arXiv subjects

Brian Neyenhuis

Publications and source records attributed to Brian Neyenhuis.

At least 19 recordsLinked to original sources

arXiv2026

Quantum Error-Corrected Computation of Molecular Energies

We present the first demonstration of an end-to-end pipeline with quantum error correction (QEC) for a quantum computation of the electronic structure of molecular systems. We calculate the ground-state energy of molecular hydrogen, using quantum phase estimation (QPE) on qubits encoded with the $[[7,1,3]]$ color code on Quantinuum H2--2. We obtain improvements in computational fidelity by (1) introducing several partially fault-tolerant (FT) techniques for the Clifford+$R_{Z}$ (arbitrary-angle single-qubit rotation) gate set, and (2) integrating Steane QEC gadgets for real-time error correction. In particular, the latter enhances the QPE circuits' performance despite the complexity of the extra QEC circuitry. The encoded circuits contain up to 1585 (546) fixed and 7202 (1702) conditional physical two-qubit gates (mid-circuit measurements), and $\sim$3900 ($\sim$760) total operations are applied on average. The energy $E$ is experimentally estimated to within $E - E_{\mathrm{FCI}} = 0.001(13)$ hartree, where $E_{\mathrm{FCI}}$ denotes the exact ground state energy within the given basis set. Additionally, we conduct numerical simulations with tunable noise parameters to identify the dominant sources of noise. We find that orienting the QEC protocols towards higher memory noise protection is the most promising avenue to improve our experimental results.

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arXiv2026

End-to-End Quantum Algorithms for the Jones Polynomial

We present an end-to-end algorithmic pipeline where a noisy digital quantum computer is used to approximate the value of the Jones polynomial at the fifth root of unity for any input link, i.e. a closed braid. This problem is DQC1-complete for Markov-closed braids and BQP-complete for Plat-closed braids, and we accommodate both versions of the problem. Even though it is widely believed that DQC1 is strictly contained in BQP, and so is 'less quantum', the resource requirements of classical algorithms for the DQC1 version are at least as high as for the BQP version, and so we potentially gain 'more advantage' by focusing on Markov-closed braids in our exposition. We demonstrate our quantum algorithm on Quantinuum's H2-2 quantum computer and show the effect of problem-tailored error-mitigation techniques. Further, leveraging that the Jones polynomial is a link invariant, we construct an efficiently verifiable benchmark to characterise the effect of noise present in a given quantum processor. In parallel, we develop and benchmark the state-of-the-art tensor-network-based classical algorithms for computing the Jones polynomial. The reconfigurable tools provided in this work allow for precise resource estimation to identify minimum link sizes for near-term quantum advantage in practice for a meaningful quantum-native problem in knot theory, if a candidate set of links are provided.

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arXiv2026

Demonstrating an unconditional separation between quantum and classical information resources

A longstanding goal in quantum information science is to demonstrate quantum computations that cannot be feasibly reproduced on a classical computer. Such demonstrations mark major milestones: they showcase fine control over quantum systems and are prerequisites for useful quantum computation. To date, quantum advantage has been demonstrated, for example, through violations of Bell inequalities and sampling-based quantum supremacy experiments. However, both forms of advantage come with important caveats: Bell tests are not computationally difficult tasks, and the classical hardness of sampling experiments relies on unproven complexity-theoretic assumptions. Here we demonstrate an unconditional quantum advantage in information resources required for a computational task, realized on Quantinuum's H1-1 trapped-ion quantum computer operating at a median two-qubit partial-entangler fidelity of 99.941(7)%. We construct a task for which the most space-efficient classical algorithm provably requires between 62 and 382 bits of memory, and solve it using only 12 qubits. Our result provides the most direct evidence yet that currently existing quantum processors can generate and manipulate entangled states of sufficient complexity to access the exponentiality of Hilbert space. This form of quantum advantage -- which we call quantum information supremacy -- represents a new benchmark in quantum computing, one that does not rely on unproven conjectures.

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arXiv2026

Digital quantum magnetism on a trapped-ion quantum computer

Digital quantum matter -- realized when discrete quantum gates approximate continuous time evolution -- is susceptible to heating into chaotic, structureless states. If digitization errors are adequately suppressed, a long-lived transient regime of approximately energy-conserving dynamics can be observed on gate-based quantum computers. Conservation of energy, in turn, enables the exploration of a wide variety of complex behaviors observed in equilibrium systems, ranging from the nontrivial microscopic origins of thermalization itself to the stabilization of effective models hosting exotic emergent properties. Here, we use Quantinuum's system model H2 quantum computer to simulate digitized dynamics of the quantum Ising model, suppressing digitization errors well enough to observe thermalization on timescales that severely challenge classical simulation methods. Relaxation of an inhomogeneous state reveals an emergent hydrodynamics due to approximate energy conservation, and we compute the associated diffusion constant. By reprogramming our simulations to take place on a triangular lattice with periodic boundary conditions, we observe thermalization consistent with emergent gauge and topological constraints resulting from lattice frustration. Our results were enabled by continued advances in two-qubit gate quality (native partial entangler fidelities of $99.94(1)\%$), and establish digital quantum computers as powerful tools for studying (effectively) continuous-time dynamics.

