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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Qudit Designs and Where to Find Them

Unitary t-designs are some of the most versatile tools in quantum information theory. Their applications range from randomized benchmarking and shadow tomography, to more fundamental ones such as emulating quantum chaos and establishing exponential separations between classical and quantum query complexity. While unitary designs originating from a group structure, such as the Clifford group, have proven to be incredibly useful for qubit systems, unfortunately, this is no longer true for qudits. In fact, the classification of finite-group representations rules out the existence of unitary 2-designs for arbitrary qudit dimensions. This severely limits the applicability of standard quantum information primitives when it comes to qudit systems. We overcome these limitations with a three-fold contribution. First, we introduce a general technique to construct families of weighted state t-designs in arbitrary qudit dimensions. These weighted state-designs generalize classical shadow tomography protocol from qubits to qudits. Second, we introduce a Clifford character RB that allows us to benchmark the qudit Clifford group in any dimension, including non-prime-power dimensions. And third, we establish bounds on the quantum circuit complexity of generating approximate unitary-designs from native gates in existing quantum hardware such as high-spin and cavity-QED qudits. Our work further highlights the analogy between spin and optical coherent states by proving that spin-GKP codewords form a state 2-design while spin coherent states do not; in direct analogy with the optical case. This work is structured as a pedagogical and self-contained introduction to unitary designs and their applications to qudit systems.

Anand, Namit [NASA, Ames; Unlisted, US] (ORCID:000↗
DOE OSTI2026

Optical nanofiber testbeds for benchmarking membrane-waveguide photonic integrated circuit platforms toward on-chip quantum inertial sensing

Recent advances in cold atom interferometry with optical and magnetic atom guides have set the stage for quantum inertial sensors capable of operating in dynamic environments. In this work, we present three key innovations—evanescent-field (EF) atom guides, optical nanofiber testbeds, and membrane-waveguide photonic integrated circuit (PIC) platforms—to advance EF-guided atom interferometry. First, we demonstrate EF atom guides on optical nanofiber testbeds, which serve as performance benchmarks for our membrane-waveguide PIC platforms. Second, we achieve low-power (⁠ ~ 5 mW) guiding of freely moving, laser-cooled 133 Cs atoms in two-color, traveling-wave EF optical dipole traps at the novel, heat-efficient magic wavelengths of 793 and 937 nm (i.e., “793/937-nm EF atom guides”). Concurrently, we design and fabricate membrane-waveguide PIC platforms for these EF atom guides; in our prior work, we showed that these structures safely accommodate 4–6 times the required optical trap power under vacuum and enable dense cold atom generation via magneto-optical trapping in the vicinity of the optical wavguide for efficient loading. Third, we verify preserved atomic coherence via microwave fields and EF-coupled Doppler-free Raman beams; to our knowledge, this is the first report of coherence fringes driven by co-propagating EF-coupled Raman beams with only 150 nW of total optical power. By providing a direct comparison between optical nanofiber testbeds and membrane-waveguide PIC platforms, our results lay critical groundwork for the on-chip realization of EF-guided atom interferometry and the development of fully integrated, compact, lightweight, and low-power quantum accelerometers and gyroscopes.

Orozco, Adrian [Sandia National Laboratories (SNL-↗
DOE OSTI2025

Quantum real-time evolution using tensor renormalization group methods

We introduce an approach for approximate real-time evolution of quantum systems using tensor renormalization group (TRG) methods originally developed for imaginary time. We use higher-order TRG to generate a coarse-grained time evolution operator for a 1+1⁢D transverse Ising model with a longitudinal field. We show that the standard tensor norm used for the singular value decomposition-based truncation is degenerate and propose an alternate method to discriminate. We show that it is effective and efficient in evolving Gaussian wave packets for one and two particles in the disordered phase, while ordered phase behavior is more challenging to capture. We compare our algorithm with local simulators for universal quantum computers and discuss possible benchmarking in the near future.

lattice gauge theory↗
DOE OSTI2021

General synthesis of single-atom catalysts with high metal loading using graphene quantum dots

