arXiv subjects

Aaron Hankin

Publications and source records attributed to Aaron Hankin.

12 recordsLinked to original sources

arXiv2026

Automated Flag-based Fault-Tolerant State Preparation using Integer Linear Programming

Post-selected stabilizer state preparation is a necessary subroutine in fault-tolerant quantum computation, both for initialization of logical qubits, and for logical-ancilla-based error correction gadgets (e.g. Steane and Knill). Therefore, reducing the number of gates needed to prepare a stabilizer state fault-tolerantly can simultaneously reduce time-to-solution and increase reliability. For small, low-distance codes such as the [[7, 1, 3]] Steane code, circuits with low gate counts can be found by inspection. This becomes impractical for larger codes, necessitating automation. There are two state-of-the-art methods for automated fault-tolerant state preparation, SAT-based stabilizer measurement and flag-at-origin. In this work, we optimize state preparation circuits using the circuit gauge operator formalism to express the construction of flag circuits as an integer linear program. This allows the construction of circuits with equal or lower gate count than the state of the art, while detecting up to three errors. We use this technique to derive a Steane error correction gadget for the [[24, 10, 4]] two-block group algebra code, and test it on Quantinuum's System Model H2 quantum computer with 10,000 shots, resulting in a logical block error rate ~0.00014 (~0.000014 per logical qubit), with ~1.6% of the shots post-selected due to weight-two errors.

quant-ph↗

arXiv2025

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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arXiv2025

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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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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arXiv2023

Theory of mirror benchmarking and demonstration on a quantum computer

A new class of protocols called mirror benchmarking was recently proposed to measure the system-level performance of quantum computers. These protocols involve circuits with random sequences of gates followed by mirroring, that is, inverting each gate in the sequence. We give a simple proof that mirror benchmarking leads to an exponential decay of the survival probability with sequence length, under the uniform noise assumption, provided the twirling group forms a 2-design. The decay rate is determined by a quantity that is a quadratic function of the error channel, and for certain types of errors is equal to the unitarity. This result yields a new method for estimating the coherence of noise. We present data from mirror benchmarking experiments run on the Honeywell System Model H1. This data constitutes a set of performance curves, indicating the success probability for random circuits as a function of qubit number and circuit depth.

quant-ph↗

arXiv2023

Experimental demonstration of the advantage of adaptive quantum circuits

Adaptive quantum circuits employ unitary gates assisted by mid-circuit measurement, classical computation on the measurement outcome, and the conditional application of future unitary gates based on the result of the classical computation. In this paper, we experimentally demonstrate that even a noisy adaptive quantum circuit of constant depth can achieve a task that is impossible for any purely unitary quantum circuit of identical depth: the preparation of long-range entangled topological states with high fidelity. We prepare a particular toric code ground state with fidelity of at least $76.9\pm 1.3\%$ using a constant depth ($d=4$) adaptive circuit, and rigorously show that no unitary circuit of the same depth and connectivity could prepare this state with fidelity greater than $50\%$.

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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 Schr\"odinger 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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arXiv2022

Characterizing a non-equilibrium phase transition on a quantum computer

At transitions between phases of matter, physical systems can exhibit universal behavior independent of their microscopic details. Probing such behavior in quantum many-body systems is a challenging and practically important problem that can be solved by quantum computers, potentially exponentially faster than by classical computers. In this work, we use the Quantinuum H1-1 quantum computer to realize a quantum extension of a simple classical disease spreading process that is known to exhibit a non-equilibrium phase transition between an active and absorbing state. Using techniques such as qubit-reuse and error avoidance based on real-time conditional logic (utilized extensively in quantum error correction), we are able to implement large instances of the model with $73$ sites and up to $72$ circuit layers, and quantitatively determine the model's critical properties. This work demonstrates how quantum computers capable of mid-circuit resets, measurements, and conditional logic enable the study of difficult problems in quantum many-body physics: the simulation of open quantum system dynamics and non-equilibrium phase transitions.

