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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Fault-tolerant resource comparison of qudit and qubit encodings for diagonal quadratic operators

Finite local Hilbert-space truncations arise naturally in quantum simulations of lattice field theories and motivate qudit encodings, but their fault-tolerant advantage over qubit encodings remains unclear. We compare the non-Clifford cost of implementing quadratic diagonal evolutions, exemplified by 𝑈 = 𝑒$^{−𝑖⁢𝑡⁢𝜙^2_𝑥}$ in a uniform field-amplitude discretization of a real scalar field, using either one logical 𝑑-level qudit or 𝑛 𝑏 = ⌈log 2⁡ 𝑑⌉ logical qubits. We analyze two standard settings: product-formula simulation and linear combination of unitaries (LCU) per block encoding, taking the resource metric to be the number of non-Clifford gates after synthesis into a discrete logical gate set. Because tight synthesis bounds for general single-qudit rotations are not known, we express the qudit constructions in terms of embedded two-level SU⁡(2) rotations and derive explicit finite-𝑑 break-even conditions for their synthesis cost; these serve as compiler targets for when qudit encodings can outperform the qubit baseline. Within the constructive models studied here, product-formula implementations would require an exponentially stronger per-primitive synthesis advantage for qudits to win asymptotically, while in the LCU setting the qubit encoding is asymptotically cheaper in 𝑑. Nevertheless, the finite-𝑑 threshold analysis identifies low-dimensional regions in which qudits can yield meaningful constant-factor savings, particularly for LCU-based implementations. As a secondary analysis of the LCU construction, we use an idealized negligible-overhead qubit-qudit code-switching model to give an absolute 𝑇-count comparison and reinterpret the savings as an allowable per-switch overhead budget.

Godwood, Samuel [Univ. of Liverpool (United Kingdo↗
DOE OSTI2025

Logical error rates for the surface code under a mixed coherent and stochastic circuit-level noise model inspired by trapped ions

With fault-tolerant quantum computing (FTQC) on the horizon, it is critical to understand sources of logical errors in plausible hardware implementations of quantum error-correcting codes. Detailed error modeling of computational instructions on particular FTQC architectures will enable the better prediction of error propagation in FT-encoded quantum circuits while revealing where greater attention is needed in hardware design. In this work, we consider logical error rates for the surface code implemented on a hypothetical grid-based trapped-ion quantum charge-coupled device architecture. Specifically, we construct logical channels for the idling surface code and examine its diamond error under a mixed coherent and stochastic circuit-level noise model inspired by trapped ions. We include the coherent dephasing noise that is known to accumulate during physical qubit idling and transport in these systems, determining idling and transport durations using the time-resolved output of an open-source trapped-ion surface code compiler. To estimate expectation values of logical Pauli observables following hardware circuits containing non-Clifford sources of noise, we utilize a Monte Carlo technique to sample from an underlying quasiprobability distribution of Clifford circuits that we independently simulate in a phase-sensitive fashion. We verify error suppression up to code distance 𝑑 = 11 at coherent dephasing rates near and below those of current-generation trapped-ion quantum computers and find that logical error rates align with those of analogous fully stochastic simulations in this regime. Exploring higher dephasing rates at 𝑑 = 3−5, we find evidence for growing coherent rotations about all three logical Pauli axes, increased diagonal logical error process matrix elements relative to those of stochastic simulations, and a reduced dephasing rate threshold. Overall, our work paves a way toward realistic hardware emulation of small fault-tolerant quantum processes, e.g., members of an FTQC instruction set.

Quantum benchmarking↗
DOE OSTI2024

Code conversion with the quantum Golay code for a universal transversal gate set

The [[7,1,3]] Steane code and [[23,1,7]] quantum Golay code have been identified as good candidates for fault-tolerant quantum computing via code concatenation. These two codes have transversal implementations of all Clifford gates but require some other scheme for fault-tolerant T gates. Using magic states, Clifford operations, and measurements is one common scheme, but magic-state distillation can have a large overhead. Code conversion is one avenue for implementing a universal gate set fault tolerantly without the use of magic-state distillation. Analogously to how the [[7,1,3]] Steane code can be fault tolerantly converted to and from the [[15,1,3]] Reed-Muller code which has a transversal T gate, the [[23,1,7]] Golay code can be converted to a [[95,1,7]] triorthogonal code with a transversal T gate. Further, a crucial ingredient of this procedure is the [[49,1,5]] triorthogonal code, which can itself be seen as being related to the self-dual [[17,1,5]] two-dimensional color code. Additionally, a method for code conversion based on a transversal CNOT between the codes, rather than stabilizer measurements, is described.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Classical shadows for quantum process tomography on near-term quantum computers

