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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Celestial Quantum Error Correction. Part II. From qudits to celestial CFT

A holographic CFT description of asymptotically flat spacetimes inherits vacuum degeneracies and IR divergences from its gravitational dual. We devise a Quantum Error Correcting (QEC) framework to encode both effects as correctable fluctuations on the CFT dual. The framework is physically motivated by embedding a chain of qudits in the so-called Klein spacetime and then taking a continuum 𝑁 → ∞ limit. At finite 𝑁 the qudit chain 1) enjoys a discrete version of celestial symmetries and 2) supports a Gottesman-Kitaev-Preskill (GKP) code. The limit results in hard states with quantized BMS hair in the celestial torus forming the logical subspace, robust under errors induced by soft radiation. Technically, the construction leverages the recently studied 𝑤 1+∞ hierarchy of soft currents and its realization from a sigma model in twistor space.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Investigating parameter trainability in the SNAP-Displacement protocol of a qudit system.

Our main focus is to investigate the sensitivity of training any of the SNAP parameters in the SNAP-Displacement protocol. We analyze conditions that could potentially lead to the Barren Plateau problem in a qudit system and draw comparisons with multi-qubit systems. The parameterized ansatz we consider consists of SNAP -Displacement blocks. We utilize techniques similar to those in [8] and [2] along with the concept of $t-$design. Through this analysis, we make the following key observations: (a) The trainability of a SNAP-parameter does not exhibit a preference for any particular direction within our cost function landscape, (b) using Haar measure properties, we establish new lemmas concerning the expectation of certain polynomial functions, and (c) utilizing these new lemmas, we identify a general condition that indicates an expected trainability advantage in a qudit system when compared to multi-qubit systems.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Building Qudit-Based Quantum Computing Processors using Superconducting RF Cavities

Superconducting radio frequency (SRF) cavities provide an excellent platform for storing quantum information as quantum d-level systems (qudits) due to their exceptionally long lifetimes and large accessible Hilbert spaces. A common strategy to manipulate the states is to use a nonlinear element like a transmon. There are, however, several challenges to building a 3D SRF architecture while maintaining a long cavity lifetime. We demonstrate our successful integration of transmons with single-cell Nb SRF cavities and the ability to prepare several non-classical states. Finally, we discuss our strategies to improve the coherence times, gate schemes, and extend the system for building a multi-qudit quantum processor.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Qudit-based quantum computing with SRF cavities at Fermilab

Superconducting radio frequency (SRF) cavities provide an excellent platform for storing quantum information as quantum $d$-level systems (qudits) due to their exceptionally long lifetimes and large accessible Hilbert spaces. A common strategy to manipulate the states is to use a nonlinear element like a transmon. There are, however, several challenges to building a 3D SRF architecture while maintaining a long cavity lifetime. We demonstrate our successful integration of transmons with single-cell Nb SRF cavities and the ability to prepare several non-classical states. Finally, we discuss our strategies to improve the coherence times, gate schemes, and extend the system for building a multi-qudit quantum processor.

Roy, Tanay↗
DOE OSTI2024

Qudit Gate Decomposition Dependence for Lattice Gauge Theories

In this work, we investigate the effect of decomposition basis on primitive qudit gates on superconducting radio-frequency cavity-based quantum computers with applications to lattice gauge theory. Three approaches are tested: SNAP & Displacement gates, ECD & single-qubit rotations $R(\theta,\phi)$, and optimal pulse control. For all three decompositions, implementing the necessary sequence of rotations concurrently rather then sequentially can reduce the primitive gate run time. The number of blocks required for the faster ECD &$R_p(\theta)$ is found to scale $\mathcal{O}(d^2)$, while slower SNAP & Displacement set scales at worst $\mathcal{O}(d)$. For qudits with $d<10$, the resulting gate times for the decompositions is similar, but strongly-dependent on experimental design choices. Optimal control can outperforms both decompositions for small $d$ by a factor of 2-12 at the cost of higher classical resources. Lastly, we find that SNAP & Displacement are slightly more robust to a simplified noise model.

Kürkçüoglu, Doga Murat↗
DOE OSTI2026

Sparse Phase Ansatzes for Resource-Efficient Qudit State Preparation via the SNAP-Displacement Protocol

Efficient preparation of nonclassical bosonic states is a central requirement for quantum computing, simulation, and precision metrology. We study resource-efficient quantum state preparation in bosonic qudit systems using the SNAP-displacement (SD) protocol. Existing SD-based approaches typically require a large number of gates and SNAP phases, resulting in complex control pulses with longer ansatz durations and amplified impact of photon-loss and control errors. In this work, we focus on the near- to medium-term regime, in which noisy quantum devices impose trade-offs on the fidelity that can be achieved, which must be taken into account. Specifically, we propose to optimize only a subset of the SNAP phases and introduce three progressively more general sparse ansatzes. To provide fine-grained control and identify the most suitable ansatz for a given target fidelity, we further employ a scalarized multi-objective optimization that trades off fidelity against either the number of phases or the duration of the ansatz. Numerical results for several target states and qudit dimensions up to $d=64$, evaluated through the hypervolume of the Pareto frontiers, show that these sparse ansatzes achieve favorable trade-offs over the fully parameterized SD protocol in both ideal and noisy settings. The advantage is strongest and most consistent when minimizing the number of phases, while improvements in ansatz duration are smaller and more dependent on the target-state family and noise level, suggesting a practical route to more efficient near- and medium-term bosonic state preparation.

