Quantum Physics
Solvable Random Unitary Dynamics in a Disordered Tomonaga-Luttinger Liquid
Tian-Gang Zhou and Thierry Giamarchi
Disordered one-dimensional interacting systems have long been characterized via conventional correlation functions. A complementary
quantum-information perspective quantifies the randomness of the
unitary ensemble dynamics generated by a
quantum system through the frame potential, which serves as a practical diagnostic for
quantum algorithmic performance. However, no analytical treatment has yet been achieved for experimentally accessible interacting one-dimensional systems. In this Letter, we derive a closed-form expression for the frame potential of a Tomonaga-Luttinger
liquid with quenched Gaussian forward-scattering disorder. Exploiting the exactly quadratic structure of the disorder-averaged Keldysh action, we show that the frame potential decays as a power law at early times and saturates to a late-time plateau controlled by a single coupling parameter. Taking the random field XXZ
spin chain as a specific microscopic realization, we show that the strongest randomness is achieved near the Heisenberg
ferromagnetic point and can be exponentially enhanced through a multiple-quench protocol. We validate our results across the entire gapless phase, with direct implications for
algorithm design in analog
quantum simulation platforms.
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Quantum Physics
Arbitrary parallel entangling gates with independent calibration on a trapped ion quantum computer
Matthew Diaz, Masoud Mohammadi-Arzanagh, Yingyue Zhu et al. (+4 more)
Parallel processing of information plays a critical role in accelerating computation. This includes
quantum computers, where parallel processing of
quantum information will play a critical role in practical
quantum advantage. Here, we demonstrate a new type of parallel entangling gates in a trapped-ion
quantum computer, that simultaneously provides efficient gate-pulse synthesis and calibration, as well as graph-pattern-agnostic implementation. We demonstrate the resulting reduced execution time in three well-known
algorithms, exhibiting disjoint gates, a
star graph and a ring graph respectively. For disjoint
qubit pairs the execution time of our parallel gates is comparable to that of a single-pair entangling gate resulting in an approximately linear speed up. For all graph patterns our parallel gate fidelities are comparable to the fidelity of a single-pair entangling gate. These advantages motivate architectures featuring multiple medium length ion chains in future
quantum computing devices.
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All authors Matthew Diaz, Masoud Mohammadi-Arzanagh, Yingyue Zhu, Mohammad Hafezi, Norbert M. Linke, Alaina M. Green, Arthur Y. Nam
Quantum Physics · Cross-listed from cond-mat.str-el
Towards a microscopic model for an electronic quantum charge liquid
Jacob R. Taylor, Sankar Das Sarma and Seth Musser
We provide a route to constructing an electronic
quantum charge
liquid (QCL), a state made up of
fermions at fractional filling of a
lattice that does not break translation. Starting with spinless
fermions at filling $\nu=3/2$ we pair them to get
bosons at filling $\nu=3/4$ per unit
cell. The tetramer model, a generalization of the dimer model, on the square
lattice is evaluated as a candidate bosonic QCL at filling $\nu = 3/4$. It is shown that these models exhibit a local $\mathbb{Z}_4$
symmetry. Upon numerical study of a family of tetramer wavefunctions it is found that while one is gapless due to $\mathrm{U}(1)^3$
symmetry at least one other can be definitively shown to be gapped. The gapped nature of this state, along with its $\mathbb{Z}_4$
symmetry, leads us to propose that it is an example of the elusive bosonic QCL displaying the minimal $\mathbb{Z}_4$ topological order. We conclude by discussing possible extensions to other
lattice geometries, electronic QCLs, and to Rydberg atoms.
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Quantum Physics
High-fidelity entangling gates and nonlocal circuits with neutral atoms
Simon J. Evered, Muqing Xu, Sophie H. Li et al. (+9 more)
Creation and manipulation of
entanglement with low error is essential in
quantum information systems. In practice, two-
qubit entangling gates constitute a dominant error source, limiting
circuit depths and performance in fault-tolerant architectures. Using a neutral-atom
quantum processor, we realize entangling CZ gates with a high Rabi frequency smooth-amplitude pulse, employing state-selective readout and
qubit reuse for fast calibration, and achieve state-of-the-art fidelities of 99.854(4)% which improve to 99.941(3)% upon loss postselection, with stable performance for 10 hours. We then use these low-error gates in
quantum circuits with coherent atom rearrangement. We first
benchmark performance by creating and disentangling cluster states, and subsequently implement scrambling
circuits featuring longer-range connectivity to study non-locally entangled states generated through chaotic dynamics. These results pave the way towards deep-
circuit, efficient fault-tolerant
quantum computation.
