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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 OSTI2020

A practical and efficient approach for Bayesian quantum state estimation

Bayesian inference is a powerful paradigm for quantum state tomography, treating uncertainty in meaningful and informative ways. Yet the numerical challenges associated with sampling from complex probability distributions hampers Bayesian tomography in practical settings. In this article, we introduce an improved, self-contained approach for Bayesian quantum state estimation. Leveraging advances in machine learning and statistics, our formulation relies on highly efficient preconditioned Crank–Nicolson sampling and a pseudo-likelihood. We theoretically analyze the computational cost, and provide explicit examples of inference for both actual and simulated datasets, illustrating improved performance with respect to existing approaches.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Quantum information meets high-energy physics: input to the update of the European strategy for particle physics

Some of the most astonishing and prominent properties of Quantum Mechanics, such as entanglement and Bell nonlocality, have only been studied extensively in dedicated low-energy laboratory setups. The feasibility of these studies in the high-energy regime explored by particle colliders was only recently shown and has gathered the attention of the scientific community. For the range of particles and fundamental interactions involved, particle colliders provide a novel environment where quantum information theory can be probed, with energies exceeding by about 12 orders of magnitude those employed in dedicated laboratory setups. Furthermore, collider detectors have inherent advantages in performing certain quantum information measurements and allow for the reconstruction of the state of the system under consideration via quantum state tomography. Here, we elaborate on the potential, challenges, and goals of this innovative and rapidly evolving line of research and discuss its expected impact on both quantum information theory and high-energy physics.

Physics↗

DOE OSTI2022

Bayesian tomography of high-dimensional on-chip biphoton frequency combs with randomized measurements

Abstract Owing in large part to the advent of integrated biphoton frequency combs, recent years have witnessed increased attention to quantum information processing in the frequency domain for its inherent high dimensionality and entanglement compatible with fiber-optic networks. Quantum state tomography of such states, however, has required complex and precise engineering of active frequency mixing operations, which are difficult to scale. To address these limitations, we propose a solution that employs a pulse shaper and electro-optic phase modulator to perform random operations instead of mixing in a prescribed manner. We successfully verify the entanglement and reconstruct the full density matrix of biphoton frequency combs generated from an on-chip Si 3 N 4 microring resonator in up to an 8 × 8-dimensional two-qudit Hilbert space, the highest dimension to date for frequency bins. More generally, our employed Bayesian statistical model can be tailored to a variety of quantum systems with restricted measurement capabilities, forming an opportunistic tomographic framework that utilizes all available data in an optimal way.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Memcomputing the Spectrum of Correlated Quantum Systems

The goals and objectives of the grant DE‐SC0020892 were to apply a new computing paradigm, MemComputing, to efficiently simulate properties of correlated quantum systems. The method has been applied to a wide set of problems ranging from quantum state tomography to finding the ground state of correlated systems. In all cases, substantial advantages compared to state-of-the-art approaches have been obtained. The project has also led to the suggestion of the transformer architecture (used nowadays in large-language models) as an efficient quantum state representation, and a better understanding of the role of memory in the generation of long-range order in neural networks. This grant has supported the work of a PhD student, inspired a new class on unconventional computing taught at the University of California, San Diego and has generated several peer-reviewed papers.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Learning Quantum States and Unitaries of Bounded Gate Complexity

While quantum state tomography is notoriously hard, most states hold little interest to practically minded tomographers. Given that states and unitaries appearing in nature are of bounded gate complexity, it is natural to ask if efficient learning becomes possible. In this work, we prove that to learn a state generated by a quantum circuit with G two-qubit gates to a small trace distance, a sample complexity scaling linearly in G is necessary and sufficient. We also prove that the optimal query complexity to learn a unitary generated by G gates to a small average-case error scales linearly in G . While sample-efficient learning can be achieved, we show that under reasonable cryptographic conjectures, the computational complexity for learning states and unitaries of gate complexity G must scale exponentially in G . We illustrate how these results establish fundamental limitations on the expressivity of quantum machine-learning models and provide new perspectives on no-free-lunch theorems in unitary learning. Together, our results answer how the complexity of learning quantum states and unitaries relate to the complexity of creating these states and unitaries. Published by the American Physical Society 2024

