuroscience, revealing the potential of our quantum algorithm to deliver real-world impacts via Mayer homology.

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arXiv2026

Multifractal and Glassy Signatures of Non-Ergodic 2D Quantum Dynamics

The fate of ergodicity and localization in disordered, interacting quantum systems in two spatial dimensions remains an outstanding open problem in non-equilibrium physics. Theoretical and numerical approaches are severely constrained by exponential Hilbert space growth. Here, we leverage the high data-acquisition rates of superconducting quantum processors to extensively sample Hilbert space configurations, effectively imaging the state as a wavefunction network (WFN). Tracking the bitstring return probability across varied disorder strengths, we find heavy-tailed distributions and power-law typical decay characteristic of glassy relaxation. Furthermore, the distribution of bitstring probabilities transitions from a Porter-Thomas form at low disorder to an eight-decade power law at stronger disorder. In the reconstructed configuration space, WFN connectivity is compatible with a random geometric network at low disorder and becomes scale-free at stronger disorder. Finally, a multifractal analysis based on the binary intrinsic dimension (BID) reveals a non-ergodic regime where the wavefunction support saturates to a finite fraction of the total Hilbert space. Together, these results rule out a direct ergodic-to-localized transition, pointing instead to an extended multifractal regime. By visualizing wavefunction dynamics directly in configuration space, this work complements traditional real-space studies, showing the potential of quantum processors to resolve long-standing questions in non-equilibrium physics.

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arXiv2026

Spectral amplification for ground-state energy estimation of electronic structure in first quantization

We demonstrate an asymptotic gate complexity improvement in first-quantized ground-state energy estimation of electronic structure Hamiltonians in a plane wave basis by employing the sum-of-squares spectral gap amplification protocol. The improvement relies on identifying a sum-of-squares representation of the Hamiltonian which provides a lower bound certificate and low cost block encoding that leads to a provably lower quantum phase estimation gate cost. This is achieved by using a sum-of-squares operator generated by the total charge density operator resulting in a block encoding normalization improvement of $λ= \mathcal{O}\left(ηΔ^{-1.5}+η^{1.5}Δ^{-1} \right)$ compared to prior work $λ= \mathcal{O}(ηΔ^{-2}+η^2Δ^{-1})$ where $η$ is the number of electrons and $Δ$ is the simulation grid spacing. The asymptotic reduction in block encoding normalization and similar block encoding costs to prior work is demonstrated to reduce resource estimates for materials and chemical systems by a factor of $2 - 44\times$ corresponding to the lowest cost estimates for ab initio materials simulation.

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arXiv2026

Precision quantum simulation of magnon spectra and interactions

Quantum simulation promises to advance materials discovery by accurately simulating complex states of matter, their microscopic excitations, and macroscopic response functions. The central challenge in resolving the underlying interacting dynamics is to combine high-fidelity evolution with the sophisticated control necessary to manipulate individual quasi-particles in quantum many-body states. Here, we report on high-precision simulation of both linear and non-linear response functions in a 2D XY spin-1/2 magnet using an analog-digital superconducting processor of up to 97 qubits. By interleaving digital gates with analog evolution precisely characterized via Hamiltonian learning, we selectively excite magnons at tunable energy densities. Measuring first the linear magnon response -- a central probe in neutron-scattering experiments -- we extract temperature-dependent spectra and lifetimes. Our results reveal stark variations in magnon decay rates across the Brillouin zone, with enhancement near van Hove singularities and suppression for edge-localized modes. Next, we perform a suite of nonlinear measurements, including the study of self-scattering mechanisms, as well as pump-probe spectroscopy to directly characterize the magnon interactions. While matrix-product state simulations capture the dynamics well in either small systems or at low temperatures, their predictions become inaccurate away from these limits. This work demonstrates precise simulation of the interacting dynamics in quantum magnets, and provides key insights into quasi-particles and their microscopic scattering mechanisms.