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All authors Simon J. Evered, Muqing Xu, Sophie H. Li, Alexandra A. Geim, J. Pablo Bonilla Ataides, Marcin Kalinowski, Dolev Bluvstein, Nishad Maskara, Christian Kokail, Markus Greiner, Vladan Vuletić, Mikhail D. Lukin
Quantum Physics
Characterization of Thermalization Behaviour in a Generalized Aubry-André Model
S. Mal, D. K. Nandy and B. K. Sahoo
Although random
matrix theory provides a fundamental framework for characterizing
quantum chaos, encompassing both ergodic and localized phases, a comprehensive understanding of the universal features governing the critical transition remains elusive in many disordered and quasi-random systems. In this study, we explore the ergodic-to-many-body localization transition in the generalized Aubry-André model with interacting spinless
fermions. Using the concept of Frobenius norm of an adiabatic gauge potential, we construct a phase diagram that captures the sensitivity of the eigenspectrum to infinitesimal adiabatic gauge deformations. To examine the stability of the critical disordered strength with respect to system size, we perform an unbiased finite-size scaling analysis via cost-function minimization techniques. Additionally, by analyzing the adjacent gap ratio and spectral form factor, we determine the scaling behavior of the Thouless time as a function of the disorder strength.
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Quantum Physics
No Tile Left Behind: Multiprogramming for Surface-Code Architectures
Archisman Ghosh, Avimita Chatterjee and Swaroop Ghosh
Fault-tolerant
quantum computing (FTQC) is emerging as the architectural regime in which practical large-scale
quantum workloads will execute. In this setting, however, multiprogramming is no longer a matter of partitioning a flat pool of
qubits.
Quantum error correction exposes a structured floorplan of data tiles, ancilla tiles, and magic-state service resources, so concurrent execution must account for compact placement, connectivity, routing headroom, and shared support infrastructure. This makes FTQC multiprogramming fundamentally harder than its NISQ counterpart: admission decisions can fragment the remaining floorplan, conservative reservations can waste ancilla, and dynamic contention across data, ancilla, and magic-state resources can degrade both throughput and quality of service. In this work, we develop a formal framework for FTQC multiprogramming that captures these structural constraints and their runtime implications. We formulate the baseline static allocation problem, extend it to limited-resource and online settings through hierarchy-aware scheduling policies, and further generalize it to cultivation-enabled architectures with dynamic magic-state generation. Through simulation on synthetic Clifford+T workloads, the proposed scheduler achieves a normalized system speedup of 3.1x, improving over prior FTQC multiprogramming baselines by ~29% while maintaining low mean slowdown.
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Quantum Physics
A Lie-algebraic Criterion for the Universality of Exponentiated Quantum Gates
Yinuo Xue, Qian Chen and Jing-Song Huang
We present a criterion that serves as the basis for a
polynomial-time
algorithm to decide whether a finite set of qudit gates exponentiated by some
Hamiltonians is universal. Our approach formulates universality in Lie algebraic terms and applies Borel–de Siebenthal theory with a diagonal generator having incommensurate spectrum. In this framework, nonuniversality is detected by invariant subspaces, equivalently by a graph-connectivity obstruction, while universality is repaired by adding generators that couple disconnected components. We further prove that two generators are sufficient for universal control. Our work reveals a profound link between qudit universality and irreducibility of Lie
algebra representations.
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Quantum Physics
Coherent Rollout Oracles for Finite-Horizon Sequential Decision Problems
Nishant Shukla
Coherent
quantum rollout for sequential decision problems requires a
unitary simulator: randomness must live in explicit
quantum registers, and basis-state selectors must be mapped to actions reversibly. With branch-dependent valid actions, this mapping is totalized coherent rank-select over an entangled $N$-bit validity mask: return the position of the $r$-th valid bit, or a sentinel if $r$ is out of range. We give the first reversible-
circuit complexity analysis of this primitive. For selector width $w = \lceil \log_2(N+1) \rceil$, rank-select admits an $O(Nw)$-gate low-ancilla bounded-span scan, proved gate-optimal in its model, and an $O(N\log w)$-gate low-ancilla blocked construction when long-range gates are available; across all bounded-fan-in layouts, the unconditional gate lower bound is $\Omega(N)$. Composing rank-select with reversible transition and predicate-evaluation
circuits gives an explicit
polynomial-size coherent rollout oracle for finite-horizon planning problems satisfying these primitive assumptions. The resulting oracle satisfies the access model of the best-arm pipeline of Wang et al., yielding $\widetilde{O}(\sqrt{k}/\varepsilon)$ coherent oracle calls against the standard classical $\Omega(k/\varepsilon^2)$ arm-pull lower bound. We give a bounded-influence lifting
theorem that extends this lower-bound construction from a base configuration to an exponential family of configurations. We instantiate the construction on SIR epidemic intervention, with a
stochastic placement-game sanity check, and machine-check the main results in Lean 4. Code and proofs: https://github.com/BinRoot/b01t/tree/main/demos/rollout.