Zhao, Haimeng (ORCID:0000000166751489)↗

DOE OSTI2024

Adiabatic quantum imaginary time evolution

We introduce an adiabatic state preparation protocol which implements quantum imaginary time evolution under the Hamiltonian of the system. Unlike the original quantum imaginary time evolution algorithm, adiabatic quantum imaginary time evolution does not require quantum state tomography during its runtime and, unlike standard adiabatic state preparation, the final Hamiltonian is not the system Hamiltonian. Instead, the algorithm obtains the adiabatic Hamiltonian by integrating a classical differential equation that ensures that one follows the imaginary time evolution state trajectory. We introduce some heuristics that allow this protocol to be implemented on quantum architectures with limited resources. We explore the performance of this algorithm via classical simulations in a one-dimensional spin model and highlight essential features that determine its cost, performance, and implementability for longer times, and compare to the original quantum imaginary time evolution for ground-state preparation. More generally, our algorithm expands the range of states accessible to adiabatic state preparation methods beyond those that are expressed as ground states of simple explicit Hamiltonians. Published by the American Physical Society 2024

Hejazi, Kasra (ORCID:000000032349478X)↗

DOE OSTI2024

Polarization–frequency hyperentangled photons: generation, characterization, and manipulation

Frequency-bin encoding is massively parallelizable and robust for optical fiber transmission. When coupled with an additional degree of freedom (DoF), the expansion of the Hilbert space allows for deterministic controlled operations between two DoFs within a single photon. Such capabilities, when combined with photonic hyperentanglement, are of great value for quantum communication protocols, including dense coding and single-copy entanglement distillation. In this talk, we present an all-fiber-coupled, ultrabroadband polarization–frequency hyperentangled source and conduct comprehensive quantum state tomography across multiple dense wavelength division multiplexing channels spanning the optical C+L-band (1530–1625 nm). In addition, we design and implement a high-fidelity controlled-NOT (cnot) operation between polarization and frequency DoFs by exploiting electro-optic phase modulation within a fiber Sagnac loop. Collectively, our hyperentangled source and two-qubit gate should unlock new opportunities for harnessing polarization–frequency resources in established telecommunication fiber networks for future quantum applications.

Lu, Hsuan-Hao↗

DOE OSTI2023

Experimental generation of polarization entanglement from spontaneous parametric down-conversion pumped by spatiotemporally highly incoherent light

Here, we investigate the cross influence of the pump coherence on the entanglement produced from spontaneous parametric down-conversion (SPDC) in different degrees of freedom (DOFs). We experimentally demonstrate the generation of polarization entanglement from SPDC pumped by a spatiotemporally highly incoherent (STHI) light-emitting diode. Our quantum state tomography measurements using multimode collection fibers to avoid postselection yield a two-qubit state with the concurrence of 0.531 ± 0.006 and purity of 0.647 ± 0.005, in excellent agreement with our theoretically predicted concurrence of 0.552 and purity of 0.652. We find that using an STHI pump reduces the entanglement and purity of the output polarization two-qubit state due to a coupling between the spatiotemporal and polarization DOFs introduced by the birefringence and dispersion of the nonlinear crystal. The viability of SPDC with STHI pumps is important for two reasons: (i) STHI sources are ubiquitous and available at a wider range of wavelengths than lasers, and (ii) the generated STHI polarization-entangled two-photon states could potentially be useful in long-distance quantum communication schemes due to their robustness to scattering.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Existence of a robust optimal control process for efficient measurements in a two-qubit system

