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DOE OSTI2025

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical optimization algorithms. Although LP decoders have been proposed for quantum codes, their performance and limitations remain relatively underexplored. In this work, we uncover a key limitation of LP decoding for quantum low-density parity-check (LDPC) codes: certain constant-weight error patterns lead to ambiguous fractional solutions that cannot be resolved through independent rounding. To address this issue, we incorporate a post-processing technique known as ordered statistics decoding (OSD), which significantly enhances LP decoding performance in practice. Our results show that LP decoding, when augmented with OSD, can outperform belief propagation with the same post-processing for intermediate code sizes of up to hundreds of qubits. These findings suggest that LP-based decoders, equipped with effective post-processing, offer a promising approach for decoding near-term quantum LDPC codes.

Gu, Shouzhen [Yale U.]↗

DOE OSTI2025

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Gu, Shouzhen [Yale U.]↗

DOE OSTI2025

Power and Limitations of Linear Programming Decoder for Quantum LDPC Codes

Gu, Shouzhen [Yale U.]↗

DOE OSTI2022

Modeling quantum state transport with SQMS devices

To scale up the Hilbert space of architectures for quantum computation involving microwave cavities, we need to control more and more photons states. A big step forward in this direction would be to connect two different cavities from a quantum mechanics point of view. In this report, we will discuss which experimental approach would be feasible to transfer a quantum state from one cavity to another. To perform this task, we will take advantage of the secondary modes of the cavities, discussing how a variable coupling between the cavity modes could help us in this process. In the end, we will see how we can create entanglement between the cavities from this procedure.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

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 OSTI2022

Energy Use in Quantum Data Centers: Scaling the Impact of Computer Architecture, Qubit Performance, Size, and Thermal Parameters

As quantum computers increase in size, the total energy used by a quantum data center, including the cooling, will become a greater concern. The cooling requirements of quantum computers, which operate at temperatures near absolute zero, are determined by computing system parameters, including the number and type of physical qubits, the packaging efficiency of the system, and the split between circuits operating at cryogenic temperatures and those operating at room temperature. When combined with thermal system parameters such as cooling efficiency and cryostat heat transfer, the total energy use can be determined using a first-principles energy model. These models show that cooling of quantum computers differs in two fundamental ways from conventional data centers: (1) the energy required for cooling is much greater than the energy required for computation, and (2) the cooling loads are sensitive to the computational architecture. The temperature requirements for different qubit types can change energy requirements by orders of magnitude. Power use and computational power, as quantified by quantum volume, are analytically correlated. Approaches are identified for minimizing energy use in integrated quantum systems relative to computational power. Furthermore, designing a sustainable quantum computer will require both efficient cooling and system design that minimizes cooling requirements.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Design of an ultra-low mode volume piezo-optomechanical quantum transducer

Coherent transduction of quantum states from the microwave to the optical domain can play a key role in quantum networking and distributed quantum computing. We present the design of a piezo-optomechanical device formed in a hybrid lithium niobate on silicon platform, that is suitable for microwave-to-optical quantum transduction. Our design is based on acoustic hybridization of an ultra-low mode volume piezoacoustic cavity with an optomechanical crystal cavity. The strong piezoelectric nature of lithium niobate allows us to mediate transduction via an acoustic mode which only minimally interacts with the lithium niobate, and is predominantly silicon-like, with very low electrical and acoustic loss. We estimate that this transducer can realize an intrinsic conversion efficiency of up to 35% with <0.5 added noise quanta when resonantly coupled to a superconducting transmon qubit and operated in pulsed mode at 10 kHz repetition rate. The performance improvement gained in such hybrid lithium niobate-silicon transducers make them suitable for heralded entanglement of qubits between superconducting quantum processors connected by optical fiber links.

Chiappina, Piero↗

DOE OSTI2021

Quantum Divide and Compute: Exploring the Effect of Different Noise Sources

Abstract Our recent work (Ayral et al. in Proceedings of IEEE computer society annual symposium on VLSI, ISVLSI, pp 138–140, 2020. 10.1109/ISVLSI49217.2020.00034 ) showed the first implementation of the Quantum Divide and Compute (QDC) method, which allows to break quantum circuits into smaller fragments with fewer qubits and shallower depth. This accommodates the limited number of qubits and short coherence times of quantum processors. This article investigates the impact of different noise sources—readout error, gate error and decoherence—on the success probability of the QDC procedure. We perform detailed noise modeling on the Atos Quantum Learning Machine, allowing us to understand tradeoffs and formulate recommendations about which hardware noise sources should be preferentially optimized. We also describe in detail the noise models we used to reproduce experimental runs on IBM’s Johannesburg processor. This article also includes a detailed derivation of the equations used in the QDC procedure to compute the output distribution of the original quantum circuit from the output distribution of its fragments. Finally, we analyze the computational complexity of the QDC method for the circuit under study via tensor-network considerations, and elaborate on the relation the QDC method with tensor-network simulation methods.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Scaling adaptive quantum simulation algorithms via operator pool tiling