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arXiv2026

Computing with many encoded logical qubits beyond break-even

High-rate quantum error correcting (QEC) codes encode many logical qubits in a given number of physical qubits, making them promising candidates for quantum computation. Implementing high-rate codes at a scale that both frustrates classical computing and improves performance by encoding requires both high fidelity gates and long-range qubit connectivity -- both of which are offered by trapped-ion quantum computers. Here, we demonstrate computations that outperform their unencoded counterparts in the high-rate $[[ k+2,\, k,\, 2 ]]$ iceberg quantum error detecting (QED) and $[[ (k_2 + 2)(k_1 + 2),\, k_2k_1,\, 4 ]]$ two-level concatenated iceberg QEC codes, using the 98-qubit Quantinuum Helios trapped-ion quantum processor. Utilizing new gadgets for encoded operations, we realize this "beyond break-even" performance with reasonable postselection rates across a range of fault-tolerant (FT) and partially-fault-tolerant (pFT) component and application benchmarks with between $48$ and $94$ logical qubits. These benchmarks include FT state preparation and measurement, QEC cycle benchmarking, logical gate benchmarking, GHZ state preparation, and a pFT quantum simulation of the three-dimensional $XY$ model of quantum magnetism. Additionally, we illustrate that postselection rates can be suppressed by increasing the code distance via concatenation. Our results represent state-of-the-art logical component and state fidelities and provide evidence that high-rate QED/QEC codes are viable on contemporary quantum computers for near-term beyond-classical-scale computation.

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arXiv2026

Superconducting pairing correlations on a trapped-ion quantum computer

The Fermi-Hubbard model is the starting point for the simulation of many strongly correlated materials, including high-temperature superconductors, whose modelling is a key motivation for the construction of quantum simulation and computing devices. However, the detection of superconducting pairing correlations has so far remained out of reach, both because of their off-diagonal character - which makes them inaccessible to local density measurements - and because of the difficulty of preparing superconducting states. Here, we report measurement of significant pairing correlations in three different regimes of Fermi-Hubbard models simulated on Quantinuum's Helios trapped-ion quantum computer. Specifically, we measure non-equilibrium pairing induced by an electromagnetic field in the half-filled square lattice model, d-wave pairing in an approximate ground state of the checkerboard Hubbard model at $1/6$-doping, and s-wave pairing in a bilayer model relevant to nickelate superconductors. These results show that a quantum computer can reliably create and probe physically relevant states with superconducting pairing correlations, opening a path to the exploration of superconductivity with quantum computers.

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arXiv2025

Certified randomness amplification by dynamically probing remote random quantum states

Cryptography depends on truly unpredictable numbers, but physical sources emit biased or correlated bits. Quantum mechanics enables the amplification of imperfect randomness into nearly perfect randomness, but prior demonstrations have required physically co-located, loophole-free Bell tests, constraining the feasibility of remote operation. Here we realize certified randomness amplification across a network by dynamically probing large, entangled quantum states on Quantinuum's 98-qubit Helios trapped-ion quantum processor. Our protocol is secure even if the remote device acts maliciously or is compromised by an intercepting adversary, provided the samples are generated quickly enough to preclude classical simulation of the quantum circuits. We stream quantum gates in real time to the quantum processor, maintain quantum state coherence for $\approx 0.9$ seconds, and then reveal the measurement bases to the quantum processor only milliseconds before measurement. This limits the time for classical spoofing to 30 ms and constrains the location of hypothetical adversaries to a $4{,}500$ km radius. We achieve a fidelity of 0.586 on random circuits with 64 qubits and 276 two-qubit gates, enabling the amplification of realistic imperfect randomness with a low entropy rate into nearly perfect randomness.

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arXiv2025

Realization of a Quantum Streaming Algorithm on Long-lived Trapped-ion Qubits

Large classical datasets are often processed in the streaming model, with data arriving one item at a time. In this model, quantum algorithms have been shown to offer an unconditional exponential advantage in space. However, experimentally implementing such streaming algorithms requires qubits that remain coherent while interacting with an external data stream. In this work, we realize such a data-streaming model using Quantinuum Helios trapped-ion quantum computer with long-lived qubits that communicate with an external server. We implement a quantum pair sketch, which is the primitive underlying many quantum streaming algorithms, and use it to solve Hidden Matching, a problem known to exhibit a theoretical exponential quantum advantage in space. Furthermore, we compile the quantum streaming algorithm to fault-tolerant quantum architectures based on surface and bivariate bicycle codes and show that the quantum space advantage persists even with the overheads of fault-tolerance.

