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DOE OSTI2024

Engineering 3D Floquet Codes by Rewinding

Floquet codes are a novel class of quantum error-correcting codes with dynamically generated logical qubits arising from a periodic schedule of noncommuting measurements. We utilize the interpretation of measurements in terms of condensation of topological excitations and the rewinding of measurement sequences to engineer new examples of Floquet codes. In particular, rewinding is advantageous for obtaining a desired set of instantaneous stabilizer groups on both toric and planar layouts. Our first example is a Floquet code with instantaneous stabilizer codes that have the same topological order as the three-dimensional (3D) toric code(s). This Floquet code also exhibits a splitting of the topological order of the 3D toric code under the associated sequence of measurements, i.e., an instantaneous stabilizer group of a single copy of the 3D toric code in one round transforms into an instantaneous stabilizer group of two copies of the 3D toric code up to nonlocal stabilizers in the following round. We further construct boundaries for this 3D code and argue that stacking it with two copies of the 3D subsystem toric code allows for a transversal implementation of the logical non-Clifford controlled-controlled- Z gate. We also show that the coupled-layer construction of the X-cube Floquet code can be modified by a rewinding schedule such that each of the instantaneous stabilizer codes is finite depth equivalent to the X-cube model up to toric codes; the X-cube Floquet code exhibits a splitting of the X-cube model into a copy of the X-cube model and toric codes under the measurement sequence. Our final 3D example is a generalization of the 2D Floquet toric code on the honeycomb lattice to three dimensions, which has instantaneous stabilizer codes with the same topological order as the 3D fermionic toric code. Published by the American Physical Society2024

Physics↗
DOE OSTI2024

Simulating Open Quantum Systems Using Hamiltonian Simulations

We present a novel method to simulate the Lindblad equation, drawing on the relationship between Lindblad dynamics, stochastic differential equations, and Hamiltonian simulations. We derive a sequence of unitary dynamics in an enlarged Hilbert space that can approximate the Lindblad dynamics up to an arbitrarily high order. This unitary representation can then be simulated using a quantum circuit that involves only Hamiltonian simulation and tracing out the ancilla qubits. There is no need for additional postselection in measurement outcomes, ensuring a success probability of one at each stage. Our method can be directly generalized to the time-dependent setting. We provide numerical examples that simulate both time-independent and time-dependent Lindbladian dynamics with accuracy up to the third order. Published by the American Physical Society 2024

Ding, Zhiyan (ORCID:000000018863403X)↗
DOE OSTI2024

Generalized Quantum Signal Processing

Quantum signal processing (QSP) and quantum singular value transformation (QSVT) currently stand as the most efficient techniques for implementing functions of block-encoded matrices, a central task that lies at the heart of most prominent quantum algorithms. However, current QSP approaches face several challenges, such as the restrictions imposed on the family of achievable polynomials and the difficulty of calculating the required phase angles for specific transformations. In this paper, we present a generalized quantum signal processing (GQSP) approach, employing general SU(2) rotations as our signal-processing operators, rather than relying solely on rotations in a single basis. Our approach lifts all practical restrictions on the family of achievable transformations, with the sole remaining condition being that | P | ≤ 1 , a restriction necessary due to the unitary nature of quantum computation. Furthermore, GQSP provides a straightforward recursive formula for determining the rotation angles needed to construct the polynomials in cases where P and Q are known. In cases where only P is known, we provide an efficient optimization algorithm capable of identifying in under a minute of GPU time, a corresponding Q for polynomials of degree on the order of 10 7 . We further illustrate GQSP simplifies QSP-based strategies for Hamiltonian simulation, offer an optimal solution to the ϵ -approximate fractional query problem that requires O ( ( 1 / δ ) + log ( 1 / ϵ ) ) queries to perform where O ( 1 / δ ) is a proved lower bound, and introduces novel approaches for implementing bosonic operators. Moreover, we propose a novel framework for the implementation of normal matrices, demonstrating its applicability through synthesis of diagonal matrices, as well as the development of a new algorithm for convolution through synthesis of circulant matrices using only O ( d log N + log 2 N ) 1 and 2-qubit gates for a filter of lengths d . Published by the American Physical Society 2024

Motlagh, Danial↗
DOE OSTI2024

Fully Scalable Randomized Benchmarking Without Motion Reversal

We introduce , a protocol that streamlines traditional RB by using circuits consisting almost entirely of independent identically distributed (IID) layers of gates. BiRB reliably and efficiently extracts the average error rate of a Clifford gate set by sending tensor-product eigenstates of random Pauli operators through random circuits with IID layers. Unlike existing RB methods, BiRB does not use motion reversal circuits—i.e., circuits that implement the identity (or a Pauli) operator—which simplifies both the method and the theory proving its reliability. Furthermore, this simplicity enables scaling BiRB to many more qubits than the most widely used RB methods. Published by the American Physical Society 2024