Transition-metal single-atom catalysts present extraordinary activity per metal atomic site, but suffer from low metal-atom densities (typically less than 5 wt% or 1 at.%), which limits their overall catalytic performance. Here we report a general method for the synthesis of single-atom catalysts with high transition-metal-atom loadings of up to 40 wt% or 3.8 at.%, representing several-fold improvements compared to benchmarks in the literature. Graphene quantum dots, later interweaved into a carbon matrix, were used as a support, providing numerous anchoring sites and thus facilitating the generation of high densities of transition-metal atoms with sufficient spacing between the metal atoms to avoid aggregation. A significant increase in activity in electrochemical CO 2 reduction (used as a representative reaction) was demonstrated on a Ni single-atom catalyst with increased Ni loading.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Quantum Logic Enhanced Sensing in Solid-State Spin Ensembles

We demonstrate quantum logic enhanced sensitivity for a macroscopic ensemble of solid-state, hybrid two-qubit sensors. We achieve over a factor of 30 improvement in the single-shot signal-to-noise ratio, translating to an ac magnetic field sensitivity enhancement exceeding an order of magnitude for time-averaged measurements. Using the electronic spins of nitrogen vacancy (NV) centers in diamond as sensors, we leverage the on-site nitrogen nuclear spins of the NV centers as memory qubits, in combination with homogeneous and stable bias and control fields, ensuring that all of the ~10 9 two-qubit sensors are sufficiently identical to permit global control of the NV ensemble spin states. We find quantum logic sensitivity enhancement for multiple measurement protocols with varying optimal sensing intervals, including XY8 and DROID-60 dynamical decoupling, as well as correlation spectroscopy, using an applied ac magnetic field signal. The results are independent of the nature of the target signal and broadly applicable to measurements using NV centers and other solid-state spin ensembles. Furthermore, this work provides a benchmark for macroscopic ensembles of quantum sensors that employ quantum logic or quantum error correction algorithms for enhanced sensitivity.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Hardware-Conscious Optimization of the Quantum Toffoli Gate

While quantum computing holds great potential in combinatorial optimization, electronic structure calculation, and number theory, the current era of quantum computing is limited by noisy hardware. Many quantum compilation approaches can mitigate the effects of imperfect hardware by optimizing quantum circuits for objectives such as critical path length. Few approaches consider quantum circuits in terms of the set of vendor-calibrated operations (i.e., native gates) available on target hardware. This manuscript expands the analytical and numerical approaches for optimizing quantum circuits at this abstraction level. We present a procedure for combining the strengths of analytical native gate-level optimization with numerical optimization. Although we focus on optimizing Toffoli gates on the IBMQ native gate set, the methods presented are generalizable to any gate and superconducting qubit architecture. Our optimized Toffoli gate implementation demonstrates an 18% reduction in infidelity compared with the canonical implementation as benchmarked on IBM Jakarta with quantum process tomography. Assuming the inclusion of multi-qubit cross-resonance (MCR) gates in the IBMQ native gate set, we produce Toffoli implementations with only six multi-qubit gates, a 25% reduction from the canonical eight multi-qubit implementations for linearly connected qubits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Qubit-Efficient Quantum Chemistry with the ADAPT Variational Quantum Eigensolver and Double Unitary Downfolding

Here, in this work, we combine the recently developed double unitary coupled cluster (DUCC) theory with the adaptive, problem-tailored variational quantum eigensolver (ADAPT-VQE) to explore the accuracy of unitary downfolded Hamiltonians for quantum simulation of chemistry. We benchmark the ability of DUCC effective Hamiltonians to recover dynamical correlation energy outside of an active space. We consider the effects of strong correlation, commutator truncation, higher-body terms, and approximate external amplitudes on the accuracy of these effective Hamiltonians. When combining these DUCC Hamiltonians with ADAPT-VQE, we observe similar convergence of the ground state as compared with bare active space Hamiltonians, demonstrating that DUCC Hamiltonians provide increased accuracy without increasing the load on the quantum processor.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Radio frequency mixing modules for superconducting qubit room temperature control systems