Ferrari Dacrema, Maurizio [Milan Polytechnic] (ORC↗
DOE OSTI2026

Noise-Directed Adaptive Remapping for Integer Optimization: from qubits to (encoded) qudits

We extend Noise-Directed Adaptive Remapping (NDAR), a recently proposed heuristic meta-algorithm that leverages device noise as a computational resource, to optimization problems over discrete (integer) domains. While originally introduced for unconstrained binary optimization, the proposed generalization introduces additional gauge degrees of freedom at the logical level, such that the gauge transformation applied at each iteration is no longer unique, allowing tailoring to particular encodings or quantum hardware. We identify encoding-dependent requirements for NDAR beyond binary domains: feasibility of the noise attractor, existence of compatible gauge transformations that preserve an efficiently implementable circuit family, and a systematic way to select the transform to apply at each step. We analyze these criteria for qudit-native and for binary, one-hot, and domain-wall qubit encodings, using the Max-k-colorable subgraph problem as a running example. We demonstrate that these encodings can exhibit distinct advantages and tradeoffs when integrated within the NDAR framework, particularly in how noise-induced dynamics interact with the solution landscape and choice of encoding. Our results indicate that NDAR-guided noise considerations provide a new criterion for comparing device-level encoding choices for quantum optimization. Finally, we outline directions toward experimental realization in superconducting qudit devices and further algorithmic improvements.

Hadfield, Stuart [RIACS, Mtn. View] (ORCID:0000000↗
DOE OSTI2026

Spontaneously Broken Noninvertible Symmetries in Transverse-Field Ising Qudit Chains

Recent developments have revealed that symmetries need not form a group, but instead can be noninvertible. Here we use analytical arguments and numerical evidence to illuminate how spontaneous symmetry breaking of a noninvertible symmetry is similar yet distinct from ordinary, invertible, symmetry breaking. We consider one-dimensional chains of group-valued qudits, whose local Hilbert space is spanned by elements of a finite group 𝐺 (reducing to ordinary qubits when 𝐺=ℤ 2 ). We construct Ising-type transverse-field Hamiltonians with Rep⁡(𝐺) symmetry whose generators multiply according to the tensor product of irreducible representations (irreps) of the group 𝐺 . For non-Abelian 𝐺 , the symmetry is noninvertible. In the symmetry broken phase there is one ground state per irrep on a closed chain. The symmetry breaking can be detected by local order parameters but, unlike the invertible case, different ground states have distinct entanglement patterns. We show that for each irrep of dimension greater than one the corresponding ground state exhibits string order, entanglement spectrum degeneracies, and has gapless edge modes on an open chain—features usually associated with symmetry-protected topological order. Consequently, domain wall excitations behave as one-dimensional non-Abelian anyons with nontrivial internal Hilbert spaces and fusion rules. Our Letter identifies properties of noninvertible symmetry breaking that existing quantum hardware can probe.

1-dimensional spin chains↗
DOE OSTI2025

Charge-Transfer States Enable Spin-Selective Formation of Quartet State Qudits in Luminescent Radical-Chromophore Dyads

Luminescent tris(2,4,6-trichlorophenyl)methyl (TTM) radicals are promising doublet emitters that have been used to generate spin-optical interfaces in molecular electron spin qudits. In particular, photoexcitation of covalent TTM-chromophore dyads can generate quartet spin states that can be detected via photoluminescence. However, the mechanism of quartet spin initialization is complicated by competing charge-transfer (CT) and energy-transfer (EnT) pathways between the radical and the chromophore. Here, we demonstrate the role of CT intermediates by engineering a covalent dyad of TTM and naphthalene-(1,4:5,8)-bis(dicarboximide) (NDI), a well-known electron acceptor chromophore. Transient absorption spectroscopy indicates that photoexcitation of TTM results in ultrafast electron transfer from 2* TTM to NDI, which kinetically outcompetes EnT. Electron paramagnetic resonance spectroscopy reveals that charge recombination proceeds via spin–orbit charge-transfer intersystem crossing to generate 3* NDI, followed by spin mixing with 2TTM to form the quartet state. Furthermore, this process uniquely spin-polarizes the quartet state, providing fundamental design principles to purify the initial wave function for quantum information processing.