Hines, Jordan (ORCID:0000000151267256)↗
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

Circuit-Based Leakage-to-Erasure Conversion in a Neutral-Atom Quantum Processor

Atom-loss errors are a major limitation of current state-of-the-art neutral-atom quantum computers and pose a significant challenge for scalable systems. In a quantum processor with cesium atoms, we demonstrate proof-of-principle circuit-based conversion of this form of leakage error to erasure errors via leakage-detection units (LDUs), which nondestructively map information about the presence or absence of the qubit onto the state of an ancilla. We benchmark the performance of the LDU using a three-outcome low-loss state-detection method and find that the LDU detects atom-loss errors with approximately 93.4% accuracy, limited by technical imperfections of our apparatus. We further compile and execute a SWAP LDU, wherein the roles of the original data atom and ancilla atom are exchanged under the action of the LDU, providing “free refilling” of atoms in the case of atom loss. This circuit-based leakage-to-erasure error conversion is a critical component of a neutral-atom quantum processor where the quantum information may significantly outlive the lifetime of any individual atom in the quantum register. Finally, we demonstrate that LDUs may also be used to handle other forms of leakage errors where population moves to states outside of the computational subspace.

Chow, Matthew N. H. [Sandia National Laboratories ↗
DOE OSTI2024

Exponential Improvements in the Simulation of Lattice Gauge Theories Using Near-Optimal Techniques

We report a first-of-its-kind analysis on post-Trotter simulation of U(1), SU(2), and SU(3) lattice gauge theories including fermions in arbitrary spatial dimension. We provide explicit circuit constructions as well as T-gate counts and logical qubit counts for Hamiltonian simulation. We find a reduction of up to 25 orders of magnitude in space-time volume over Trotter methods for simulations of non-Abelian lattice gauge theories relevant to the standard model. This improvement results from our algorithm having polynomial scaling with the number of colors in the gauge theory, achieved by utilizing oracle constructions relying on the sparsity of physical operators, in contrast to the exponential scaling seen in state-of-the-art Trotter methods, which employ explicit mappings onto Pauli operators. Our work demonstrates that the use of advanced algorithmic techniques leads to dramatic reductions in the cost of simulating fundamental interactions, bringing it in step with resources required for first-principles quantum simulation of chemistry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Toward a 2D Local Implementation of Quantum Low-Density Parity-Check Codes

Geometric locality is an important theoretical and practical factor for quantum low-density parity-check (qLDPC) codes that affects code performance and ease of physical realization. For device architectures restricted to two-dimensional (2D) local gates, naively implementing the high-rate codes suitable for low-overhead fault-tolerant quantum computing incurs prohibitive overhead. In this work, we present an error-correction protocol built on a bilayer architecture that aims to reduce operational overheads when restricted to 2D local gates by measuring some generators less frequently than others. We investigate the family of bivariate-bicycle qLDPC codes and show that they are well suited for a parallel syndrome-measurement scheme using fast routing with local operations and classical communication (LOCC). Through circuit-level simulations, we find that in some parameter regimes, bivariate-bicycle codes implemented with this protocol have logical error rates comparable to the surface code while using fewer physical qubits. Published by the American Physical Society 2025

Berthusen, Noah (ORCID:0000000275862786)↗
DOE OSTI2025

Noisy Approach to Intrinsically Mixed-State Topological Order

We propose a general framework for studying two-dimensional (2D) topologically ordered states subject to local correlated errors and show that the resulting mixed state can display (imTO)—topological order that is not expected to occur in the ground state of 2D local gapped Hamiltonians. Specifically, we show that decoherence, previously interpreted as anyon condensation in a doubled Hilbert space, is more naturally phrased as, and provides a physical mechanism for, “gauging out” anyons in the original Hilbert space. We find that gauging out anyons generically results in imTO, with the decohered mixed state strongly symmetric under certain anomalous 1-form symmetries. This framework lays bare a striking connection between the decohered density matrix and , which can appear as anomalous surface states of three-dimensional topological orders. Through a series of examples, we show that the decohered state can display a classical memory, encode logical qubits (i.e., exhibit a quantum memory), and even host chiral or nonmodular topological order. We argue that a partial classification of imTO is given in terms of nonmodular braided-fusion categories. Published by the American Physical Society 2025