Adaptive variational quantum simulation algorithms use information from a quantum computer to dynamically create optimal trial wave functions for a given problem Hamiltonian. A key ingredient in these algorithms is a predefined operator pool from which trial wave functions are constructed. Finding suitable pools is critical for the efficiency of the algorithm as the problem size increases. Here, we present a technique called operator pool tiling that facilitates the construction of problem-tailored pools for arbitrarily large problem instances. By first performing an Adaptive Derivative-Assembled Problem-Tailored Ansatz Variational Quantum Eigensolver (ADAPT-VQE) calculation on a smaller instance of the problem using a large, but computationally inefficient, operator pool, we extract the most relevant operators and use them to design more efficient pools for larger instances. We demonstrate the method here on strongly correlated quantum spin models in one and two dimensions, finding that ADAPT automatically finds a highly effective ansatz for these systems. Given that many problems, such as those arising in condensed matter physics, have a naturally repeating lattice structure, we expect the pool tiling method to be a widely applicable technique apt for such systems. Published by the American Physical Society 2024

Van Dyke, John S. (ORCID:0000000167815480)↗

DOE OSTI2020

A quantum algorithm to efficiently sample from interfering binary trees

Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by a binary tree, we construct an explicit quantum algorithm that runs in polynomial time to sample from the process once. The corresponding naive Markov Chain algorithm does not produce the correct probability distribution and an explicit classical calculation of the full distribution requires exponentially many operations. Finally, the problem can be reduced to a system of two qubits with repeated measurements, shedding light on a quantum-inspired efficient classical algorithm.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Qubit Assignment Using Time Reversal

As quantum computers with large numbers of qubits become increasingly available, experiments executed on a given device may not utilize all available qubits. In this case, the outcome of executing a quantum program will depend on the ability to efficiently select a subset of high-performing physical qubits. For any given quantum program and device there are many ways to assign physical qubits for execution of the program, and assignments will differ in performance due to the variability in quality across qubits and entangling operations on a single device. Evaluating the performance of each assignment using fidelity estimation introduces significant experimental overhead and will be infeasible for many applications, while relying on standard device benchmarks provides incomplete information about the performance of any specific program. Furthermore, the number of possible assignments grows combinatorially in the number of qubits on the device and in the program, motivating the use of heuristic optimization techniques. We demonstrate a practical solution to the problem of qubit assignment by using simulated annealing with a cost function based on the Loschmidt echo, a diagnostic that measures the reversibility of a quantum process. We provide theoretical justification for this choice of cost function by demonstrating that the optimal qubit assignment coincides with the optimal qubit assignment based on state fidelity in the weak error limit, and we provide experimental justification using diagnostics performed on Google’s superconducting qubit devices. We then establish the performance of simulated annealing for qubit assignment using classical simulations of noisy devices as well as optimization experiments performed on a quantum processor. Our results demonstrate that the use of Loschmidt echoes and simulated annealing provides a scalable and flexible approach to optimizing qubit assignment on near-term hardware.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

A Quantum-Classical Collaborative Training Architecture Based on Quantum State Fidelity

Recent advancements have highlighted the limitations of current quantum systems, particularly the restricted number of qubits available on near-term quantum devices. This constraint greatly inhibits the range of applications that can leverage quantum computers. Moreover, as the available qubits increase, the computational complexity grows exponentially, posing additional challenges. Consequently, there is an urgent need to use qubits efficiently and mitigate both present limitations and future complexities. To address this, existing quantum applications attempt to integrate classical and quantum systems in a hybrid framework. In this study, we concentrate on quantum deep learning and introduce a collaborative classical-quantum architecture called co-TenQu. The classical component employs a tensor network for compression and feature extraction, enabling higher-dimensional data to be encoded onto logical quantum circuits with limited qubits. On the quantum side, we propose a quantum-state-fidelity-based evaluation function to iteratively train the network through a feedback loop between the two sides. co-TenQu has been implemented and evaluated with both simulators and the IBM-Q platform. Compared to state-of-the-art approaches, co-TenQu enhances a classical deep neural network by up to 41.72% in a fair setting. Additionally, it outperforms other quantum-based methods by up to 1.9 times and achieves similar accuracy while utilizing 70.59% fewer qubits.

42 ENGINEERING↗

DOE OSTI2024

Denoising and Extension of Response Functions in the Time Domain

Response functions of quantum systems, such as electron Green’s functions, magnetic, or charge susceptibilities, describe the response of a system to an external perturbation. They are the central objects of interest in field theories and quantum computing and measured directly in experiment. Further, response functions are intrinsically causal. In equilibrium and steady-state systems, they correspond to a positive spectral function in the frequency domain. Since response functions define an inner product on a Hilbert space and thereby induce a positive definite function, the properties of this function can be used to reduce noise in measured data and, in equilibrium and steady state, to construct positive definite extensions for data known on finite time intervals, which are then guaranteed to correspond to positive spectra.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Understanding Quantum Control Processor Capabilities and Limitations through Circuit Characterization