Charge transfer↗
DOE OSTI2025

Schrödinger cat states of a nuclear spin qudit in silicon

High-dimensional quantum systems are a valuable resource for quantum information processing. They can be used to encode error-correctable logical qubits, which has been demonstrated using continuous-variable states in microwave cavities or the motional modes of trapped ions. For example, high-dimensional systems can be used to realize ‘Schrödinger cat’ states, which are superpositions of widely displaced coherent states that can be used to illustrate quantum effects at large scales. Recent proposals have suggested encoding qubits in high-spin atomic nuclei, which are finite-dimensional systems that can host hardware-efficient versions of continuous-variable codes. Here, in this study, we demonstrate the creation and manipulation of Schrödinger cat states using the spin-7/2 nucleus of an antimony atom embedded in a silicon nanoelectronic device. We use a multi-frequency control scheme to produce spin rotations that preserve the symmetry of the qudit, and we constitute logical Pauli operations for qubits encoded in the Schrödinger cat states. Our work demonstrates the ability to prepare and control non-classical resource states, which is a prerequisite for applications in quantum information processing and quantum error correction, using our scalable, manufacturable semiconductor platform.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Toward quantum networking with frequency-bin qudits

Quantum networking holds tremendous promise in transforming computation and communication. Entangled-photon sources are critical for quantum repeaters and networking, while photonic integrated circuits are vital for miniaturization and scalability. In this talk, we focus on generating and manipulating frequency-bin entangled states within integrated platforms. We encode quantum information as a coherent superposition of multiple optical frequencies; this approach is favorable due to its amenability to high-dimensional entanglement and compatibility with fiber transmission. We successfully generate and measure the density matrix of biphoton frequency combs from integrated silicon nitride microrings, fully reconstructing the state in an 8 × 8 two-qudit Hilbert space, the highest so far for frequency bins. Moreover, we employ Vernier electro-optic phase modulation methods to perform time-resolved measurements of biphoton correlation functions. Currently, we are exploring bidirectional pumping of microrings to generate indistinguishable entangled pairs in both directions, aiming to demonstrate key networking operations such as entanglement swapping and Greenberger–Horne–Zeilinger state generation in the frequency domain.

Myilswamy, Karthik V.↗
DOE OSTI2025

Ultracoherent SRF Cavity-Based Multi-Qudit Platform with Error-Resilient Control

Superconducting radio-frequency (SRF) cavities offer a promising platform for quantum computing due to their long coherence times, yet integrating nonlinear elements like transmons for control often introduces additional loss. We report a multimode quantum system based on a 2-cell elliptical shaped SRF cavity, comprising two cavity modes weakly coupled to an ancillary transmon circuit, designed to preserve coherence while enabling efficient control of the cavity modes. We mitigate the detrimental effects of the transmon decoherence through careful design optimization that reduces transmon-cavity couplings and participation in the dielectric substrate and lossy interfaces, to achieve single-photon lifetimes of 20.6\,ms and 15.6\,ms for the two modes, and a pure dephasing time exceeding 40\,ms. This marks an order-of-magnitude improvement over prior 3D multimode memories. Leveraging sideband interactions and novel error-resilient protocols, including measurement-based correction and post-selection, we achieve high-fidelity control over quantum states. This enables the preparation of Fock states up to $N = 20$ with fidelities exceeding 95\%, the highest reported to date to the authors' knowledge, as well as two-mode entanglement with an estimated coherence-limited fidelities of 99.9\% after post-selection. These results establish our platform as a robust foundation for quantum information processing, allowing for future extensions to high-dimensional qudit encodings.

Kim, T. [Northwestern U.]↗
DOE OSTI2025

Parametric and Robustness Studies of Qudit Mediated Quantum State Transfer and Entanglement Creation

The large number of available states participating in quantum state evolution in a system of qudits translates into better thermal resilience, for quantum state transfer (QST) and distributed entangled states, than a system of 2-level qubits. In this report we study the dependence of fidelities of the above processes on various system parameters. Sensitivity to modes of dissipation and errors is also studied. An alternative and potentially more efficient scheme to create Bell states is used.

Chao, Yu-Chiu [Fermilab] (ORCID:000900039584159X)↗
DOE OSTI2025

Fast Machine Learning for Quantum Control of Microwave Qudits on Edge Hardware

Quantum optimal control is a promising approach to improve the accuracy of quantum gates, but it relies on complex algorithms to determine the best control settings. CPU or GPU-based approaches often have delays that are too long to be applied in practice. It is paramount to have systems with extremely low delays to quickly and with high fidelity adjust quantum hardware settings, where fidelity is defined as overlap with a target quantum state. Here, we utilize machine learning (ML) models to determine control-pulse parameters for preparing Selective Number-dependent Arbitrary Phase (SNAP) gates in microwave cavity qudits, which are multi-level quantum systems that serve as elementary computation units for quantum computing. The methodology involves data generation using classical optimization techniques, ML model development, design space exploration, and quantization for hardware implementation. Our results demonstrate the efficacy of the proposed approach, with optimized models achieving low gate trace infidelity near $10^{-3}$ and efficient utilization of programmable logic resources.

Sanders, Flor [Columbia U.]↗
DOE OSTI2025

Near-Term Application Engineering Challenges in Emerging Superconducting Qudit Processors

We review the prospects to build quantum processors based on superconducting transmons and radiofrequency cavities for testing applications in the NISQ era. We identify engineering opportunities and challenges for implementation of algorithms in simulation, combinatorial optimization, and quantum machine learning in qudit-based quantum computers.

Venturelli, Davide [RIACS, Mtn. View] (ORCID:00000↗