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Quantum Physics
Heralding probability optimization for nonclassical light generated by photon counting measurements on multimode Gaussian states
Jaromír Fiurášek
Generation of highly non-classical
quantum states of light is essential for optical
quantum information processing and
quantum metrology. Given the lack of sufficiently strong nonlinear interactions between optical fields, the commonly employed optical
quantum-state preparation schemes are conditional, based on nonlinearity induced by heralding
photon number measurement on a part of a multimode squeezed Gaussian state. Development and optimization of such probabilistic
quantum-state engineering schemes represents one of the central challenges in current
quantum optics. As technology advances and experiments progress to detection of higher numbers of
photons, the maximization of the heralding probability becomes essential to ensure sufficiently high state-preparation rates. Here, we show that for the conditional
quantum state preparation schemes based on Gaussian states and
photon number measurements the maximization of the heralding probability can be formulated as finding solution to a system of
polynomial equations, which offers an efficient way to find the optimal configuration and allows us to apply techniques dedicated specifically to solving such systems of equations. Our approach can seamlessly incorporate bounds on the available single-mode quadrature squeezing, which is highly experimentally relevant. We mainly consider generation of finite superpositions of Fock states but show that the approach can be straightforwardly extended to generation of squeezed superpositions of Fock states. We focus on Gaussian states with vanishing coherent displacements, hence the conditionally generated states have well defined
photon number parity. We illustrate our general methodology through examples of generation of single-mode states with two and three heralding modes, and generation of two-mode states with two heralding modes.
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Quantum Physics
Testing a continuous-variable noncontextuality inequality with a hybrid-encoded system
Yu Meng, Ying Wang, Clara Henke et al. (+7 more)
Continuous-variable
quantum systems are promising candidates for
quantum computing and
quantum information processing. It is widely known that quadrature measurements on Gaussian continuous-variable systems admit a noncontextual hidden-variable description. Here, we demonstrate that this description fails once the same Gaussian correlations are instead probed using Hadamard tests. We realize the test with a hybrid discrete–continuous-variable system—the polarization and spatial modes of a single
photon deterministically generated from an InAs/GaAs
quantum emitter, with the controlled operations being the phase-space displacements selected through the Gottesman–Kitaev–Preskill correspondence. By directly measuring the correlations of the operators, we observe a violation of the noncontextual hidden-variable inequality by 380 standard deviations and independently bound the residual noncommutativity of the implemented operations. Our results open up new possibilities for studying fundamental
quantum physics using photonic-encoded continuous-variable systems.
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All authors Yu Meng, Ying Wang, Clara Henke, Nikolai Bart, Arne Ludwig, Peter Lodahl, Jonas S. Neergaard-Nielsen, Ulrik L. Andersen, Leonardo Midolo, Zheng-Hao Liu
Quantum Physics
QCalEval: Benchmarking Vision-Language Models for Quantum Calibration Plot Understanding
Shuxiang Cao, Zijian Zhang, Abhishek Agarwal et al. (+29 more)
Quantum computing calibration depends on interpreting experimental data, and calibration plots provide the most universal human-readable representation for this task, yet no systematic evaluation exists of how well
vision-
language models (VLMs) interpret them. We introduce QCalEval, the first VLM
benchmark for
quantum calibration plots: 243 samples across 87 scenario types from 22 experiment families, spanning superconducting
qubits and neutral atoms, evaluated on six question types in both zero-shot and in-context learning settings. The best general-purpose zero-shot model reaches a mean score of 72.3, and many open-weight models degrade under multi-image in-context learning, whereas frontier closed models improve substantially. A supervised fine-tuning ablation at the 9-billion-parameter scale shows that SFT improves zero-shot performance but cannot close the
multimodal in-context learning gap. As a reference case study, we release NVIDIA Ising Calibration 1, an open-weight model based on Qwen3.5-35B-A3B that reaches 74.7 zero-shot average score.
