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DOE OSTI2024

Cross-Cap Defects and Fault-Tolerant Logical Gates in the Surface Code and the Honeycomb Floquet Code

We consider the Z 2 toric code, surface code, and Floquet code defined on a nonorientable surface, which can be considered as families of codes extending Shor’s nine-qubit code. We investigate the fault-tolerant logical gates of the Z 2 toric code in this setup, which corresponds to e ↔ m exchanging symmetry of the underlying Z 2 gauge theory. We find that nonorientable geometry provides a new way for the emergent symmetry to act on the code space, and discover the new realization of the fault-tolerant Hadamard gate of the two-dimensional surface code with a single cross cap connecting the vertices nonlocally along a slit, dubbed a nonorientable surface code. This Hadamard gate can be realized by a constant-depth local unitary circuit modulo nonlocality caused by a cross cap. Via folding, the nonorientable surface code can be turned into a bilayer local quantum code, where the folded cross cap is equivalent to a bilayer twist terminated on a gapped boundary and the logical Hadamard only contains local gates with intralayer couplings when being away from the cross cap, as opposed to the interlayer couplings on each site needed in the case of the folded surface code. We further obtain the complete logical Clifford gate set for a stack of nonorientable surface codes and similarly for codes defined on Klein-bottle geometries. We then construct the honeycomb Floquet code in the presence of a single cross cap, and find that the period of the sequential Pauli measurements acts as a H Z logical gate on the single logical qubit, where the cross cap enriches the dynamics compared with the orientable case. We find that the dynamics of the honeycomb Floquet code is precisely described by a condensation operator of the Z 2 gauge theory, and illustrate the exotic dynamics of our code in terms of a condensation operator supported at a nonorientable surface. Published by the American Physical Society 2024

Physics↗

DOE OSTI2024

Fully Scalable Randomized Benchmarking Without Motion Reversal

We introduce , a protocol that streamlines traditional RB by using circuits consisting almost entirely of independent identically distributed (IID) layers of gates. BiRB reliably and efficiently extracts the average error rate of a Clifford gate set by sending tensor-product eigenstates of random Pauli operators through random circuits with IID layers. Unlike existing RB methods, BiRB does not use motion reversal circuits—i.e., circuits that implement the identity (or a Pauli) operator—which simplifies both the method and the theory proving its reliability. Furthermore, this simplicity enables scaling BiRB to many more qubits than the most widely used RB methods. Published by the American Physical Society 2024

Hines, Jordan (ORCID:0000000151267256)↗

DOE OSTI2025

Generalized Cycle Benchmarking Algorithm for Characterizing Midcircuit Measurements

Midcircuit measurements (MCMs) are crucial ingredients in the development of fault-tolerant quantum computation. While there have been rapid experimental progresses in realizing MCMs, a systematic method for characterizing noisy MCMs is still under exploration. In this work, we develop a cycle benchmarking (CB)-type algorithm to characterize noisy MCMs. The key idea is to use a joint Fourier transform on the classical and quantum registers and then estimate parameters in the Fourier space, analogous to Pauli fidelities used in CB-type algorithms for characterizing the Pauli-noise channel of Clifford gates. Furthermore, we develop a theory of the noise learnability of MCMs, which determines what information can be learned about the noise model (in the presence of state preparation and terminating measurement noise) and what cannot, which shows that all learnable information can be learned using our algorithm. As an application, we show how to use the learned information to test the independence between measurement noise and state-preparation noise in an MCM. Finally, we conduct numerical simulations to illustrate the practical applicability of the algorithm. Similar to other CB-type algorithms, we expect the algorithm to provide a useful toolkit that is of experimental interest. Published by the American Physical Society 2025

Zhang, Zhihan (ORCID:0009000862907691)↗

DOE OSTI2025

High-Power Clock Laser Spectrally Tailored for High-Fidelity Quantum State Engineering

Highly frequency-stable lasers are ubiquitous tools for optical-frequency metrology, precision interferometry, and quantum information science. While making a universally applicable laser is unrealistic, spectral noise can be tailored for specific applications. Here we report a high-power 698-nm clock laser with a maximum output of 4W and minimized frequency noise up to a few kHz Fourier frequency, together with long-term instability of 3.5 × 10 −17 at one to thousands of seconds. The laser-frequency noise is precisely characterized with atom-based spectral analysis that employs a pulse sequence designed to suppress sensitivity to intensity noise. This method provides universally applicable tunability of the spectral response and analysis of quantum sensors over a wide frequency range. With the optimized laser system characterized by this technique, we achieve an average single-qubit Clifford gate fidelity of up to 𝐹$^2_1$ = 0.999⁢64⁢(3) when simultaneously driving 3000 optical qubits with a homogeneous Rabi frequency ranging from 10 Hz to 1 kHz. This result represents the highest single optical-qubit-gate fidelity for a large number of atoms.