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arXiv2025

Certified randomness using a trapped-ion quantum processor

While quantum computers have the potential to perform a wide range of practically important tasks beyond the capabilities of classical computers, realizing this potential remains a challenge. One such task is to use an untrusted remote device to generate random bits that can be certified to contain a certain amount of entropy. Certified randomness has many applications but is fundamentally impossible to achieve solely by classical computation. In this work, we demonstrate the generation of certifiably random bits using the 56-qubit Quantinuum H2-1 trapped-ion quantum computer accessed over the internet. Our protocol leverages the classical hardness of recent random circuit sampling demonstrations: a client generates quantum "challenge" circuits using a small randomness seed, sends them to an untrusted quantum server to execute, and verifies the server's results. We analyze the security of our protocol against a restricted class of realistic near-term adversaries. Using classical verification with measured combined sustained performance of $1.1\times10^{18}$ floating-point operations per second across multiple supercomputers, we certify $71,313$ bits of entropy under this restricted adversary and additional assumptions. Our results demonstrate a step towards the practical applicability of today's quantum computers.

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arXiv2024

Probing critical states of matter on a digital quantum computer

Although quantum mechanics underpins the microscopic behavior of all materials, its effects are often obscured at the macroscopic level by thermal fluctuations. A notable exception is a zero-temperature phase transition, where scaling laws emerge entirely due to quantum correlations over a diverging length scale. The accurate description of such transitions is challenging for classical simulation methods of quantum systems, and is a natural application space for quantum simulation. These quantum simulations are, however, not without their own challenges \textemdash~representing quantum critical states on a quantum computer requires encoding entanglement of a large number of degrees of freedom, placing strict demands on the coherence and fidelity of the computer's operations. Using Quantinuum's H1-1 quantum computer, we address these challenges by employing hierarchical quantum tensor-network techniques, creating the ground state of the critical transverse-field Ising chain on 128-sites with sufficient fidelity to extract accurate critical properties of the model. Our results suggest a viable path to quantum-assisted tensor network contraction beyond the limits of classical methods.

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arXiv2024

Experiments with the 4D Surface Code on a QCCD Quantum Computer

Single-shot quantum error correction has the potential to speed up quantum computations by removing the need for multiple rounds of syndrome extraction in order to be fault-tolerant. Using Quantinuum's H2 trapped-ion quantum computer, we implement the [[33,1,4]] 4D surface code and perform the first experimental demonstration of single-shot quantum error correction with bare ancilla qubits. We conduct memory experiments comparing the 2D and 4D surface codes and find that despite differences in qubit use and syndrome extraction circuit depth, the 4D surface code matches or outperforms the 2D surface code in both the fault-tolerant and single-shot regimes.

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arXiv2024

Demonstration of quantum computation and error correction with a tesseract code

A critical milestone for quantum computers is to demonstrate fault-tolerant computation that outperforms computation on physical qubits. The tesseract subsystem color code protects four logical qubits in 16 physical qubits, to distance four. Using the tesseract code on Quantinuum's trapped-ion quantum computers, we prepare high-fidelity encoded graph states on up to 12 logical qubits, beneficially combining for the first time fault-tolerant error correction and computation. We also protect encoded states through up to five rounds of error correction. Using performant quantum software and hardware together allows moderate-depth logical quantum circuits to have an order of magnitude less error than the equivalent unencoded circuits.

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arXiv2024

Qutrit Toric Code and Parafermions in Trapped Ions

The development of programmable quantum devices can be measured by the complexity of manybody states that they are able to prepare. Among the most significant are topologically ordered states of matter, which enable robust quantum information storage and processing. While topological orders are more readily accessible with qudits, experimental realisations have thus far been limited to lattice models of qubits. Here, we prepare a ground state of the Z3 toric code state on 24 qutrits in a trapped ion quantum processor with fidelity per qutrit exceeding 96.5(3)%. We manipulate two types of defects which go beyond the conventional qubit toric code: a parafermion, and its bound state which is related to charge conjugation symmetry. We further demonstrate defect fusion and the transfer of entanglement between anyons and defects, which we use to control topological qutrits. Our work opens up the space of long-range entangled states with qudit degrees of freedom for use in quantum simulation and universal error-correcting codes.