As the number of qubits in nascent quantum processing units increases, the connectorized RF (radio frequency) analog circuits used in first generation experiments become exceedingly complex. The physical size, cost, and electrical failure rate all become limiting factors in the extensibility of control systems. We have developed a series of compact RF mixing boards to address this challenge by integrating I/Q quadrature mixing, intermediate frequency/LO (local oscillator)/RF power level adjustments, and direct current bias fine tuning on a 40 × 80 mm 2 four-layer printed circuit board with electromagnetic interference shielding. The RF mixing module is designed to work with RF and LO frequencies between 2.5 and 8.5 GHz. The typical image rejection and adjacent channel isolation are measured to be ~27 dBc and ~50 dB. By scanning the drive phase in a loopback test, the module short-term amplitude and phase linearity are typically measured to be 5 ×10 -4 (V pp /V mean ) and 1 ×10 -3 radian (pk-pk). The operation of the RF mixing board was validated by integrating it into the room temperature control system of a superconducting quantum processor and executing randomized benchmarking characterization of single and two qubit gates. We measured a single-qubit process infidelity of 9.3(3) × 10 -4 and a two-qubit process infidelity of 2.7(1) × 10 -2 .

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Stochastic quantum Krylov protocol with double-factorized Hamiltonians

Here we propose a class of randomized quantum Krylov diagonalization (rQKD) algorithms capable of solving the eigenstate estimation problem with modest quantum resource requirements. Compared to previous real-time evolution quantum Krylov subspace methods, our approach expresses the time evolution operator e –i$\widehat{H}$$\tau$ as a linear combination of unitaries and subsequently uses a stochastic sampling procedure to reduce circuit depth requirements. While our methodology applies to any Hamiltonian with fast-forwardable subcomponents, we focus on its application to the explicitly double-factorized electronic-structure Hamiltonian. To demonstrate the potential of the proposed rQKD algorithm on near-term quantum devices, we provide numerical benchmarks for a variety of molecular systems with circuit-based state-vector simulators including the effects of sampling noise, achieving ground-state energy errors of less than 1 kcal mol -1 with circuit depths orders of magnitude shallower than those required for low-rank deterministic Trotter-Suzuki decompositions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Globally Optimizing QAOA Circuit Depth for Constrained Optimization Problems

We develop a global variable substitution method that reduces n-variable monomials in combinatorial optimization problems to equivalent instances with monomials in fewer variables. We apply this technique to 3-SAT and analyze the optimal quantum unitary circuit depth needed to solve the reduced problem using the quantum approximate optimization algorithm. For benchmark 3-SAT problems, we find that the upper bound of the unitary circuit depth is smaller when the problem is formulated as a product and uses the substitution method to decompose gates than when the problem is written in the linear formulation, which requires no decomposition.

3-SAT↗
DOE OSTI2025

Q-Cluster: Quantum Error Mitigation Through Noise-Aware Unsupervised Learning

Quantum error mitigation (QEM) is critical in reducing the impact of noise in the pre-fault-tolerant era, and is expected to complement error correction in fault-tolerant quantum computing (FTQC). In this work, we propose a novel QEM approach, Q-Cluster, that uses unsupervised learning (clustering) to reshape the measured bit-string distribution. Our approach starts with a simplified bit-flip noise model. It first performs clustering on noisy measurement results, i.e., bit-strings, based on the Hamming distance. The centroid of each cluster is calculated using a qubit-wise majority vote. Next, the noisy distribution is adjusted with the clustering outcomes and the bitflip error rates using Bayesian inference. Our simulation results show that Q-Cluster can mitigate high noise rates (up to 40% per qubit) with the simple bit-flip noise model. However, real quantum computers do not fit such a simple noise model. To address the problem, we (a) apply Pauli twirling to tailor the complex noise channels to Pauli errors, and (b) employ a machine learning model, ExtraTrees regressor, to estimate an effective bit-flip error rate using a feature vector consisting of machine calibration data (gate & measurement error rates), circuit features (number of qubits, numbers of different types of gates, etc.) and the shape of the noisy distribution (entropy). Our experimental results show that our proposed Q-Cluster scheme improves the fidelity by a factor of 1.46x, on average, compared to the unmitigated output distribution, for a set of low-entropy benchmarks on five different IBM quantum machines. Our approach outperforms the state-of-art QEM approaches RZNE [28], M3 [24], Hammer [35], and QBEEP [33] by 1.26x,1.29x,1.47x, and 2.65 x, respectively.