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All authors Shuxiang Cao, Zijian Zhang, Abhishek Agarwal, Grace Bratrud, Niyaz R. Beysengulov, Daniel C. Cole, Alejandro Gómez Frieiro, Elena O. Glen, Hao Hsu, Gang Huang, Raymond Jow, Greshma Shaji, Tom Lubowe, Ligeng Zhu, Luis Mantilla Calderón, Nicola Pancotti, Joel Pendleton, Brandon Severin, Charles Etienne Staub, Sara Sussman, Antti Vepsäläinen, Neel Rajeshbhai Vora, Yilun Xu, Varinia Bernales, Daniel Bowring, Elica Kyoseva, Ivan Rungger, Giulia Semeghini, Sam Stanwyck, Timothy Costa, Alán Aspuru-Guzik, Krysta Svore
Quantum Physics · Cross-listed from physics.optics
Optimized thermal control of a dual-wavelength-resonant nonlinear cavity
Fabian Meylahn, Henning Vahlbruch and Benno Willke
Optical resonator-enhanced nonlinear interactions are of great importance for the efficient generation of continuous-wave second harmonic generation, optical parametric oscillation, frequency mixing, and the generation of squeezed light. In order to maximize these interactions within the intra-cavity nonlinear material, high intensities, optimal phase matching, and simultaneous resonance of all interacting fields are required. However, the dispersion of the optical resonator often prevents the co-resonance of multiple wavelengths. Here, we present a novel implementation using a monolithic bimetallic heat sink for controlling the resonator dispersion based on a shallow temperature gradient directly applied to a section of the nonlinear
crystal. This method enables precise dispersion control and is designed to minimize mechanical and thermal stresses in the nonlinear
crystal, thus providing an additional method for designing highly efficient and reliable resonator-enhanced nonlinear devices for demanding applications such as gravitational wave detection,
quantum optics, and frequency conversion.
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Quantum Physics
Quantum limit cycles with continuous symmetries from coherent parametric driving: exact solutions and many-body extensions
Sihan Chen and Aashish A. Clerk
There is widespread interest in many-body
quantum systems that exhibit limit-cycle or time-crystalline behaviour. An ideal
quantum limit cycle would be realized using fully coherent driving (to minimize noise) and also have a continuous internal
symmetry (to ensure generation of monochromatic radiation). While these two requirements may seem incompatible, we introduce in this work a large class of multi-mode bosonic limit cycle models based on coherent parametric driving which possess an O(N) continuous
symmetry. Surprisingly, the full
quantum dissipative steady state of these models can be found exactly. They exhibit rich physics, including steady state
entanglement, reduced phase
diffusion and the possibility of realizing
quantum limit
tori. The basic mechanism we identify provides a unified way to understand how coherent parametric driving can yield
symmetry-enriched limit cycles, and also helps us understand related models where the relevant
symmetries are weakly broken. The models we study are compatible with a range of different experimental platforms, including
quantum optical setups and superconducting
quantum circuits.
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Quantum Physics
MCMit: Hardware-Software Co-Design for Mid-Circuit Measurement Error Mitigation
Emmanouil Giortamis, Felix Gust, Aleksandra Świerkowska et al. (+7 more)
Distributed
Quantum Computing (DQC) and
Quantum Error Correction (QEC) rely on dynamic
circuits that include Mid-
Circuit Measurements (MCMs) and classical feedback. These operations present a major bottleneck: MCMs suffer from high error rates that lead to real-time branching errors, while MCM and classical feedback latencies amplify decoherence errors. Current hardware controllers,
qubit-state discriminators, and software error mitigation techniques fail to address these challenges holistically. We propose MCMit, a hardware-software co-design to mitigate branching and latency-induced errors. MCMit introduces a scalable, constant-latency multi-control branch instruction for faster classical feedback and two
qubit-state discriminators, a
transformer, and a CNN, with high accuracy even under short measurement durations. On the software side, static MCM elimination and
stochastic branching complement the hardware by mitigating residual branching errors that persist despite hardware improvements. We implement MCMit on Qubic and evaluate it using experimentally extracted QPU readout traces. Our branch instruction reduces feedback latency by up to 70%, improving
circuit depths by up to $7\times$ over Qubic. Our CNN discriminator achieves up to 62% higher accuracy for short measurement durations than the baselines, driving $1.2-9.4\times$ lower logical error rates in QEC. Last, our software mitigation improves fidelity by 18–30% over baseline methods in DQC workloads.
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All authors Emmanouil Giortamis, Felix Gust, Aleksandra Świerkowska, Sandra Stankovic, Innocenzo Fulginiti, Yanbin Chen, Xiaorang Guo, Benjamin Lienhard, Martin Schulz, Pramod Bhatotia
Quantum Physics
Minimum Toffoli depth for the multi-controlled Toffoli gate via teleportation
Spyros Tserkis, Muhammad Umer, Eleftherios Mastorakis et al. (+1 more)
The decomposition of complex
quantum operations into experimentally feasible gate sets has been a central challenge since the early development of
quantum computing. The multi-controlled Toffoli (MCT) gate is a key example, with applications across a wide range of
quantum algorithms, whose decomposition into smaller gates, however, typically leads to deep
circuits. In this work, we introduce a teleportation-based decomposition that implements an MCT gate. This decomposition has unit Toffoli depth, independent of the number of controls, while achieving the lowest Toffoli count among existing approaches for more than five controls at the cost of a linear overhead in ancilla
qubits. We also investigate the parameter regimes in which the teleportation-based decomposition is preferable by analyzing the relative quality of distributed
entanglement and Toffoli gates. We further demonstrate the advantages of this implementation in
circuits that rely on MCT gates, such as the adder operator,
quantum read-only
memory,
quantum neurons, and
quantum decision trees.