Sohal, Ramanjit (ORCID:0000000292975715)↗
DOE OSTI2025

Efficiently Verifiable Quantum Advantage on Near-Term Analog Quantum Simulators

Existing schemes for demonstrating quantum computational advantage are subject to various practical restrictions, including the hardness of verification and challenges in experimental implementation. Meanwhile, analog quantum simulators have been realized in many experiments to study novel physics. In this work, we propose a quantum advantage protocol based on verification of an analog quantum simulation, in which the verifier need only run an O ( λ 2 ) -time classical computation, and the prover need only prepare O ( 1 ) samples of a history state and perform O ( λ 2 ) single-qubit measurements, for a security parameter λ . We also propose a near-term feasible strategy for honest provers and discuss potential experimental realizations. Published by the American Physical Society 2025

Liu, Zhenning (ORCID:000000020794419X)↗
DOE OSTI2025

Practical Introduction to Benchmarking and Characterization of Quantum Computers

Rapid progress in quantum technology has transformed quantum computing and quantum information science from theoretical possibilities into tangible engineering challenges. Breakthroughs in quantum algorithms, quantum simulations, and quantum error correction are bringing useful quantum computation closer to fruition. These remarkable achievements have been facilitated by advances in quantum characterization, verification, and validation (QCVV). QCVV methods and protocols enable scientists and engineers to scrutinize, understand, and enhance the performance of quantum information-processing devices. In this tutorial, we review the fundamental principles underpinning QCVV, and introduce a diverse array of QCVV tools used by quantum researchers. We define and explain QCVV’s core models and concepts—quantum states, measurements, and processes—and illustrate how these building blocks are leveraged to examine a target system or operation. We survey and introduce protocols ranging from simple qubit characterization to advanced benchmarking methods. Along the way, we provide illustrated examples and detailed descriptions of the protocols, highlight the advantages and disadvantages of each, and discuss their potential scalability to future large-scale quantum computers. This tutorial serves as a guidebook for researchers unfamiliar with the benchmarking and characterization of quantum computers, and also as a detailed reference for experienced practitioners.

open quantum systems & decoherence↗
DOE OSTI2025

Constant-Overhead Fault-Tolerant Bell-Pair Distillation Using High-Rate Codes

We present a fault-tolerant Bell-pair distillation scheme achieving constant overhead through high-rate quantum low-density parity-check (qLDPC) codes. Our approach maintains a constant distillation rate equal to the code rate while requiring no additional overhead beyond the physical qubits of the code. Full circuit-level analysis demonstrates fault-tolerance for input Bell-pair infidelities below a threshold ∼10%, readily achievable with near-term capabilities. Unlike previous proposals, our scheme keeps the output Bell pairs encoded in qLDPC codes at each node, eliminating unencoding overhead and enabling direct use in distributed quantum applications through recent advances in qLDPC computation. These results establish qLDPC-based distillation as a practical route toward resource-efficient quantum networks and distributed quantum computing.

quantum communication, protocols & technology↗
DOE OSTI2026

Correlated Noise Estimation with Quantum Sensor Networks

We address the metrological problem of estimating collective stochastic properties imprinted on a network of quantum sensors. Canonical examples include center-of-mass quadrature fluctuations in a system of bosonic modes and correlated dephasing in an ensemble of qubits (e.g., spins), bosons, or fermions. We develop a theoretical framework to determine the limits of correlated (weak) noise estimation with quantum sensor networks and reveal the requirements for entanglement advantage. Notably, an advantage emerges from the synergistic interplay between quantum correlations of the sensors and “classical” correlations of the noises. Here, we determine optimal entangled probe states and identify a sensing protocol—reminiscent of a many-body echo—that achieves the fundamental limits of measurement sensitivity for a broad class of problems, unveiling a route toward entanglement-enhanced metrology of correlated many-body phenomena.

Quantum metrology↗
DOE OSTI2026

Braiding of Majorana zero modes in vortex cores

Here, we demonstrate the successful simulation of $\sqrt{𝑍-}$, $\sqrt{𝑋-}$, and 𝑋-quantum gates using Majorana zero modes (MZMs) that emerge in magnetic vortices located in topological superconductors. We compute the transition probabilities and geometric phase differences accounting for the full many-body dynamics and show that qubit states can be read out by fusing the vortex core MZMs and measuring the resulting charge density. We visualize the gate processes using the time- and energy-dependent nonequilibrium local density of states. Our results demonstrate the feasibility of employing vortex core MZMs for the realization of fault-tolerant topological quantum computing.