atomic gases↗

DOE OSTI2023

TISCC: A Surface Code Compiler and Resource Estimator for Trapped-Ion Processors

We introduce the Trapped-Ion Surface Code Compiler (TISCC), a software tool that generates circuits for a universal set of surface code patch operations in terms of a native trapped-ion gate set. To accomplish this, TISCC manages an internal representation of a trapped-ion system where a repeating pattern of trapping zones and junctions is arranged in an arbitrarily large rectangular grid. Surface code operations are compiled by instantiating surface code patches on the grid and using methods to generate transversal operations over data qubits, rounds of error correction over stabilizer plaquettes, and/or lattice surgery operations between neighboring patches. Beyond the implementation of a basic surface code instruction set, TISCC contains corner movement functionality and a patch translation that is implemented using ion movement alone. Except in the latter case, all TISCC functionality is extensible to alternative grid-like hardware architectures. TISCC output has been verified using the Oak Ridge Quasi-Clifford Simulator (ORQCS).

LeBlond, Tyler↗

DOE OSTI2024

ORNL-QCI/TISCC

LeBlond, Tyler↗

DOE OSTI2024

Inexpensive and durable aerogel-based VIP cores

The goal of this project was development of low-cost aerogels to be used as cores of Vacuum Insulated Panels (VIP). The specific aims were: 1. Aerogels to be based on phenolic chemistry to minimize flammability. 2. Aerogels to be in monolithic form and to have mechanical properties sufficient to allow their use as cores of VIPs without collapsing after evacuation. 3. Aerogels to have a cost per kg lower than the cost of fumed silica, one of the most common VIP cores. The achievements are: 1. Phenolic aerogels have been fabricated in monolithic form with thermal conductivity of 0.023 W/m·K, density ~ 0.25 g/cm 3 and a modulus of compression > 10 MPa. The aerogels can withstand the stresses of VIP evacuation without any appreciable deformation. 2. Drying of aerogels was carried in the initial stages of the project via sublimation of frozen solvents, following the procedure described in M. F. Bertino and T. Selden, “Fabrication of Aerogels and Aerogel Composites by Ambient Pressure Sublimation of Frozen Solvents”, PCT/US20/39485. Monoliths as large as 30 x 30 x 2 cm can be fabricated with the proprietary ambient fabrication technique which are free of cracks and warping. 3. Cost analysis was carried out and refined multiple times, cost drivers were identified, and the fabrication procedure was streamlined. Our cost model yields an aerogel cost of $\$$5.78/kg, which compares well with the price of fumed silica ($\$$6.2/kg FOB New York as of March 2023). 4. The monoliths can be cut into custom shapes and used as VIP cores. Cores fabricated with our technique have a thermal conductivity λ = 0.011 W/m·K at a pressure >10 mbar. 5. A variant of the technology yielded fireproof materials, described in M. F. Bertino, T. Moon, G. Waller, J. Ko and D. Clifford, “Fireproof thermal insulation”, Provisional Patent Application 63/415,386. 6. A spin-off company was created (ThermaGel Innovations, Inc.) which licensed technologies developed under this award. PI Bertino is a board member of the newco which is now raising capital to build a pilot plant.

36 MATERIALS SCIENCE↗

DOE OSTI2022

Mitiq: A software package for error mitigation on noisy quantum computers

We introduce Mitiq, a Python package for error mitigation on noisy quantum computers. Error mitigation techniques can reduce the impact of noise on near-term quantum computers with minimal overhead in quantum resources by relying on a mixture of quantum sampling and classical post-processing techniques. Mitiq is an extensible toolkit of different error mitigation methods, including zero-noise extrapolation, probabilistic error cancellation, and Clifford data regression. The library is designed to be compatible with generic backends and interfaces with different quantum software frameworks. We describe Mitiq using code snippets to demonstrate usage and discuss features and contribution guidelines. We present several examples demonstrating error mitigation on IBM and Rigetti superconducting quantum processors as well as on noisy simulators.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

NoRA: A Tensor Network Ansatz for Volume-Law Entangled Equilibrium States of Highly Connected Hamiltonians