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All authors Spyros Tserkis, Muhammad Umer, Eleftherios Mastorakis, Dimitris G. Angelakis
Quantum Physics
Quantum channels preserving sigma-additivity on diagonal von Neumann algebras and Ulam measurable cardinals
S. V. Dzhenzher
This paper investigates the interplay between the properties of
quantum states on the
Hilbert space \(\ell_2(\kappa)\) and the set-theoretic nature of the cardinal $\kappa$. We focus on the existence of singular $\sigma$-additive states~— functionals whose induced measures are $\sigma$-additive yet vanish on singletons. While the existence of such states is known to be equivalent to the Ulam measurability of $\kappa$, their structural and dynamical properties remain largely unexplored. We prove that any $\sigma$-additive state on the diagonal
algebra is representable as a Pettis integral over a singular $\sigma$-additive measure, extending the classical representation theory to the non-normal sector. Furthermore, we construct a class of
quantum channels using $\sigma$-complete ultrafilters that map normal states to singular $\sigma$-additive states, effectively <<archiving>> information into the singular part of the state space.
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Quantum Physics
A Quantum Spectral Framework for Solving PDEs
Chih-Kang Huang, Giacomo Antonioli and Frédéric Barbaresco
Partial differential equations (PDEs) are fundamental across numerous scientific fields. As these problems scale to high dimensions, classical numerical schemes introduce severe computational bottlenecks, known as the curse of dimensionality. Attempts to solve this problem typically rely on either classical sparsity and low-rank decompositions, or neural network surrogate models. On the other hand,
Quantum Computing offers a promising alternative, as it allows us to operate in significantly larger spaces while demanding far fewer resources. In this work, we present a
quantum subroutine to solve second-order linear PDEs by exploiting the structural properties of the filter in
Fourier space using
Quantum Block Encoding (QBE) with
quantum reversible arithmetic. This approach serves as a specialized alternative to standard
quantum matrix inversion, which typically relies solely on
Quantum Singular Value Transformation (QSVT) without exploiting the inherent structural properties of the
matrix. We validate the proposed methodology against its classical counterpart to prove its correctness. This framework provides a foundation for extending these methods toward
quantum group
Fourier transforms, wavelet-based analysis, and equivariant
quantum neural networks (EQNNs), offering a promising path toward solving broader classes of problems, including nonlinear PDEs.
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Quantum Physics · Cross-listed from physics.app-ph
A unified quantum random walk model for internal crystal effects in dynamical diffraction
Owen Lailey, Dusan Sarenac, David G. Cory et al. (+2 more)
The theory of dynamical diffraction (DD) in perfect
crystals is the backbone of high-precision
neutron and X-ray diffraction experiments, enabling accurate determination of
crystal structure factors and the realization of perfect
crystal interferometers. In practice, however, real
crystals exhibit deformations and imperfections, including surface roughness, defects, temperature gradients, angled
crystal faces, and
curvature, that degrade interferometer performance and are difficult to model using conventional DD theory, particularly in complex geometries. To address these challenges, a
quantum information (QI) model for DD has been under development, with demonstrated experimental agreement for both ideal
crystals and in the presence of some imperfections such as surface roughness and defects. Here, we present a unified
quantum random walk model that is now suitable for reproducing all established DD effects. We demonstrate this by incorporating a broad range of internal
crystal effects influencing DD intensity distributions, including linear temperature gradients, the DD Talbot effect, and angled or miscut
crystals. These results establish the QI model as a comprehensive and flexible framework for experimental analysis, as well as for the design of next-generation perfect
crystal neutron interferometers and
neutron optical components, such as condensing monochromators.