The verification of quantum entanglement is essential for quality control in quantum communication. In this work we propose an efficient protocol to directly verify the two-qubit entanglement of a known target state through a single-expectation-value measurement. Our method provides exact entanglement quantification using the concurrence measure without performing quantum state tomography. We prove the existence of a unitary transformation that drives a known initial state of a two-qubit system to a designated final state, where the trace over a chosen observable directly yields the concurrence of the initial state. Furthermore, we implement an optimal control process of that transformation and demonstrate its effectiveness through numerical simulations. We also show that this process is robust to environmental noise. Our approach offers advantages in directly verifying entanglement with low circuit depth, making it suitable for industrial-scale quality control of entanglement generation. Our results presented here provide mathematical justification for our earlier computational experiments.

Rodriguez, Ricardo [McPherson Coll.] (ORCID:000000↗

DOE OSTI2026

Phase-Dependent Squeezing in Dual-Comb Interferometry

Manipulating the quantum noise of continuous-wave lasers through squeezing has reshaped optical interferometry. However, progress in optical frequency comb interferometry with pulsed squeezed sources has been limited, despite the role of frequency combs in ultraprecise optical metrology. Here, we introduce a new time-domain approach to characterizing squeezed femtosecond light pulses using dual-comb interferometry. Time-domain interferograms are generated via multiheterodyne beating between the modes of a Kerr soliton-squeezed frequency comb and a coherent state comb. The interferogram noise reveals phase-dependent squeezing and antisqueezing, dipping as much as 3.8 ± 0.2 dB below the shot noise level at alternating zero crossings. We model this nonstationary quantum noise as a periodic optical displacement of the squeezed comb by the coherent comb. These results support a route toward quantum-enhanced dual-comb timing applications and high-speed quantum state tomography with dual-comb interferometers.

Herman, Daniel Issac [University of Colorado, Boul↗

DOE OSTI2025

Unorthodox Parallelization for Bayesian Quantum State Estimation

Bayesian inference enables informationally efficient quantum state tomography (QST) yet is challenging to scale computationally. We demonstrate a parallelizable Bayesian QST method that, although unorthodox, proves remarkably practical, attaining significant speedups in multiqubit state estimation.

Nguyen, Hanson H. [Arizona State University] (ORCI↗

DOE OSTI2021

Attention-based quantum tomography

Abstract With rapid progress across platforms for quantum systems, the problem of many-body quantum state reconstruction for noisy quantum states becomes an important challenge. There has been a growing interest in approaching the problem of quantum state reconstruction using generative neural network models. Here we propose the ‘attention-based quantum tomography’ (AQT), a quantum state reconstruction using an attention mechanism-based generative network that learns the mixed state density matrix of a noisy quantum state. AQT is based on the model proposed in ‘Attention is all you need’ by Vaswani et al (2017 NIPS ) that is designed to learn long-range correlations in natural language sentences and thereby outperform previous natural language processing (NLP) models. We demonstrate not only that AQT outperforms earlier neural-network-based quantum state reconstruction on identical tasks but that AQT can accurately reconstruct the density matrix associated with a noisy quantum state experimentally realized in an IBMQ quantum computer. We speculate the success of the AQT stems from its ability to model quantum entanglement across the entire quantum system much as the attention model for NLP captures the correlations among words in a sentence.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Testbed and Experiments for Quantum-Conventional Networking

The realization of quantum networks requires the development of devices and methods unprecedented in conventional networks, and yet they critically depend on the latter for implementing foundational blocks and essential operations. We describe a testbed to support the development and testing of their functionality and performance by providing quantum and conventional data planes and devices, together with a secure conventional control plane. It incorporates a variety of entangled photon sources, qubit technologies, detector technologies, photonic components, and supporting conventional switches and workstations. It implements a novel fiber telescoping scheme that provides suites of connections using fiber spools and inground-aerial fiber loops. We briefly summarize a variety of experiments conducted over this testbed including: (i) flex-grid quantum connection experiments, (ii) quantum state and channel tomography, (iii) utilization of quantum key distribution keys to secure conventional encryption and firewall devices, (iv) comparative study of analytical capacity estimates and entanglement throughput, (v) deployed squeezing coexisting with conventional communications, and (iv) measurement of polarization time variation.