Quantum process tomography is a powerful tool for understanding quantum channels and characterizing the properties of quantum devices. Inspired by recent advances using classical shadows in quantum state tomography [H.-Y. Huang, R. Kueng, and J. Preskill, .], we have developed ShadowQPT, a classical shadow method for quantum process tomography. We introduce two related formulations with and without ancilla qubits. ShadowQPT stochastically reconstructs the Choi matrix of the device allowing for an classical evaluation of the device on arbitrary inputs with respect to arbitrary outputs. Using shadows, we then show how to compute overlaps, generate all k -weight reduced processes, and perform reconstruction via Hamiltonian learning. These latter two tasks are efficient for large systems as the number of quantum measurements needed scales only logarithmically with the number of qubits. A number of additional approximations and improvements are developed, including the use of a pair-factorized Clifford shadow and a series of postprocessing techniques that significantly enhance the accuracy for recovering the quantum channel. We have implemented ShadowQPT using both Pauli and Clifford measurements on the IonQ trapped ion quantum computer for quantum processes up to n = 4 qubits, and we achieved good performance. Published by the American Physical Society 2024

Levy, Ryan (ORCID:0000000349527156)↗
DOE OSTI2026

Robust Design Under Uncertainty in Quantum Error Mitigation

Error mitigation techniques are crucial to achieving near-term quantum advantage. Classical postprocessing of quantum computation outcomes is a popular approach for error mitigation, which includes methods, such as zero noise extrapolation, virtual distillation, and learning-based error mitigation. However, these techniques have limitations due to the propagation of uncertainty resulting from the finite shot number of a quantum measurement. In this work, we introduce general and unbiased methods for quantifying the uncertainty and error of error-mitigated observables based on the strategic sampling of error mitigation outcomes. We then extend our approach to demonstrate the optimization of performance and robustness of error mitigation under uncertainty. To illustrate our methods, we apply them to zero noise extrapolation and Clifford date regression in the ground state of the XY model simulated using depolarizing and International Business Machines Corporation (IBM) Toronto noise models, respectively. In particular, we optimize the choice of noise levels and the allocation of shots for zero noise extrapolation and the distribution of the training circuits for Clifford data regression. While our methods are readily applicable to any postprocessing-based error mitigation approach, in practice they must not be prohibitively expensive—even though they perform optimizations of the error mitigation hyperparameters requiring sampling of a statistical distribution of error mitigation outcomes. By leveraging surrogate-based optimization, we show that our methods can efficiently perform optimal design for a zero noise extrapolation implementation. We then further demonstrate the transferability of learned zero noise extrapolation hyperparameters to other similar circuits.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Unifying and benchmarking state-of-the-art quantum error mitigation techniques

Error mitigation is an essential component of achieving a practical quantum advantage in the near term, and a number of different approaches have been proposed. In this work, we recognize that many state-of-the-art error mitigation methods share a common feature: they are data-driven, employing classical data obtained from runs of different quantum circuits. For example, Zero-noise extrapolation (ZNE) uses variable noise data and Clifford-data regression (CDR) uses data from near-Clifford circuits. We show that Virtual Distillation (VD) can be viewed in a similar manner by considering classical data produced from different numbers of state preparations. Observing this fact allows us to unify these three methods under a general data-driven error mitigation framework that we call UNIfied Technique for Error mitigation with Data (UNITED). In certain situations, we find that our UNITED method can outperform the individual methods (i.e., the whole is better than the individual parts). Specifically, we employ a realistic noise model obtained from a trapped ion quantum computer to benchmark UNITED, as well as other state-of-the-art methods, in mitigating observables produced from random quantum circuits and the Quantum Alternating Operator Ansatz (QAOA) applied to Max-Cut problems with various numbers of qubits, circuit depths and total numbers of shots. We find that the performance of different techniques depends strongly on shot budgets, with more powerful methods requiring more shots for optimal performance. For our largest considered shot budget (10 10 ), we find that UNITED gives the most accurate mitigation. Hence, our work represents a benchmarking of current error mitigation methods and provides a guide for the regimes when certain methods are most useful.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Can Error Mitigation Improve Trainability of Noisy Variational Quantum Algorithms?

