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At least 19 records
All sourcesNASA NTRSDOE OSTI
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 OSTI2026

Error-mitigated nonorthogonal quantum eigensolver via shadow tomography

We present a shadow-tomography-enhanced nonorthogonal quantum eigensolver (NOQE) for more efficient and accurate electronic structure calculations on near-term quantum devices. By integrating shadow tomography into the NOQE, the measurement cost scales linearly rather than quadratically with the number of reference states, while also reducing the required qubits and circuit depth by half. This approach enables extraction of all matrix elements via randomized measurements and classical postprocessing. We analyze its sample complexity and show that, for small systems, it remains constant in the high-precision regime, while for larger systems, it scales linearly with the system size. We further apply shadow-based error mitigation to suppress noise-induced bias without increasing quantum resources. Demonstrations on the hydrogen molecule in the strongly correlated regime achieve chemical accuracy under realistic noise, showing that our method is both resource-efficient and noise-resilient for practical quantum chemistry simulations in the near term.

quantum algorithms & computation↗
DOE OSTI2023

Shadow process tomography of quantum channels

Quantum process tomography is a critical capability for building quantum computers, enabling quantum networks, and understanding quantum sensors. Like quantum state tomography, the process tomography of an arbitrary quantum channel requires a number of measurements that scales exponentially in the number of quantum bits affected. However, the recent field of shadow tomography, applied to quantum states, has demonstrated the ability to extract key information about a state with only polynomially many measurements. In this work, we apply the concepts of shadow state tomography to the challenge of characterizing quantum processes. Furthermore, we make use of the Choi isomorphism to directly apply rigorous bounds from shadow state tomography to shadow process tomography, and we find additional bounds on the number of measurements that are unique to process tomography. Our results, which include algorithms for implementing shadow process tomography, enable new techniques including evaluation of channel concatenation and the application of channels to shadows of quantum states. This provides a dramatic improvement for understanding large-scale quantum systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Efficient Measurement-Driven Eigenenergy Estimation with Classical Shadows

Quantum algorithms exploiting real-time evolution under a target Hamiltonian have demonstrated remarkable efficiency in extracting key spectral information. However, the broader potential of these methods, particularly beyond ground-state calculations, is underexplored. In this work, we introduce the framework of multiobservable dynamic mode decomposition (MODMD), which combines the observable dynamic mode decomposition (DMD), a measurement-driven eigensolver tailored for near-term implementation, with classical shadow tomography. MODMD leverages random scrambling in the classical shadow technique to construct, with exponentially reduced resource requirements, a signal subspace that encodes rich spectral information. Notably, we replace typical Hadamard-test circuits with a protocol designed to predict low-rank observables, thereby broadening the use of classical shadow tomography for predicting many low-rank observables. We establish theoretical guarantees on the spectral approximation from MODMD, taking into account distinct sources of error. In the ideal case, we prove that the spectral error scales as exp (−Δ⁢𝐸⁢𝑡 max ), where Δ⁢𝐸 is the Hamiltonian spectral gap and 𝑡 max is the maximal simulation time. This analysis provides a rigorous justification of the rapid convergence observed across simulations. To demonstrate the utility of our framework, we consider its application to fundamental tasks, such as determining the low-lying, i.e., ground or excited, energies of representative many-body systems. Our work paves the path for efficient designs of measurement-driven algorithms on near-term and early fault-tolerant quantum devices.

quantum algorithms & computation↗
DOE OSTI2024

Quantum Circuit Cutting for Classical Shadows

Classical shadow tomography is a sample-efficient technique for characterizing quantum systems and predicting many of their properties. Circuit cutting is a technique for dividing large quantum circuits into smaller fragments that can be executed more robustly using fewer quantum resources. We introduce a divide-and-conquer circuit cutting method for estimating the expectation values of observables using classical shadows. We derive a general formula for making predictions using the classical shadows of circuit fragments from arbitrarily cut circuits and provide the sample complexity analysis for the case when observables factorize across fragments. Then, we numerically show that our divide-and-conquer method outperforms traditional uncut shadow tomography when estimating high-weight observables that act non-trivially on many qubits and discuss the mechanisms for this advantage.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2025