Majorana bound states↗
DOE OSTI2026

Fast Sideband Control of a Multimode Cavity Memory with Weak Dispersive Coupling to a Transmon

Mitigating ancilla-mediated error channels is a critical challenge in controlling high-quality superconducting cavities using circuit quantum electrodynamics (cQED). We address this by weakening the dispersive coupling while demonstrating fast, high-fidelity multimode control through transmon-mediated sideband interactions. We implement transmon-cavity SWAP gates with speeds up to 30 times larger than the bare dispersive coupling. Combined with transmon rotations, this enables universal state preparation in a single mode, though achieving unitary gates and extending control to multiple modes remains a challenge. In this work, we overcome this limitation by introducing two control strategies: (i) a shelving technique that stores populations in sideband-transparent states, and (ii) a method that exploits the dispersive shift to implement photon-number-selective transmon-cavity SWAP gates. We use these protocols to prepare Fock and binomial code states across any of the ten modes of a multimode cavity with millisecond coherence times—serving as a multimode quantum memory. We demonstrate unitaries that encode and decode an arbitrary qubit state from the transmon into corresponding vacuum and Fock state superpositions, as well as entangled NOON states of cavity mode pairs—a scheme extendable to arbitrary multimode Fock encodings in the cavity modes. Furthermore, we implement a new binomial encoding gate that converts arbitrary transmon superpositions into binomial code states in any cavity mode at a rate exceeding the dispersive shifts in our system, achieving an average post-selected state fidelity of 96.3% in a 4 μ⁢s gate time. By using precalibrated transmon and sideband pulses, our work demonstrates multimode control with significantly reduced calibration overhead, enabling efficient unitary operations using sideband interactions in multimode cQED systems.

Huang, Jordan [Rutgers Univ., Piscataway, NJ (Unit↗
DOE OSTI2026

Quantum simulation of QED in Coulomb gauge

A recent work considered quantum simulation of Quantum Electrodynamics on a lattice in the Coulomb gauge with gauge degrees of freedom represented in the occupation basis in momentum space. In this work, we consider the more efficient representation of the gauge degrees of freedom in field basis in position space and develop a quantum algorithm for real-time simulation. We show that the continuum Coulomb gauge Hamiltonian is equivalent to the temporal gauge Hamiltonian when acting on physical states consisting of fermion and transverse gauge fields. The Coulomb gauge Hamiltonian is discretized by using the Green’s function of the discrete Laplacian operator under the Dirichlet boundary conditions. Both the continuum Coulomb gauge Hamiltonian and the discretized one proposed here guarantee that the unphysical longitudinal gauge fields are decoupled and commute with the corresponding Hamiltonian. Thus there is no need to impose any constraint. The local gauge field basis and the canonically conjugate variable basis are swapped efficiently using the quantum Fourier transform. We prove that the qubit cost to represent physical states and the gate count for real-time simulation scale polynomially with the lattice size, energy, time, accuracy, and Hamiltonian parameters in lattice units. The gate cost here for implementing the time evolution of the gauge field is reduced at least by a factor on the order of 10 8 for modest lattice size and accuracy level compared with the previous work.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Precision study of the massive Schwinger model near quantum criticality

We perform a numerical analysis of the massive Schwinger model in the presence of a background electric field. Using the Density Matrix Renormalization Group approach, we efficiently compute the spectrum of the Schwinger model on a staggered lattice with up to 3000 qubits. As a result, we achieve a precise computation of the critical mass of the massive Schwinger model to five digits using four different “criticality criteria,” observing perfect agreement among them Additionally, we discuss the effect of a four-fermion operator deformation of the Schwinger model and compute the critical mass for various values of the deformation parameter.

Critical phenomena↗
DOE OSTI2025

Solving reaction dynamics with quantum computing algorithms

The description of quantum many-body dynamics is extremely challenging on classical computers, as it can involve many degrees of freedom. However, the time evolution of quantum states is a natural application for quantum computers that are designed to efficiently perform unitary transformations. Here, in this paper, we study quantum algorithms for response functions, relevant for describing different reactions governed by linear response. We focus on nuclear-physics applications and consider a qubit-efficient mapping on the lattice, which can efficiently represent the large volumes required for realistic scattering simulations. For the case of a contact interaction, we develop an algorithm for time evolution based on the Trotter approximation that scales logarithmically with the lattice size and is combined with quantum phase estimation. We eventually focus on the nuclear two-body system and a typical response function relevant for electron scattering as an example. We also investigate ground-state preparation and examine the total circuit depth required for a realistic calculation and the hardware noise level required to interpret the signal.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