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arXiv2021

Realizing a dynamical topological phase in a trapped-ion quantum simulator

Nascent platforms for programmable quantum simulation offer unprecedented access to new regimes of far-from-equilibrium quantum many-body dynamics in (approximately) isolated systems. Here, achieving precise control over quantum many-body entanglement is an essential task for quantum sensing and computation. Extensive theoretical work suggests that these capabilities can enable dynamical phases and critical phenomena that exhibit topologically-robust methods to create, protect, and manipulate quantum entanglement that self-correct against large classes of errors. However, to date, experimental realizations have been confined to classical (non-entangled) symmetry-breaking orders. In this work, we demonstrate an emergent dynamical symmetry protected topological phase (EDSPT), in a quasiperiodically-driven array of ten $^{171}\text{Yb}^+$ hyperfine qubits in Honeywell's System Model H1 trapped-ion quantum processor. This phase exhibits edge qubits that are dynamically protected from control errors, cross-talk, and stray fields. Crucially, this edge protection relies purely on emergent dynamical symmetries that are absolutely stable to generic coherent perturbations. This property is special to quasiperiodically driven systems: as we demonstrate, the analogous edge states of a periodically driven qubit-array are vulnerable to symmetry-breaking errors and quickly decohere. Our work paves the way for implementation of more complex dynamical topological orders that would enable error-resilient techniques to manipulate quantum information.

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arXiv2021

Holographic dynamics simulations with a trapped ion quantum computer

Quantum computers have the potential to efficiently simulate the dynamics of many interacting quantum particles, a classically intractable task of central importance to fields ranging from chemistry to high-energy physics. However, precision and memory limitations of existing hardware severely limit the size and complexity of models that can be simulated with conventional methods. Here, we demonstrate and benchmark a new scalable quantum simulation paradigm--holographic quantum dynamics simulation--which uses efficient quantum data compression afforded by quantum tensor networks along with opportunistic mid-circuit measurement and qubit reuse to simulate physical systems that have far more quantum degrees of freedom than can be captured by the available number of qubits. Using a Honeywell trapped ion quantum processor, we simulate the non-integrable (chaotic) dynamics of the self-dual kicked Ising model starting from an entangled state of $32$ spins using at most $9$ trapped ion qubits, obtaining excellent quantitative agreement when benchmarking against dynamics computed directly in the thermodynamic limit via recently developed exact analytical techniques. These results suggest that quantum tensor network methods, together with state-of-the-art quantum processor capabilities, enable a viable path to practical quantum advantage in the near term.

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arXiv2018

An experiment on multiple pathway quantum interference for the advanced undergraduate physics laboratory

We present results on a multiple-optical-path quantum interference project suitable for the advanced undergraduate laboratory. The experiments combine a conceptually rich set of atomic physics experiments which may be economically developed at a technical level accessible to undergraduate physics or engineering majors. In the experiments, diode-laser driven two-quantum, two-color excitation of cesium atoms in a vapor cell is investigated and relative strengths of the individual hyperfine components in the $6s^{2}S_{1/2} \rightarrow 7s^{2}S_{1/2}$ transition are determined. Measurement and analysis of the spectral variation of the two quantum excitation rate clearly shows strong variations due to interfering amplitudes in the overall transition amplitude. Projects such as the one reported here allow small teams of undergraduate students with combined interests in experimental and theoretical physics to construct instrumentation, perform sophisticated experiments, and do realistic modelling of the results.

physics.ed-ph↗

arXiv2015

Robust quantum logic in neutral atoms via adiabatic Rydberg dressing

We study a scheme for implementing a controlled-Z (CZ) gate between two neutral-atom qubits based on the Rydberg blockade mechanism in a manner that is robust to errors caused by atomic motion. By employing adiabatic dressing of the ground electronic state, we can protect the gate from decoherence due to random phase errors that typically arise because of atomic thermal motion. In addition, the adiabatic protocol allows for a Doppler-free configuration that involves counterpropagating lasers in a $σ_+/σ_-$ orthogonal polarization geometry that further reduces motional errors due to Doppler shifts. The residual motional error is dominated by dipole-dipole forces acting on doubly-excited Rydberg atoms when the blockade is imperfect. For reasonable parameters, with qubits encoded into the clock states of $^{133}$Cs, we predict that our protocol could produce a CZ gate in $<10$ $μ$s with error probability on the order of $10^{-3}$.

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