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All authors Owen Lailey, Dusan Sarenac, David G. Cory, Michael G. Huber, Dmitry A. Pushin
Quantum Physics
Proof of the Error Scaling for Universally Robust Dynamical Decoupling Sequences
Domenico D'Alessandro, Phattharaporn Singkanipa and Daniel Lidar
Universally robust dynamical decoupling (UR$n$) sequences were proposed to compensate pulse imperfections arising from arbitrary experimental parameters while achieving high-order error suppression with only a linear increase in the number of pulses. Although their performance was supported by analytical arguments, numerical simulations, and experiments, a complete mathematical proof of the claimed order of error compensation has been absent. In this work, we present a rigorous proof for UR$n$ DD sequences with even $n$. Using a series expansion of a quantity whose modulus is the fidelity $F$, we derive necessary and sufficient conditions for the cancellation of its coefficients up to, but not including, order $n$. The UR$n$ phase prescription satisfies these conditions, and therefore $1-F=O(\epsilon^n)$. Our results establish the UR$n$ construction on firm analytical grounds and clarify the structure responsible for its high-order robustness.
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Quantum Physics
A symmetry-protected pseudo-Hermitian phase of quantum memory-kernel generators
Kejun Liu
The Jaynes-Cummings (JC) model, introduced in 1963 and central to cavity
quantum electrodynamics, describes a two-level system coupled to a single bosonic mode under the rotating-wave approximation. When the mode is projected out via the Nakajima-Zwanzig (NZ) formalism, the
memory-kernel generator QLQ is manifestly non-Hermitian – yet we prove analytically that its spectrum is strictly real at every coupling and every finite truncation, for both
vacuum and thermal baths. For the
vacuum bath the characteristic
polynomial factorises completely; the nonzero
eigenvalues reproduce the JC dressed-state ladder for n >= 2, while the lowest mode is suppressed by exactly sqrt(2) relative to the bare-
Hamiltonian prediction. For any thermal Gibbs state, the squared generator reduces to an asymmetric rank-one perturbation symmetrised by a closed-form diagonal metric, with
eigenvalues guaranteed real by Cauchy interlacing. We construct a positive-definite metric eta_osc intertwining QLQ with its adjoint on the nonzero spectral subspace, proving hidden pseudo-Hermiticity. A classification
theorem extends these results to the full U(1)-conserving single-
photon-exchange class with arbitrary complex couplings. The phase boundary under counter-rotating deformation is mapped analytically at resonance and numerically across the coupling-truncation plane, revealing a weak-coupling protected wedge, re-entrant real-spectrum bubbles, and N-universal plateaus organised by a three-family band catalog with closed-form level spacings. The full phase structure is proved well-defined in the N -> infinity thermodynamic limit. The sqrt(2) suppression provides a platform-independent experimental falsification target spanning seven orders of magnitude in coupling strength.
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Quantum Physics
Mixed-dimensional quantum MacWilliams identity: Bounds for codes and absolutely maximally entangled states in heterogeneous systems
David González-Lociga and Simeon Ball
As emerging
quantum architectures evolve into heterogeneous networks combining different physical substrates, such as
qubits for logic and higher-dimensional qudits for robust communication, the traditional scalar metrics of
quantum error correction become insufficient. To address this, we introduce a mathematical framework based on dimension multisets to characterize
quantum error-correcting codes (QECC) and absolutely maximally entangled (AME) states in mixed-dimensional
Hilbert spaces. By replacing scalar weights with multisets, we accurately capture the exact physical composition of error supports across these diverse systems. Our central result is the mixed-dimensional
quantum MacWilliams identity, which establishes the formal algebraic relationship between Shor-Laflamme enumerators and
unitary weight enumerators. From this foundation, we deduce the mixed-dimensional shadow identity and derive rigorous, generalized constraints on code parameters, explicitly formulating the mixed-dimensional
quantum Hamming, Singleton and Scott bounds, and developing a linear program to systematically evaluate code viability. For the Singleton bound, a tighter bound that has no homogeneous analogue is derived for pure mixed-dimensional codes. Finally, we deploy this enumerator machinery to thoroughly analyze AME states, utilizing shadow inequalities to constrain their existence and introducing a combinatorial grid method for the explicit construction of mixed-dimensional tripartite AME states.
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Quantum Physics
Pulse Quality Optimisation in Quantum Optimal Control
Dylan Lewis and Roeland Wiersema
Quantum optimal control methods are widely used to design experimental control pulses such as
laser amplitudes, phases, or detunings, that implement a target
unitary evolution. In practice, what makes a pulse "good" depends not only on its fidelity, but also on the experimental setting and the relevant hardware constraints. Here, we introduce
geometric quantum control with kernel optimisation (GECKO), a model-agnostic method for improving control pulses after a high-fidelity solution has been found. GECKO uses the Riemannian geometry of the special
unitary group to identify directions in pulse space that leave the implemented
unitary unchanged to first order, allowing one to traverse level sets of the control landscape while optimising a chosen differentiable pulse-quality function. We demonstrate GECKO on a transverse-field Ising
Hamiltonian implementing CZ and CNOT gates, optimising pulse properties including spectral filtering, smoothness, robustness to parameter deviations, and pulse duration. In all cases, GECKO finds substantially improved pulse solutions.