Rao, Nageswara [ORNL] (ORCID:0000000234085941)↗

DOE OSTI2022

Dimension-adaptive machine learning-based quantum state reconstruction

Here, we introduce an approach for performing quantum state reconstruction on systems of n qubits using a machine learning-based reconstruction system trained exclusively on m qubits, where m ≥ n. This approach removes the necessity of exactly matching the dimensionality of a system under consideration with the dimension of a model used for training. We demonstrate our technique by performing quantum state reconstruction on randomly sampled systems of one, two, and three qubits using machine learning-based methods trained exclusively on systems containing at least one additional qubit. The reconstruction time required for machine learning-based methods scales significantly more favorably than the training time; hence this technique can offer an overall saving of resources by leveraging a single neural network for dimension-variable state reconstruction, obviating the need to train dedicated machine learning systems for each Hilbert space.

42 ENGINEERING↗

DOE OSTI2019

Unidirectional distributed acoustic reflection transducers for quantum applications

Recent significant advances in coupling superconducting qubits to acoustic wave resonators have led to demonstrations of quantum control of surface and bulk acoustic resonant modes as well as Wigner tomography of quantum states in these modes. These advances were achieved through the efficient coupling afforded by piezoelectric materials combined with GHz-frequency acoustic Fabry-Perot cavities. Quantum control of itinerant surface acoustic waves appears in reach but is challenging due to the limitations of conventional transducers in the appropriate gigahertz-frequency band. In particular, gigahertz-frequency unidirectional transducers would provide an important addition to the desired quantum toolbox, promising unit efficiency with directional control over the surface acoustic wave emission pattern. Here, we report the design, fabrication, and experimental characterization of unidirectional distributed acoustic reflection transducers demonstrating a high transduction frequency of 4.8GHz with a peak directivity larger than 25dB and a directivity greater than 15dB over a bandwidth of 17MHz. A numerical model reproduces the main features of the transducer response quite well, with ten adjustable parameters (most of which are constrained by geometric and physical considerations). Finally, this represents a significant step toward quantum control of itinerant quantum acoustic waves.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2026

Solovay-Kitaev Algorithm and Randomized Compilation Data Availability

This zipped folder contains simulation notebooks, simulated data, and experimental data from the QSCOUT trapped-ion device that were used in the publication "Solovay-Kitaev Algorithm and Randomized Compilation" (https://doi.org/10.1103/ll6m-dbl7). The raw data is in the form of measurement outcomes of simple tomographic quantum circuits that were executed on the QSCOUT device and simulated using JAQALPAQ. These data are used to create plots within the jupyter notebooks that were included in the publication.

Quantum benchmarking↗

DOE OSTI2024

Quantum Tensor-Product Decomposition from Choi-State Tomography

The Schmidt decomposition is the go-to tool for measuring bipartite entanglement of pure quantum states. Similarly, it is possible to study the entangling features of a quantum operation using its operator-Schmidt or tensor-product decomposition. While quantum technological implementations of the former are thoroughly studied, entangling properties on the operator level are harder to extract in the quantum computational framework because of the exponential nature of sample complexity. Here, we present an algorithm for unbalanced partitions into a small subsystem and a large one (the environment) to compute the tensor-product decomposition of a unitary the effect of which on the small subsystem is captured in classical memory, while the effect on the environment is accessible as a quantum resource. This quantum algorithm may be used to make predictions about operator nonlocality and effective open quantum dynamics on a subsystem, as well as for finding low-rank approximations and low-depth compilations of quantum circuit unitaries. We demonstrate the method and its applications on a time-evolution unitary of an isotropic Heisenberg model in two dimensions. Published by the American Physical Society 2024

Mansuroglu, Refik (ORCID:000000017352513X)↗