Variational Quantum Algorithms (VQAs) are often viewed as the best hope for near-term quantum advantage. However, recent studies have shown that noise can severely limit the trainability of VQAs, e.g., by exponentially flattening the cost landscape and suppressing the magnitudes of cost gradients. Error Mitigation (EM) shows promise in reducing the impact of noise on near-term devices. Thus, it is natural to ask whether EM can improve the trainability of VQAs. In this work, we first show that, for a broad class of EM strategies, exponential cost concentration cannot be resolved without committing exponential resources elsewhere. This class of strategies includes as special cases Zero Noise Extrapolation, Virtual Distillation, Probabilistic Error Cancellation, and Clifford Data Regression. Second, we perform analytical and numerical analysis of these EM protocols, and we find that some of them (e.g., Virtual Distillation) can make it harder to resolve cost function values compared to running no EM at all. As a positive result, we do find numerical evidence that Clifford Data Regression (CDR) can aid the training process in certain settings where cost concentration is not too severe. Our results show that care should be taken in applying EM protocols as they can either worsen or not improve trainability. On the other hand, our positive results for CDR highlight the possibility of engineering error mitigation methods to improve trainability.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Recursive algorithm for constructing antisymmetric fermionic states in first quantization mapping

We devise a deterministic quantum algorithm to produce antisymmetric states of single-particle orbitals in the first quantization mapping. Unlike sorting-based antisymmetrization algorithms, which require ordered input states and high Clifford-gate overhead, our approach initializes the state of each particle independently. For a system of $η$ particles and $N$ single-particle states, our algorithm prepares antisymmetrized states of non-trivial localized (e.g., Hartree-Fock) orbitals using $O(η^2\sqrt{N})$ $T$-gates, outperforming alternative algorithms when $η ≲ \sqrt{N}$. To achieve such scaling, we require $O(\sqrt{N})$ dirty ancilla qubits for intermediate calculations. Knowledge of the single-particle states to be antisymmetrized can be leveraged to further improve the efficiency of the circuit, and a measurement-based variant reduces gate cost by roughly a factor of two. We show example circuits for two- and three-particle systems and discuss the generalization to an arbitrary number of particles. For a specific three-particle example, we decompose the circuit into Clifford $+T$ gates and study the impact of noise on the prepared state.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1993

On the spring and mass of the Dirac oscillator

The Dirac oscillator is a relativistic generalization of the quantum harmonic oscillator. In particular, the square of the Hamiltonian for the Dirac oscillator yields the Klein-Gordon equation with a potential of the form: (ar(sub 2) + b(L x S)), where a and b are constants. To obtain the Dirac oscillator, a 'minimal substitution' is made in the Dirac equation, where the ordinary derivative is replaced with a covariant derivative. However, an unusual feature of the covariant derivative in this case is that the potential is a non-trivial element of the Clifford algebra. A theory which naturally gives rise to gage potentials which are non-trivial elements of the Clifford algebra is that based on local automorphism invariance. An exact solution of the automorphism gage field equations which reproduces both the potential term and the mass term of the Dirac oscillator is presented.

Crawford, James P.↗
NASA NTRS1996

STS-76 Flight Day 7

On this seventh day of the STS-76 mission, the flight crew, Cmdr. Kevin P. Chilton, Pilot Richard A Searfoss, and Mission Specialists Linda M. Godwin, Michael R. Clifford, and Ronald M. Sega are shown bidding the Mir crew and Shannon W. Lucid an emotional farewell, Chilton calling it 'a bittersweet moment.' The Atlantis and Mir commanders, Chilton and Onufrienko, along with spacewalkers Godwin and Clifford took time out to talk with CBS' 'Up to the Minute.' The space flyers discussed the success of their joint mission and the 6-hour spacewalk. The astronauts and cosmonauts exchanged handshakes and hugs in the Mir core module, and then praised both mission control centers, Houston and Kaliningrad for their support throughout the joint phase of the mission.