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Quantum Physics
Beyond Single Trajectories: Optimal Control and Jordan-Lie Algebra in Hybrid Quantum Walks for Combinatorial Optimization
Tianen Chen and Yun Shang
The
Quantum Approximate Optimization
Algorithm (QAOA) follows a single, fixed
evolution path, overlooking the potential computational advantage of coherently superposing multiple trajectories. Here we overcome this limitation with a hybrid
quantum walk (HQW) ansatz that super poses multiple
Hamiltonian-driven paths coherently within each
circuit layer via a dynamical coin operator. QAOA emerges as a special case of this framework with a static Pauli-X coin. Using Pontryagin's minimum principle, we derive the optimal form of the coin operator, demonstrating that it generally differs from a constant gate. A dynamical Lie
algebra analysis reveals that HQW generates a strictly larger Jordan-Lie
algebra, providing an algebraic foundation for its enhanced expressivity. Especially, we reveal the connection between the unique Jordan product negativity in HQW's DLA and its performance advantages. Numerical experiments on Max-Cut and Maximum Independent Set problems show that HQW systematically outperforms QAOA in convergence speed, solution accuracy, and robustness. Our work establishes a path-superposition paradigm for
quantum optimization, combining optimal control theory with algebraic structure to guide the design of advanced
quantum algorithms.
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Quantum Physics
Quantum-Inspired Robust and Scalable SAR Object Classification
Maximilian Scharf, Marco Trenti, Felix Bock et al. (+5 more)
SAR image classification naturally has to deal with huge noise and a high dynamic range particularly requiring robust classification models. Additionally, the deployment of these models on edge devices, such as drones and military aircraft, requires a careful balance between model size and classification accuracy. This study explores the potential of tensor networks to meet these robustness requirements, specifically evaluating their resilience to data poisoning. Unlike previous works that concentrated on conventional neural networks for SAR object detection, this research focuses on the robustness and model reduction capabilities of tensor networks in object classification. Our findings indicate that tensor networks are adept at addressing both the challenges of robustness and the need for model efficiency, thereby contributing valuable insights to the ongoing discourse in radar applications and deep learning methodologies in general.
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All authors Maximilian Scharf, Marco Trenti, Felix Bock, Padraig Davidson, Tobias Brosch, Benjamin Rodrigues de Miranda, Sigurd Huber, Timo Felser
Quantum Physics
Numerically-Exact Quantum-Simulation Approach for Two-Dimensional Spectroscopy of Open Quantum Systems
Yi-Xuan Yao, Hao-Yue Zhang, Cheng-Ge Liu et al. (+3 more)
Two-dimensional spectroscopy (2DS) is a powerful ultrafast technique for probing electronic and vibrational dynamics in complex microscopic systems. Extracting detailed information on system dynamics and system-bath interactions from 2DS experiments requires precise theoretical simulations for comparison, which motivates the development of numerically-exact and computationally-efficient simulation approaches. Here, we propose a
quantum-simulation approach for 2DS based on the bath-engineering technique (BET), which has been successfully employed in
quantum simulations of open
quantum dynamics. To demonstrate our approach, we first simulate the 2DS of a driven four-level system in
chiral enantiodetection, where we also assess the applicability of the center-line slope (CLS) method for extracting time correlation functions (TCFs) from the 2DS. We further apply our approach to the 2DS of ${\rm Rh(CO)_2C_5H_7O_2}$ (RDC) dissolved in chloroform, where the results reproduce the main spectral patterns observed in experiments. Our work provides a numerically-exact and efficient framework for simulating 2DS, and can offer additional insight into the dynamics of open
quantum systems.
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All authors Yi-Xuan Yao, Hao-Yue Zhang, Cheng-Ge Liu, Rong-Hang Chen, Qing Ai, Franco Nori
Quantum Physics · Cross-listed from physics.app-ph
Quantum sensing-enabled deuterium NMR spectroscopy with nanoscale sensitivity at low magnetic fields
Dileep Singh, Riley W. Hooper, Christoph Findler et al. (+2 more)
Nuclear magnetic resonance (NMR) spectroscopy provides unparalleled access to molecular structure and dynamics but is traditionally limited by weak signal strength, requiring large sample volumes and high
magnetic fields. Here, we demonstrate nanoscale deuterium (2H) NMR spectroscopy using nitrogen vacancy (NV) centers in diamond, reproducing the characteristic quadrupolar powder line shapes that are present in the conventional bulk NMR spectra. By detecting statistical
spin fluctuations from nanometer scale detection volumes, our approach delivers a sensitivity enhancement of six to eight orders of magnitude over inductive detection while operating at
magnetic fields two orders of magnitude lower than those used in conventional NMR. Temperature dependent measurements of a deuterated
polymer and molecular solid reveal distinct motional averaging and phase transitions with nanoscale sensitivity. Powder-like NV detected 2H NMR establishes a powerful tool for probing molecular dynamics on the nanoscale and, in the ultimate limit, at the single molecule level - capabilities beyond those of most existing spectroscopic techniques.