Motivated by the ground state structure of quantum models with all-to-all interactions such as mean-field quantum spin glass models and the Sachdev-Ye-Kitaev (SYK) model, we propose a tensor network architecture which can accomodate volume law entanglement and a large ground state degeneracy. We call this architecture the non-local renormalization ansatz (NoRA) because it can be viewed as a generalization of MERA, DMERA, and branching MERA networks with the constraints of spatial locality removed. We argue that the architecture is potentially expressive enough to capture the entanglement and complexity of the ground space of the SYK model, thus making it a suitable variational ansatz, but we leave a detailed study of SYK to future work. We further explore the architecture in the special case in which the tensors are random Clifford gates. Here the architecture can be viewed as the encoding map of a random stabilizer code. We introduce a family of codes inspired by the SYK model which can be chosen to have constant rate and linear distance at the cost of some high weight stabilizers. We also comment on potential similarities between this code family and the approximate code formed from the SYK ground space.

Physics↗

DOE OSTI2025

Improving the efficiency of learning-based error mitigation

Error mitigation will play an important role in practical applications of near-term noisy quantum computers. Current error mitigation methods typically concentrate on correction quality at the expense of frugality (as measured by the number of additional calls to quantum hardware). To fill the need for highly accurate, yet inexpensive techniques, we introduce an error mitigation scheme that builds on Clifford data regression (CDR). The scheme improves the frugality by carefully choosing the training data and exploiting the symmetries of the problem. We test our approach by correcting long range correlators of the ground state of XY Hamiltonian on IBM Toronto quantum computer. We find that our method is an order of magnitude cheaper while maintaining the same accuracy as the original CDR approach. The efficiency gain enables us to obtain a factor of 10 improvement on the unmitigated results with the total budget as small as 2 ⋅ 10 5 shots. Furthermore, we demonstrate orders of magnitude improvements in frugality for mitigation of energy of the LiH ground state simulated with IBM's Ourense-derived noise model.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Dual-unitary shadow tomography

We introduce a classical shadow tomography scheme based on dual-unitary brick-wall circuits termed "dual-unitary shadow tomography" (DUST). For this we study operator spreading and Pauli weight dynamics in one-dimensional qubit systems, evolved by random two-local dual-unitary gates arranged in a brick-wall structure, ending with a final measurement layer. We do this by deriving general constraints on the Pauli weight transfer matrix and specializing to the case of dual-unitarity. We first show that dual-unitaries must have a minimal amount of entropy production. Remarkably, we find that operator spreading in these circuits have a rich structure resembling that of relativistic quantum field theories, with massless chiral excitations that can decay or fuse into each other, which we call left- or right-movers. We develop a mean-field description of the Pauli weight in terms of $\rho(x,t)$, which represents the probability of having nontrivial support at site $x$ and depth $t$ starting from a fixed weight distribution. We develop an equation of state for $\rho(x,t)$, and simulate it numerically using Monte Carlo simulations. Lastly, we demonstrate that the fast-thermalizing properties of dual-unitary circuits make them better at predicting large operators than shallow brick-wall Clifford circuits. Our results are robust to finite-size effects due to the chirality of dual-unitary brick-wall circuits.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Instability of steady-state mixed-state symmetry-protected topological order to strong-to-weak spontaneous symmetry breaking

Recent experimental progress in controlling open quantum systems enables the pursuit of mixed-state nonequilibrium quantum phases. We investigate whether open quantum systems hosting mixed-state symmetry-protected topological states as steady states retain this property under symmetric perturbations. Focusing on the decohered cluster state – a mixed-state symmetry-protected topological state protected by a combined strong and weak symmetry – we construct a parent Lindbladian that hosts it as a steady state. This Lindbladian can be mapped onto exactly solvable reaction-diffusion dynamics, even in the presence of certain perturbations, allowing us to solve the parent Lindbladian in detail and reveal previously-unknown steady states. Using both analytical and numerical methods, we find that typical symmetric perturbations cause strong-to-weak spontaneous symmetry breaking at arbitrarily small perturbations, destabilize the steady-state mixed-state symmetry-protected topological order. However, when perturbations introduce only weak symmetry defects, the steady-state mixed-state symmetry-protected topological order remains stable. Additionally, we construct a quantum channel which replicates the essential physics of the Lindbladian and can be efficiently simulated using only Clifford gates, Pauli measurements, and feedback.