Source record↗
NASA NTRS1996

STS-76 Flight Day 1

On this first day of the STS-76 mission, the flight crew, Cmdr. Kevin P. Chilton, Pilot Richard A Searfoss, and Mission Specialists Shannon W. Lucid, Linda M. Godwin, Michael R. Clifford, and Ronald M. Sega, are shown performing prelaunch and launch activities for the night launch of the Space Shuttle Atlantis. The primary objective of this mission is the third docking between the Mir Space Station and Atlantis and a crew transfer. Lucid will remain onboard the Mir for about four months. Other activities include an EVA by Godwin and Clifford, logistics operations, and scientific research with a SPACEHAB module, some middeck experiments, and a Get Away Special (GAS) canister. Also, almost a ton of equipment and supplies will be transferred to the Mir. Experiments include the Mir Electric Field Characterization (MEFC), European Space Agency (ESA) Biorack life sciences experiment, Queens University Experiment in Liquid Diffusion (QUELD), Optizone Liquid Phase Sintering Experiment (OLIPSE), and a Naval Research Laboratory (NRL) GAS payload Trapped Ions in Space (TRIS), which will measure low-energy particle radiation in the inner magnetosphere. This mission also will include a KidSat, a prototype of Earth viewing cameras and instruments, that allow students in grades K-12 to see and direct the capture of pictures from space. Footage from Mission control is also included.

Source record↗
NASA NTRS1996

STS-76 Flight Day 8

On this eighth day of the STS-76 mission, the flight crew, Cmdr. Kevin P. Chilton, Pilot Richard A. Searfoss, and Mission Specialists Linda M. Godwin, Michael R. Clifford, and Ronald M. Sega are shown undocking from the Mir Space Station. With Mir some 60 nautical miles behind them, the Atlantis astronauts prepared for the return to Earth. Chilton, Searfoss and Clifford perform a routine checkout of Atlantis' flight control surfaces and a hotfire test of the orbiter's reaction control system jets. Views include the undocking maneuver; Atlantis as seen from the Mir Space Station; Atlantis' fly-round of Mir; and the firing of the Reaction Control System (RCS) primary thrusters.

Source record↗
NASA NTRS1996

STS-76 Post Flight Press Conference

The flight crew of the STS-76 Space Shuttle Orbiter Atlantis; Cmdr. Kevin P. Chilton, Pilot Richard A. Searfoss, and Mission Specialists Linda M. Godwin, Michael R. Clifford, and Ronald M. Sega present an overview of their mission. Highlights STS-76 include the first spacewalk by U.S. astronauts while the shuttle is attached to the Russian Space Station Mir, and the transfer of Shannon W. Lucid to the Mir-21 crew, the first American woman to serve as a Mir station researcher. She will remain aboard the orbiting station until Atlantis again docks with Mir in early August. Video footage includes the following: prelaunch and launch activities; shuttle launch; in-orbit rendezous; in-orbit docking between Mir and the orbiter; general crew activities; tranfer of supplies; Godwin and Clifford's EVA; undocking maneuvers; and the re-entry and landing of the orbiter.

Source record↗
NASA NTRS1996

STS-76 Mission Highlights Resource Tape

The flight crew of the STS-76 mission, Cmdr. Kevin P. Chilton, Pilot Richard A. Searfoss, and Mission Specialists Shannon W. Lucid, Linda M. Godwin, Michael R. Clifford, and Ronald M. Sega, present a video mission over-view of their space flight. Images include: pre-launch activities such as eating the traditional breakfast, crew suit-up, and the ride out to the launch pad. Also, included are various panoramic views of the shuttle on the pad. The crew can be seen being readied in the white room' for their mission. After the closing of the hatch and arm retraction, launch activities are shown including countdown, engine ignition, launch, and the separation of the Solid Rocket Boosters. Once in orbit, various view of the Mir Space Station can be seen as the shuttle begins its approach and docking. There several views of Godwin and Clifford as they spent six hours spacewalking in Atlantis's cargo bay and on the exterior of the Mir's docking module. The mission ending re-entry and landing can also be seen.