42 ENGINEERING↗
DOE OSTI2023

Demonstration of Quantum Energy Teleportation on Superconducting Quantum Hardware

Teleporting physical quantities to remote locations remains a key challenge for quantum information science and technology. Quantum teleportation has enabled the transfer of quantum information, but teleportation of quantum physical quantities has not yet been realized. Here we report the realization and observation of quantum energy teleportation on real superconducting quantum hardware. We achieve this by using several IBM superconducting quantum computers. The results are consistent with the exact solution of the theory and are improved by the mitigation of measurement error. Quantum energy teleportation requires only local operations and classical communication. Furthermore, our results provide a realistic benchmark that is fully achievable with current quantum computing and communication technologies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Quantum Gauge Networks: A New Kind of Tensor Network

Although tensor networks are powerful tools for simulating low-dimensional quantum physics, tensor network algorithms are very computationally costly in higher spatial dimensions. We introduce quantum gauge networks: a different kind of tensor network ansatz for which the computation cost of simulations does not explicitly increase for larger spatial dimensions. We take inspiration from the gauge picture of quantum dynamics, which consists of a local wavefunction for each patch of space, with neighboring patches related by unitary connections. A quantum gauge network (QGN) has a similar structure, except the Hilbert space dimensions of the local wavefunctions and connections are truncated. We describe how a QGN can be obtained from a generic wavefunction or matrix product state (MPS). All 2k-point correlation functions of any wavefunction for M many operators can be encoded exactly by a QGN with bond dimension O(M k ). In comparison, for just k = 1, an exponentially larger bond dimension of 2 M/6 is generically required for an MPS of qubits. We provide a simple QGN algorithm for approximate simulations of quantum dynamics in any spatial dimension. The approximate dynamics can achieve exact energy conservation for time-independent Hamiltonians, and spatial symmetries can also be maintained exactly. We benchmark the algorithm by simulating the quantum quench of fermionic Hamiltonians in up to three spatial dimensions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Quantum Optimization: Potential, Challenges, and the Path Forward

Recent advances in quantum computers are demonstrating the ability to solve problems at a scale beyond brute force classical simulation. As such, a widespread interest in quantum algorithms has developed in many areas, with optimization being one of the most pronounced domains. Across computer science and physics, there are a number of algorithmic approaches, often with little linkage. This is further complicated by the fragmented nature of the field of mathematical optimization, where major classes of optimization problems, such as combinatorial optimization, convex optimization, non-convex optimization, and stochastic extensions, have devoted communities. With these aspects in mind, this work draws on multiple approaches to study quantum optimization. Provably exact versus heuristic settings are first explained using computational complexity theory — highlighting where quantum advantage is possible in each context. Then, the core building blocks for quantum optimization algorithms are outlined to subsequently define prominent problem classes and identify key open questions that, if answered, will advance the field. The effects of scaling relevant problems on noisy quantum devices are also outlined in detail, alongside meaningful benchmarking problems. We underscore the importance of benchmarking by proposing clear metrics to conduct appropriate comparisons with classical optimization techniques. Lastly, we highlight two domains – finance and sustainability – as rich sources of optimization problems that could be used to benchmark, and eventually validate, the potential real-world impact of quantum optimization.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Atomic Structure, Dynamics, Changes in Chemical Bonding and Semiconductor-Metal Transition in Sb 2 Se 3 : A Remarkable Material for Quantum Networks and Energy Applications