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arXiv2024

The computational power of random quantum circuits in arbitrary geometries

Empirical evidence for a gap between the computational powers of classical and quantum computers has been provided by experiments that sample the output distributions of two-dimensional quantum circuits. Many attempts to close this gap have utilized classical simulations based on tensor network techniques, and their limitations shed light on the improvements to quantum hardware required to frustrate classical simulability. In particular, quantum computers having in excess of $\sim 50$ qubits are primarily vulnerable to classical simulation due to restrictions on their gate fidelity and their connectivity, the latter determining how many gates are required (and therefore how much infidelity is suffered) in generating highly-entangled states. Here, we describe recent hardware upgrades to Quantinuum's H2 quantum computer enabling it to operate on up to $56$ qubits with arbitrary connectivity and $99.843(5)\%$ two-qubit gate fidelity. Utilizing the flexible connectivity of H2, we present data from random circuit sampling in highly connected geometries, doing so at unprecedented fidelities and a scale that appears to be beyond the capabilities of state-of-the-art classical algorithms. The considerable difficulty of classically simulating H2 is likely limited only by qubit number, demonstrating the promise and scalability of the QCCD architecture as continued progress is made towards building larger machines.

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arXiv2024

Evidence of Scaling Advantage for the Quantum Approximate Optimization Algorithm on a Classically Intractable Problem

The quantum approximate optimization algorithm (QAOA) is a leading candidate algorithm for solving optimization problems on quantum computers. However, the potential of QAOA to tackle classically intractable problems remains unclear. Here, we perform an extensive numerical investigation of QAOA on the low autocorrelation binary sequences (LABS) problem, which is classically intractable even for moderately sized instances. We perform noiseless simulations with up to 40 qubits and observe that the runtime of QAOA with fixed parameters scales better than branch-and-bound solvers, which are the state-of-the-art exact solvers for LABS. The combination of QAOA with quantum minimum finding gives the best empirical scaling of any algorithm for the LABS problem. We demonstrate experimental progress in executing QAOA for the LABS problem using an algorithm-specific error detection scheme on Quantinuum trapped-ion processors. Our results provide evidence for the utility of QAOA as an algorithmic component that enables quantum speedups.

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arXiv2024

Benchmarking logical three-qubit quantum Fourier transform encoded in the Steane code on a trapped-ion quantum computer

We implement logically encoded three-qubit circuits for the quantum Fourier transform (QFT), using the [[7,1,3]] Steane code, and benchmark the circuits on the Quantinuum H2-1 trapped-ion quantum computer. The circuits require multiple logical two-qubit gates, which are implemented transversally, as well as logical non-Clifford single-qubit rotations, which are performed by non-fault-tolerant state preparation followed by a teleportation gadget. First, we benchmark individual logical components using randomized benchmarking for the logical two-qubit gate, and a Ramsey-type experiment for the logical $T$ gate. We then implement the full QFT circuit, using two different methods for performing a logical control-$T$, and benchmark the circuits by applying it to each basis state in a set of bases that is sufficient to lower bound the process fidelity. We compare the logical QFT benchmark results to predictions based on the logical component benchmarks.

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arXiv2023

Fault-Tolerant One-Bit Addition with the Smallest Interesting Colour Code

Fault-tolerant operations based on stabilizer codes are the state of the art in suppressing error rates in quantum computations. Most such codes do not permit a straightforward implementation of non-Clifford logical operations, which are necessary to define a universal gate set. As a result, implementations of these operations must either use error-correcting codes with more complicated error correction procedures or gate teleportation and magic states, which are prepared at the logical level, increasing overhead to a degree that precludes near-term implementation. In this work, we implement a small quantum algorithm, one-qubit addition, fault-tolerantly on the Quantinuum H1-1 quantum computer, using the [[8,3,2]] colour code. By removing unnecessary error-correction circuits and using low-overhead techniques for fault-tolerant preparation and measurement, we reduce the number of error-prone two-qubit gates and measurements to 36. We observe arithmetic errors with a rate of $\sim 1.1 \times 10^{-3}$ for the fault-tolerant circuit and $\sim 9.5 \times 10^{-3}$ for the unencoded circuit.

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arXiv2023

Topological Order from Measurements and Feed-Forward on a Trapped Ion Quantum Computer

Quantum systems evolve in time in one of two ways: through the Schrödinger equation or wavefunction collapse. So far, deterministic control of quantum many-body systems in the lab has focused on the former, due to the probabilistic nature of measurements. This imposes serious limitations: preparing long-range entangled states, for example, requires extensive circuit depth if restricted to unitary dynamics. In this work, we use mid-circuit measurement and feed-forward to implement deterministic non-unitary dynamics on Quantinuum's H1 programmable ion-trap quantum computer. Enabled by these capabilities, we demonstrate for the first time a constant-depth procedure for creating a toric code ground state in real-time. In addition to reaching high stabilizer fidelities, we create a non-Abelian defect whose presence is confirmed by transmuting anyons via braiding. This work clears the way towards creating complex topological orders in the lab and exploring deterministic non-unitary dynamics via measurement and feed-forward.

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