Continuing the scaling of quantum computers hinges on building classical control hardware pipelines that are scalable, extensible, and provide real time response. The instruction set architecture (ISA) of the control processor provides functional abstractions that map high-level semantics of quantum programming languages to low-level pulse generation by hardware. Here, we provide a methodology to quantitatively assess the effectiveness of the ISA to encode quantum circuits for intermediate-scale quantum devices with O(10 2 ) qubits. The characterization model that we define reflects performance, the ability to meet timing constraint implications, scalability for future quantum chips, and other important considerations making them useful guides for future designs. Using our methodology, we propose scalar (QUASAR) and vector (qV) quantum ISAs as extensions and compare them with other ISAs in metrics such as circuit encoding efficiency, the ability to meet real-time gate cycle requirements of quantum chips, and the ability to scale to more qubits.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Observation of Coexisting Weak Localization and Superconducting Fluctuations in Strained Sn 1– x In x Te Thin Films

Topological superconductors have attracted tremendous excitement as they are predicted to host Majorana zero modes that can be utilized for topological quantum computing. Candidate topological superconductor Sn 1–x In x Te thin films (0 < x < 0.3) grown by molecular beam epitaxy and strained in the (111) plane are shown to host quantum interference effects in the conductivity coexisting with superconducting fluctuations above the critical temperature T c . An analysis of the normal state magnetoresistance reveals these effects. A crossover from weak antilocalization to localization is consistently observed in superconducting samples, indicating that superconductivity originates dominantly from charge carriers occupying trivial states that may be strongly spin–orbit split. A large enhancement of the conductivity is observed above T c , indicating the presence of superconducting fluctuations. Furthermore, our results motivate a re-examination of the debated pairing symmetry of this material when subjected to quantum confinement and lattice strain.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

DOE OSTI2025

Exact closed-form unitary transformations of fermionic operators

Unitary transformations play a fundamental role in many-body physics, and except for special cases, they are not expressible in closed form. We present closed-form expressions for unitary transformations generated by a single fermionic operator for Hermitian and anti-Hermitian generators. We demonstrate the usefulness of these expressions in formal analyses of unitary transformations and numerical applications to Hamiltonian downfolding in quantum computing and Heisenberg dynamics. Furthermore, this work paves the way for new analytical treatments of unitary transformations and numerical many-body methods for fermions.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2021

First-Principles Predictions of Out-of-Plane Group IV and V Dimers as High-Symmetry, High-Spin Defects in Hexagonal Boron Nitride

Hexagonal boron nitride (h-BN) has been recently found to host a variety of quantum point defects, which are promising candidates as single-photon sources for solid-state quantum nanophotonic applications. Most recently, optically addressable spin qubits in h-BN have been the focus of intensive research due to their unique potential in quantum computation, communication, and sensing. However, the number of high-symmetry, high-spin defects that are desirable for developing spin qubits in h-BN is highly limited. Here, we combine density functional theory (DFT) and quantum embedding theories to show that out-of-plane X N Y i dimer defects (X, Y = C, N, P, and Si) form a new class of stable C 3v spin-triplet defects in h-BN. We find that the dimer defects have a robust 3 A 2 ground state and 3 E excited state, both of which are isolated from the h-BN bulk states. We show that 1 E and 1 A shelving states exist and they are positioned between the 3 E and 3 A 2 states for all the dimer defects considered in this study. To support future experimental identification of the X N Y i dimer defects, we provide extensive characterization of the defects in terms of their spin and optical properties. We predict that the zero-phonon line of the spin-triplet X N Y i defects lies in the visible range (800 nm to 500 nm). We compute the zero-field splitting of the dimers’ spin to range from 1.79 GHz (Si N P i o ) to 29.5 GHz (C N N i o ). Furthermore, our results broaden the scope of high-spin defect candidates that would be useful for the development of spin-based solid-state quantum technologies in two-dimensional hexagonal boron nitride.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Dangling Bonds as Possible Contributors to Charge Noise in Silicon and Silicon–Germanium Quantum Dot Qubits

Spin qubits based on Si and Si 1–x Ge x quantum dot architectures exhibit among the best coherence times of competing quantum computing technologies, yet they still suffer from charge noise that limit their qubit gate fidelities. Identifying the origins of these charge fluctuations is therefore a critical step toward improving Si quantum-dot-based qubits. Here, we use hybrid functional calculations to investigate possible atomistic sources of charge noise, focusing on charge trapping at Si and Ge dangling bonds (DBs). We evaluate the role of global and local environment in the defect levels associated with DBs in Si, Ge, and Si 1–x Ge x alloys, and consider their trapping and excitation energies within the framework of configuration coordinate diagrams. We additionally consider the influence of strain and oxidation in charge-trapping energetics by analyzing Si and GeSi DBs in SiO 2 and strained Si layers in typical Si 1–x Ge x quantum dot heterostructures. Our results identify that Ge dangling bonds are more problematic charge-trapping centers both in typical Si 1–x Ge x alloys and associated oxidation layers, and they may be exacerbated by compositional inhomogeneities. In conclusion, these results suggest the importance of alloy homogeneity and possible passivation schemes for DBs in Si-based quantum dot qubits and are of general relevance to mitigating possible trap levels in other Si, Ge, and Si 1–x Ge x -based metal-oxide-semiconductor stacks and related devices.

36 MATERIALS SCIENCE↗