Antimony sesquiselenide has become an outstanding functional material for photovoltaics, energy storage and transformation, memory and photonic applications. Sb 2 Se 3 is one of the most successful emerging solar light absorbers and has also been identified as a highly promising ultralow-loss phase-change material (PCM) for next-generation coherent nanophotonic processors, photonic tensor cores, quantum and neuromorphic networks. Unlike benchmark telluride PCMs, Sb 2 Se 3 features a quasi-one-dimensional (1D) crystalline structure consisting of (Sb 4 Se 6 ) ∞ ribbons, lacks the typical PCM chemical bonding, and undergoes an extended semiconductor-metal transition above the melting point. Consequently, the origin of high optical contrast between crystalline (SET) and amorphous (RESET) logic states remains elusive and presents a significant challenge. Using high-energy X-ray diffraction and Raman spectroscopy over a wide temperature range, supported by first-principles simulations and complemented by thermal, optical and electrical measurements, as well as by 121 Sb-Mossbauer spectroscopy, the quasi-1D network of orthorhombic antimony sesquiselenide was found to undergo significant evolution in amorphous and supercooled Sb 2 Se 3 , leading to lower coordination, shorter interatomic distances and a higher p-electron density on antimony, indicating changes in chemical bonding. The observed novel Sb 2 Se 3 nanocrystalline polymorph, characterized by trigonal antimony coordination and more isolated Sb-Se ribbons, could help reduce multiple trapping defect states in the bandgap, which are typical of orthorhombic Sb 2 Se 3 , thereby enhancing the power-conversion efficiency of photovoltaic devices. Semimetallic and metallic liquid Sb 2 Se 3 exhibit a gradual transformation into a denser 2D and/or 3D network with higher antimony coordination. Localized electron states in the pseudogap are becoming extended, leading to an increase in electronic conductivity σ following the relationship σ ∝ N(E F ) 2 . Liquid Sb 2 Se 3 also appears to be strongly fragile, with a nonmonotonic change in viscosity and higher atomic mobility in the metallic liquid. Furthermore, these results explain extraordinary functionalities of Sb 2 Se 3 for photonic and energy applications.

antimony↗
DOE OSTI2021

Adaptive pruning-based optimization of parameterized quantum circuits

Abstract Variational hybrid quantum–classical algorithms are powerful tools to maximize the use of noisy intermediate-scale quantum devices. While past studies have developed powerful and expressive ansatze, their near-term applications have been limited by the difficulty of optimizing in the vast parameter space. In this work, we propose a heuristic optimization strategy for such ansatze used in variational quantum algorithms, which we call ‘parameter-efficient circuit training (PECT)’. Instead of optimizing all of the ansatz parameters at once, PECT launches a sequence of variational algorithms, in which each iteration of the algorithm activates and optimizes a subset of the total parameter set. To update the parameter subset between iterations, we adapt the Dynamic Sparse Reparameterization scheme which was originally proposed for training deep convolutional neural networks. We demonstrate PECT for the Variational Quantum Eigensolver, in which we benchmark unitary coupled-cluster ansatze including UCCSD and k -UpCCGSD, as well as the Low-Depth Circuit Ansatz (LDCA), to estimate ground state energies of molecular systems. We additionally use a layerwise variant of PECT to optimize a hardware-efficient circuit for the Sycamore processor to estimate the ground state energy densities of the one-dimensional Fermi-Hubbard model. From our numerical data, we find that PECT can enable optimizations of certain ansatze that were previously difficult to converge and more generally can improve the performance of variational algorithms by reducing the optimization runtime and/or the depth of circuits that encode the solution candidate(s).

Physics↗
DOE OSTI2020

Time-dependent variational principle for mixed matrix product states in the thermodynamic limit

Here, we describe a time evolution algorithm for quantum spin chains whose Hamiltonians are composed of an infinite uniform left and right bulk part, and an arbitrary finite region in between. The left and right bulk parts are allowed to be different from each other. The algorithm is based on the time-dependent variational principle (TDVP) of matrix product states. It is inversion-free and very simple to adapt from an existing TDVP code for finite systems. The importance of working in the projective Hilbert space is highlighted. We study the quantum Ising model as a benchmark and an illustrative example. The spread of information after a local quench is studied in both the ballistic and the diffusive case. We also offer a derivation of TDVP directly from symplectic geometry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