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arXiv2026

A Denser Planar Surface Code

We present a quantum code implementable on a regular $2$D hex grid with an estimated encoding rate up to $4.5\times$ of that of a rotated surface code patch using circuit-level noise in a one- and two-qubit $10^{-3}$ error uniform depolarizing model. Our approach is based on yoking a dense packing of surface code twist defects, enabled by new stabilizer measurement cycles with an optimal four layers of nearest-neighbor two-qubit gates, almost no distance-reducing hook errors, and efficient decoding. We demonstrate a space-efficient architecture for computing on densely packed logical qubits, including new padding-free lattice surgery protocols in an optimal bounding box of $2d^2$ data and measurement qubits per patch. Assuming a $1μ$s surface code cycle time and a $10μ$s reaction time, these developments enable chemically accurate ground state phase estimation of a broad class of `utility-scale' electronic structure simulation problems such as the $108$ spin-orbital FeMoco-based nitrogen fixation catalyst in under a month with $89$k noisy superconducting qubits. We elucidate a Pareto frontier of space-time trade-offs and find a minimum physical quantum volume of $1.3$ mega-qubit-hours. These correspond to a $36\times$ space and $6.6\times$ spacetime improvement, respectively, over our previous state-of-the-art minimum-Toffoli resource estimates (Phys. Rev. X 15, 041016).

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arXiv2026

Quantum simulation of electronic structure via quantum fast multipole method

Here we describe an approach for simulating electronic structure on quantum computers with significantly lower asymptotic complexity than prior work. The approach uses a real-space first-quantised representation of the molecular Hamiltonian which we propagate using high-order product formulae. Essential for this low complexity is the use of a technique similar to the fast multipole method for computing the Coulomb operator with $\widetilde{\cal O}(η)$ complexity for a simulation with $η$ particles. We show how to modify this algorithm so that it can be implemented on a quantum computer. We ultimately demonstrate an approach with $t(η^{4/3}N^{1/3} + η^{1/3} N^{2/3} ) (ηNt/ε)^{o(1)}$ gate complexity, where $N$ is the number of grid points, $ε$ is target precision, and $t$ is the duration of time evolution. This is roughly a speedup by ${\cal O}(η)$ over most prior algorithms. We provide lower complexity than all prior work for $N<η^7$ (the regime of practical interest), with only first-quantised interaction-picture simulations providing better performance for $N>η^7$. As with the classical fast multipole method, large particle numbers $η\gtrsim 10^3$ would be needed to realise this advantage.

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arXiv2026

Securing Elliptic Curve Cryptocurrencies against Quantum Vulnerabilities: Resource Estimates and Mitigations

This whitepaper seeks to elucidate implications that the capabilities of developing quantum architectures have on blockchain vulnerabilities and mitigation strategies. First, we provide new resource estimates for breaking the 256-bit Elliptic Curve Discrete Logarithm Problem, the core of modern blockchain cryptography. We demonstrate that Shor's algorithm for this problem can execute with either <1200 logical qubits and <90 million Toffoli gates or <1450 logical qubits and <70 million Toffoli gates. In the interest of responsible disclosure, we use a zero-knowledge proof to validate these results without disclosing attack vectors. On superconducting architectures with 1e-3 physical error rates and planar connectivity, those circuits can execute in minutes using fewer than half a million physical qubits. We introduce a critical distinction between fast-clock (such as superconducting and photonic) and slow-clock (such as neutral atom and ion trap) architectures. Our analysis reveals that the first fast-clock CRQCs would enable on-spend attacks on public mempool transactions of some cryptocurrencies. We survey major cryptocurrency vulnerabilities through this lens, identifying systemic risks associated with advanced features in some blockchains such as smart contracts, Proof-of-Stake consensus, and Data Availability Sampling, as well as the enduring concern of abandoned assets. We argue that technical solutions would benefit from accompanying public policy and discuss various frameworks of digital salvage to regulate the recovery or destruction of dormant assets while preventing adversarial seizure. We also discuss implications for other digital assets and tokenization as well as challenges and successful examples of the ongoing transition to Post-Quantum Cryptography (PQC). Finally, we urge all vulnerable cryptocurrency communities to join the ongoing migration to PQC without delay.

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arXiv2026

Observation of disorder-induced superfluidity

The emergence of states with long-range correlations in a disordered landscape is rare, as disorder typically suppresses the particle mobility required for long-range coherence. But when more than two energy levels are available per site, disorder can induce resonances that locally enhance mobility. Here we explore phases arising from the interplay between disorder, kinetic energy, and interactions on a superconducting processor with qutrit readout and control. Compressibility measurements distinguish an incompressible Mott insulator from surrounding compressible phases and reveal signatures of glassiness, reflected in non-ergodic behavior. Spatially-resolved two-point correlator measurements identify regions of the phase diagram with a non-vanishing condensate fraction. We also visualize the spectrum by measuring the dynamical structure factor. A linearly-dispersing phonon mode materializes in the superfluid, appearing even when disorder is introduced to the clean Mott insulator. Our results provide strong experimental evidence for disorder-induced superfluidity.