Shah, Jeet [University of Maryland, College Park, ↗

NASA NTRS1977

Modelling the effects of turbulence on acoustic wave propagation

A review of recent theoretical modeling of the effects of turbulence on acoustic wave propagation is presented. The Born approximation limit of the smoothing method of Keller and of the kinetic theory method of Howe are compared with the classical perturbation results of Chernov. Secular growth is observed in the higher order terms of the kinetic theory method of Howe when multiple scaling is ignored. The forward propagation - beam broadening model of Brown and Clifford is discussed as well as the single scatter model of DeLoach and of Rudd. Each model is examined with respect to its prediction of conservation of energy.

Harris, W. L.↗

NASA NTRS1979

Atmospheric turbulence effects on aircraft noise propagation

The Brown and Clifford model for the apparent sound attenuation cuased by atmospheric turbulence was reviewed and extended. Calculations, based on the model, were made for the predicted sound attenuation for a tower-mounted loudspeaker-type sound source and for an airplane sound source. The important parameters in the model are identified and discussed. A model for sound fluctuations is also presented and a practical experimental program to validate the models described.

Chapkis, R. L.↗

NASA NTRS1986

Injection of dust into the Martian atmosphere - Evidence from the Viking Gas Exchange experiment

The hypothesis that predawn midlatitude storms are triggered by a soil humidification process is examined. A freeze/thaw model of the process is evaluated in the Viking Gas Exchange experiments conducted on Mars. The humidification-driven desorption and desiccation state of Martian soil samples are analyzed. The periodic humidification of equatorial regolith soil is studied in terms of pore space pressure during desorption events and soil diffusivity; the thermal properties of the regolith surface layer are modeled using the program of Clifford (1984). Consideration is given to the diurnal and seasonal cycles of the humidification process, the permanent, low-albedo features in the midlatitudes, and the production of H2SO4 and HCl aerosols.

Huguenin, R. L.↗

NASA NTRS1991

Heterodyne Doppler 1-micron lidar measurement of reduced effective telescope aperture due to atmospheric turbulence

A pulsed Nd:YAG bistatic focused-beam lidar allowing simultaneous heterodyne and direct detection of the same lidar returns has been experimentally employed to ascertain the effect of atmospheric turbulence on heterodyne and direct-detection lidar at 1 micron, by measuring the average carrier-to-noise ratio and statistical fluctuation level in the return signals under various experimental and atmospheric conditions. Atmospheric turbulence is found capable of reducing the lidar receiver's effective telescope aperture and heterodyne detection efficiency. This observed effective-aperture limitation functionally resembles predictions based on the Clifford and Wandzura (1981) heterodyne wavefront detection theory.

Chan, Kin Pui↗

NASA NTRS1993

On harmonic oscillators and their Kemmer relativistic forms

It is shown that Dirac (Kemmer) equations are intimately connected with (para)supercharges coming from (para)supersymmetric quantum mechanics, a nonrelativistic theory. The dimensions of the irreducible representations of Clifford (Kemmer) algebras play a fundamental role in such an analysis. These considerations are illustrated through oscillator like interactions, leading to (para)relativistic oscillators.

Debergh, Nathalie↗

NASA NTRS1993

Equatorial ground ice on Mars: Steady-state stability

Current Martian equatorial surface temperatures are too warm for water ice to exist at the surface for any appreciable length of time before subliming into the atmosphere. Subsurface temperatures are generally warmer still and, despite the presence of a diffusive barrier of porous regolith material, it has been shown by Smoluchowski, Clifford and Hillel, and Fanale et al. that buried ground ice will also sublime and be lost to the atmosphere in a relatively short time. We investigate the behavior of this subliming subsurface ice and show that it is possible for ice to maintain at a steady-state depth, where sublimation and diffusive loss to the atmosphere is balanced by resupply from beneath by diffusion and recondensation of either a deeper buried ice deposits or ground water. We examine the behavior of equatorial ground ice with a numercial time-marching molecular diffusion model. In our model we allow for diffusion of water vapor through a porous regolith, variations in diffusivity and porosity with ice content, and recondensation of sublimed water vapor. A regolith containing considerable amounts of ice can still be very porous, allowing water vapor to diffuse up from deeper within the ice layer where temperatures are warmer due to the geothermal gradient. This vapor can then recondense nearer to the surface where ice had previously sublimed and been lost to the atmosphere. As a result we find that ice deposits migrate to find a steady-state depth, which represents a balance between diffusive loss to the atmosphere through the overlying porous regolith and diffusive resupply through a porous icy regolith below. This depth depends primarily on the long-term mean surface temperature and the nature of the geothermal gradient, and is independent of the ice-free porosity and the regolith diffusivity. Only the rate of loss of ground ice depends on diffusive properties.

Mellon, Michael T.↗