Real classical shadows

Efficiently learning expectation values of a quantum state using classical shadow tomography has become a fundamental task in quantum information theory. In a classical shadows protocol, one measures a state in a chosen basis $\mathcal{W}$ after it has evolved under a unitary transformation randomly sampled from a chosen distribution $\mathcal{U}$. In this work we study the case where $\mathcal{U}$ corresponds to either local or global orthogonal Clifford gates, and $\mathcal{W}$ consists of real-valued vectors. Our results show that for various situations of interest, this ‘real’ classical shadow protocol improves the sample complexity over the standard scheme based on general Clifford unitaries. For example, when one is interested in estimating the expectation values of arbitrary real-valued observables, global orthogonal Cliffords typically decrease the required number of samples by a factor of two. More dramatically, for k-local observables composed only of real-valued Pauli operators, sampling local orthogonal Cliffords leads to a reduction by an exponential-in-k factor in the sample complexity over local unitary Cliffords. Finally, we show that by measuring in a basis containing complex-valued vectors, orthogonal shadows can, in the limit of large system size, exactly reproduce the original unitary shadows protocol.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Group-theoretic error mitigation enabled by classical shadows and symmetries

Abstract Estimating expectation values is a key subroutine in quantum algorithms. Near-term implementations face two major challenges: a limited number of samples required to learn a large collection of observables, and the accumulation of errors in devices without quantum error correction. To address these challenges simultaneously, we develop a quantum error-mitigation strategy called symmetry-adjusted classical shadows , by adjusting classical-shadow tomography according to how symmetries are corrupted by device errors. As a concrete example, we highlight global U(1) symmetry, which manifests in fermions as particle number and in spins as total magnetization, and illustrate their group-theoretic unification with respective classical-shadow protocols. We establish rigorous sampling bounds under readout errors obeying minimal assumptions, and perform numerical experiments with a more comprehensive model of gate-level errors derived from existing quantum processors. Our results reveal symmetry-adjusted classical shadows as a low-cost strategy to mitigate errors from noisy quantum experiments in the ubiquitous presence of symmetry.

Zhao, Andrew (ORCID:0000000202990277)↗
DOE OSTI2026

Correlated purification for restoring 𝑁-representability in quantum simulation

Experimentally measured reduced density matrices (RDMs) often violate constraints that ensure they represent N-electron states—known as N-representability conditions—because of statistical and hardware noise. In this work, we present a correlated purification framework based on semidefinite programming to restore the accuracy of a noisy, unphysical two-electron RDM (2-RDM). The method performs a bi-objective optimization that minimizes both the many-electron energy and the nuclear norm of the correction to the measured 2-RDM. The nuclear norm, often employed in matrix completion, promotes low-rank corrections, while the energy term acts as a regularization term that can improve the purity of the ground state. While the method is particularly effective for ground states, it can also be applied to excited and nonstationary states by decreasing the weight of the energy relative to the error norm. In an application to fermionic shadow tomography of large hydrogen chains, correlated purification yields substantial reductions in both energy and 2-RDM error, achieving chemical accuracy across dissociation curves. This framework provides a robust strategy for tomography in many-body quantum simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

State preparation and measurement in a quantum simulation of the $O(\mathrm{3})$ sigma model

Recently, Singh and Chandrasekharan [Phys. Rev. D 100, 054505 (2019)] showed that fixed points of the nonlinear O ( 3 ) sigma model can be reproduced near a quantum phase transition of a spin model with just two qubits per lattice site. In a paper by the NuQS Collaboration [Phys. Rev. Lett. 123, 090501 (2019)], the proposal is made to simulate such field theories on a quantum computer using the universal properties of a similar model. In this paper, following that direction, we demonstrate how to prepare the ground state of the model from Singh and Chandrasekharan and measure a dynamical quantity of interest, the O ( 3 ) Noether charge, on a quantum computer. In particular, we apply Trotter methods to obtain results for the complexity of adiabatic ground state preparation in both the weak-coupling and quantum-critical regimes and use shadow tomography to measure the dynamics of local observables. Finally, we then present and analyze a quantum algorithm based on nonunitary randomized simulation methods that may yield an approach suitable for intermediate-term noisy quantum devices.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Optimal Twirling Depth for Classical Shadows in the Presence of Noise