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arXiv2025

Magic state cultivation on a superconducting quantum processor

Fault-tolerant quantum computing requires a universal gate set, but the necessary non-Clifford gates represent a significant resource cost for most quantum error correction architectures. Magic state cultivation offers an efficient alternative to resource-intensive distillation protocols; however, testing the proposal's assumptions represents a challenging departure from quantum memory experiments. We present an experimental study of magic state cultivation on a superconducting quantum processor. We implement cultivation, including code-switching into a surface code, and develop a fault-tolerant measurement protocol to bound the magic state fidelity. Cultivation reduces the error by a factor of 40, with a state fidelity of 0.9999(1) (retaining 8% of attempts). Our results experimentally establish magic state cultivation as a viable solution to one of quantum computing's most significant challenges.

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arXiv2025

The Grand Challenge of Quantum Applications

This perspective outlines promising pathways and critical obstacles on the road to developing useful quantum computing applications, drawing on insights from the Google Quantum AI team. We propose a five-stage framework for this process, spanning from theoretical explorations of quantum advantage to the practicalities of compilation and resource estimation. For each stage, we discuss key trends, milestones, and inherent scientific and sociological impediments. We argue that two central stages -- identifying concrete problem instances expected to exhibit quantum advantage, and connecting such problems to real-world use cases -- represent essential and currently under-resourced challenges. Throughout, we touch upon related topics, including the promise of generative artificial intelligence for aspects of this research, criteria for compelling demonstrations of quantum advantage, and the future of compilation as we enter the era of early fault-tolerant quantum computing.

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arXiv2025

Quantum-Classical Separation in Bounded-Resource Tasks Arising from Measurement Contextuality

The prevailing view is that quantum phenomena can be harnessed to tackle certain problems beyond the reach of classical approaches. Quantifying this capability as a quantum-classical separation and demonstrating it on current quantum processors has remained elusive. Using a superconducting qubit processor, we show that quantum contextuality enables certain tasks to be performed with success probabilities beyond classical limits. With a few qubits, we illustrate quantum contextuality with the magic square game, as well as quantify it through a Kochen--Specker--Bell inequality violation. To examine many-body contextuality, we implement the N-player GHZ game and separately solve a 2D hidden linear function problem, exceeding classical success rate in both. Our work proposes novel ways to benchmark quantum processors using contextuality-based algorithms.

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arXiv2025

The FLuid Allocation of Surface code Qubits (FLASQ) cost model for early fault-tolerant quantum algorithms

Holistic resource estimates are essential for guiding the development of fault-tolerant quantum algorithms and the computers they will run on. This is particularly true when we focus on highly-constrained early fault-tolerant devices. Many attempts to optimize algorithms for early fault-tolerance focus on simple metrics, such as the circuit depth or T-count. These metrics fail to capture critical overheads, such as the spacetime cost of Clifford operations and routing, or miss they key optimizations. We propose the FLuid Allocation of Surface code Qubits (FLASQ) cost model, tailored for architectures that use a two-dimensional lattice of qubits to implement the two-dimensional surface code. FLASQ abstracts away the complexity of routing by assuming that ancilla space and time can be fluidly rearranged, allowing for the tractable estimation of spacetime volume while still capturing important details neglected by simpler approaches. At the same time, it enforces constraints imposed by the circuit's measurement depth and the processor's reaction time. We apply FLASQ to analyze the cost of a standard two-dimensional lattice model simulation, finding that modern advances (such as magic state cultivation and the combination of quantum error correction and mitigation) reduce both the time and space required for this task by an order of magnitude compared with previous estimates. We also analyze the Hamming weight phasing approach to synthesizing parallel rotations, revealing that despite its low T-count, the overhead from imposing a 2D layout and from its use of additional ancilla qubits will make it challenging to benefit from in early fault-tolerance. We hope that the FLASQ cost model will help to better align early fault-tolerant algorithmic design with actual hardware realization costs without demanding excessive knowledge of quantum error correction from quantum algorithmists.

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arXiv2025

A simplified version of the quantum OTOC$^{(2)}$ problem

This note presents a simplified version of the OTOC$^{(2)}$ problem that was recently experimentally implemented by Google Quantum AI and collaborators. We present a formulation of the problem for growing input size and hope this spurs further theoretical work on the problem.

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