Source record↗
NASA NTRS2004

Lithospheric Dynamics of Mars: Water, Flow, and Failure

Some of the largest Martian erosive features were influenced by groundwater, and include valley networks, outflow channels, and possibly landslides. We argue that hydrothermal systems attending crustal formation processes were able to drive sufficient groundwater to the surface to form the Noachian southern highlands valley networks, which show a spatial correlation to crustal magnetic anomalies, also results of crustal formation. Hydrothermal activity is quantified through numerical simulations of convection in a porous medium due to the presence of a hot intruded magma chamber. The parameter space includes magma chamber depth, volume, aspect ratio, and host rock permeability and porosity. For permeabilities as low as l0(exp -17) sq m and intrusion volumes as low as 50 km , the total discharge due to intrusions building that part of the southern highlands crust associated with magnetic anomalies spans a comparable range as the inferred discharge from the overlying valley networks. The Hesperian circum-Chryse outflow channels are further manifestations of groundwater discharge and Clifford and Parker (2001) suggest that the large volumes of water required for their formation flows beneath a confining cryosphere from the South Pole where meltwater beneath an ice cap recharges a global aquifer. We argue that recharge occurs instead over the nearby Tharsis aquifer at high obliquity, assisted by cryosphere melting due to volcanic activity. Numerical simulations quantify the strength and duration of outflow discharge given either South Polar or Tharsis recharge. The contribution of South Pole recharge given Clifford and Parker aquifer properties is negligible compared to that of the initial Tharsis inventory. Tharsis recharge, despite the restrictions of improved aquifer properties, makes a significant contribution and, unlike South Pole recharge under the same conditions, fulfills discharge requirements. Groundwater may have influenced long run-out landslide formation in the Valles Marineris. We present simulations of Martian, terrestrial, and lunar landslides that gauge the role of pore fluid pressure in reproducing accurate geometries and run-out with frictional, Bingham, and fluidization rheologies. The results indicate that pore fluid is a necessary component of Martian landslide formation and we suggest scenarios that might explain its presence.

Grimm, Robert E.↗
DOE OSTI2025

Magic State Distillation using Asymptotically Good Codes on Qudits

Qudits offer the potential for low-overhead magic state distillation, although previous results for asymptotically good codes have required qudit dimension $q\gg 100$ or code length $\mathcal{N}\gg 100$. These parameters far exceed experimental demonstrations of qudit platforms, and thus motivate the search for better codes. Using a novel lifting procedure, we construct the first family of good triorthogonal codes on the $\mathbb{F}_{2^{2m}}$ alphabet with $m \geq 3$ that lies above the Tsfasman-Vladut-Zink bound. These codes yield a family of asymptotically good quantum codes with transversal CCZ gates, enabling constant space overhead magic state distillation with qudit dimension as small as $q=64$. Further, we identify a promising code with parameters $[[42,14,6]]_{64}$. Finally, we show that a distilled $|{CCZ}\rangle_{2^{2m}}$ can be reduced to a $|{CCZ}\rangle_{2^n}$ state for arbitrary $n$ with a constant-depth Clifford circuit of at most 9 computational basis measurements, 12 single-qudit and 9 two-qudit Clifford gates.

Cervia, Michael J. [Washington U., Seattle] (ORCID↗
NASA NTRS1993

The role of the geothermal gradient in the emplacement and replenishment of ground ice on Mars

Knowledge of the mechanisms by which ground ice is emplaced, removed, and potentially replenished, are critical to understanding the climatic and hydrologic behavior of water on Mars, as well as the morphologic evolution of its surface. Because of the strong temperature dependence of the saturated vapor pressure of H2O, the atmospheric emplacement or replenishment of ground ice is prohibited below the depth at which crustal temperatures begin to monotonically increase due to geothermal heating. In contrast, the emplacement and replenishment of ground ice from reservoirs of H2O residing deep within the crust can occur by at least three different thermally-driven processes, involving all three phases of water. In this regard, Clifford has discussed how the presence of a geothermal gradient as small as 15 K/km can give rise to a corresponding vapor pressure gradient sufficient to drive the vertical transport of 1 km of water from a reservoir of ground water at depth to the base of the cryosphere every 10(exp 6) - 10(exp 7) years. This abstract expands on this earlier treatment by considering the influence of thermal gradients on the transport of H2O at temperatures below the freezing point.

Clifford, Stephen M.↗
DOE OSTI2026

Analyzing the Free States of one Quantum Resource Theory as Resource States of Another

In the context of quantum resource theories (QRTs), free states are defined as those that can be obtained at no cost under a certain restricted set of conditions. However, when taking a free state from one QRT and evaluating it through the optics of another QRT, it might well turn out that the state is now extremely resourceful. Such realization has recently prompted numerous works characterizing states across several QRTs. Here, in this work, we contribute to this body of knowledge by analyzing the resourcefulness in free states for—and across witnesses of—the QRTs of multipartite entanglement, fermionic non-Gaussianity, imaginarity, realness, spin coherence, Clifford non-stabilizerness, $S_n$-equivariance, and non-uniform entanglement. We provide rigorous theoretical results as well as present numerical studies that showcase the rich and complex behavior that arises in this type of cross-examination.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