The classical shadows protocol is an efficient strategy for estimating properties of an unknown state p using a small number of state copies and measurements. In its original form, it involves twirling the state with unitaries from some ensemble and measuring the twirled state in a fixed basis. It was recently shown that for computing local properties, optimal sample complexity (copies of the state required) is remarkably achieved for unitaries drawn from shallow depth circuits composed of local entangling gates, as opposed to purely local (zero depth) or global twirling (infinite depth) ensembles. Here, we consider the sample complexity as a function of the depth of the circuit, in the presence of noise. We find that this noise has important implications for determining the optimal twirling ensemble. Under fairly general conditions, we (i) show that any single-site noise can be accounted for using a depolarizing noise channel with an appropriate damping parameter f, (ii) compute thresholds f th at which optimal twirling reduces to local twirling for Pauli operators, (iii) nth order Renyi entropies (n ≥2), and (iv) provide a meaningful upper bound t max on the optimal circuit depth for any finite noise strength f, which applies to observables and entanglement entropy measurements. In conclusion, these thresholds strongly constrain the search for optimal strategies to implement shadow tomography and are easily tailored to the experimental system at hand.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Continuous-Variable Quantum State Designs: Theory and Applications

We generalize the notion of quantum state designs to infinite-dimensional spaces. We first prove that, under the definition of continuous-variable (CV) state t -designs from [Blume-Kohout , ], no state designs exist for t ≥ 2 . Similarly, we prove that no CV unitary t -designs exist for t ≥ 2 . We propose an alternative definition for CV state designs, which we call rigged t -designs, and provide explicit constructions for t = 2 . As an application of rigged designs, we develop a design-based shadow-tomography protocol for CV states. Using energy-constrained versions of rigged designs, we define an average fidelity for CV quantum channels and relate this fidelity to the CV entanglement fidelity. As an additional result of independent interest, we establish a connection between torus 2-designs and complete sets of mutually unbiased bases. Published by the American Physical Society 2024

Physics↗
DOE OSTI2021

4D Proxy Imaging of Fracture Dilation and Stress Shadowing Using Electrical Resistivity Tomography During High Pressure Injections into a Dense Rock Formation

Fluid flow through fractured rock systems is governed in large part by the distribution, interconnectivity, and size of fracture apertures. In-situ stress is one of the primary factors controlling fracture aperture, and one that is altered significantly during high-pressure fluid injections or extractions. Interactions between stress, pore pressure, aperture, and fluid flow can result in complex and evolving poroelastic behavior with significant implications regarding the predictability and risk of developing and managing deep subsurface reservoirs (geothermal, fossil energy, and geologic carbon sequestration). In saturated crystalline rocks, bulk electrical conductivity is highly sensitive to porosity, and therefore to fracture aperture size and distribution. We demonstrate the use of time-lapse 3D electrical resistivity tomography for remotely monitoring stress induced changes in aperture distribution during high pressure injections into a fractured rock system at a scale of tens of meters. Results reveal a complex and continuously evolving stress field involving aperture dilations in the natural fracture system and aperture contractions in adjacent zones of shadow stress. Results provide information about the spatiotemporal changes in the system behavior and point to the potential of electrical imaging for autonomously and remotely monitoring evolving stress conditions by proxy through changes in bulk electrical conductivity.

electrical resisitivity tomography, stress, 4D Tim↗
DOE OSTI2021

Fermionic Partial Tomography via Classical Shadows

Here we propose a tomographic protocol for estimating any k-body reduced density matrix (k-RDM) of an n-mode fermionic state, a ubiquitous step in near-term quantum algorithms for simulating many-body physics, chemistry, and materials. Our approach extends the framework of classical shadows, a randomized approach to learning a collection of quantum-state properties, to the fermionic setting. Our sampling protocol uses randomized measurement settings generated by a discrete group of fermionic Gaussian unitaries, implementable with linear-depth circuits. We prove that estimating all k-RDM elements to additive precision ϵ requires on the order of ($^{n}_{k}$)k 3/2 log(n)/ϵ 2 repeated state preparations, which is optimal up to the logarithmic factor. Furthermore, numerical calculations show that our protocol offers a substantial improvement in constant overheads for k ≥ 2, as compared to prior deterministic strategies. We also adapt our method to particle-number symmetry, wherein the additional circuit depth may be halved at the cost of roughly 2–5 times more repetitions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Regularizing least squares quantum state tomography with classical shadows

Classical shadows herald remarkable opportunities for resource-efficient quantum estimation. Although superficially disconnected from traditional inference methods, we show how classical shadows fit under a larger umbrella of least squares regularization, revealing tradeoffs with related methods.

Zhu, Zhihui [Ohio State University]↗
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)↗