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All authors Dileep Singh, Riley W. Hooper, Christoph Findler, Utsab Banerjee, Dominik B. Bucher
Quantum Physics
Toward fault-tolerant quantum computation exploiting quantum spatial distribution and gauge symmetry
Ryo Asaka
We explore how the integrated use of
quantum spatial distribution (QSD), or more specifically, a superposition of both
spin and position states of particles, and gauge
symmetry (GS) within Poulin's stabilizer formalism enhances
quantum error correction. The study employs $3+2$ particles on nested squares proposed in the companion paper (arXiv:2504.07941), where three of them encode Shor's nine-
qubit code and the remaining two detect errors in this code through their
spin state measurements. The first result is that the GS offers resilience against three types of noise acting on a particle: arbitrary decoherence of its
spin or position state, and dephasing of both states, which completely or partly destroys its QSD. To show that, we formulate a noise model unifying the above noise sources and prove the correctability of this unified model under our error-correcting scheme. The second result is that the QSD provides architectural flexibility, allowing us to stack the error-correcting systems both vertically and horizontally. Indeed, we present implementations of the error detection (stabilizer measurement), logical Hadamard and Toffoli gates, and a
quantum adder with the required interactions only between nearest-neighbor and next-nearest-neighbor particles. Here, our treatment of the dynamics of particles, each having
spin and position degrees of freedom, under nontrivial noise and gate operations indicates that the stabilizer formalism is a powerful tool for describing
quantum many-body dynamics.
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Quantum Physics
Ground-state energies of Ising models calculated using the samples from a quantum computer that simulates short-time evolution
John P. T. Stenger, C. Stephen Hellberg and Daniel Gunlycke
We find the ground-state energy of the Ising model using the Cascaded Variational
Quantum Eigensolver (CVQE)
algorithm with the Guided-Sampling Ansatz (GSA) using up to 63
qubits on a
quantum computer. We study a heavy-hex
lattice to match the
qubit architecture, allowing us to perform calculations in the
quantum utility regime. We study both a homogeneous and random-coupling model. We locate the boundary of acceptable
quantum errors as a function of the number of
qubits and coupling strength. An entropic analysis is performed giving insights into the
quantum computing performance. A subspace analysis is performed that suggests that the Ising model is especially suited for near-term
quantum computing.
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Quantum Physics
Polynomial Resource Classification of Quantum Circuit Familes via Classical Shadows
Andrew Maciejunes, Ross Gore, Sachin Shetty et al. (+1 more)
We compare four
polynomial-resource measurement strategies, (I) $Z$-basis-only, (II) nearest-neighbor $ZZ$ (NN), (III) multi-basis ($Z$, $X$, $Y$), and (IV) classical shadows, for classifying three
quantum circuit families: IQP, Clifford, and Clifford$+T$. We find $Z$-only measurements outperform multi-basis and classical shadows across all
qubit counts and all four classifiers evaluated, and the $O(\nqubits)$-feature NN strategy matches $Z$-only to within $0.02$ in Random Forest accuracy. The best result is a Random Forest accuracy of $0.91$ at 4–5
qubits under $Z$-only ($0.89$ for NN, $0.85$ for multi-basis, $0.67$ for shadows). All four strategies collapse to near-chance accuracy ($\approx 0.33$) above approximately 12
qubits under the quadratic shot budget $\shots = 16\nqubits^2$. These findings indicate that the discriminative signal between these
circuit families is concentrated in local, nearest-neighbor $Z$-basis correlations, consistent with the diagonal gate structure of IQP
circuits, and that additional Pauli correlator types or long-range correlations carry no compensating discriminative power for this task. We provide a formal theoretical framework showing that
circuits with high diagonal fraction in a given basis concentrate their correlator structure in that basis, and that any deviation from the dominant basis incurs a provably higher
estimator variance. These results establish that a quadratic shot budget is insufficient for reliable classification above approximately 12
qubits, but do not rule out the existence of a subquadratic or otherwise more efficient
polynomial-resource strategy; whether any
polynomial measurement protocol can classify these families at large
qubit counts remains an open question.
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All authors Andrew Maciejunes, Ross Gore, Sachin Shetty, Barry Ezell
Quantum Physics
Direct characterization of classical dephasing noise for a qubit
Yuan-De Jin, Zheng-Fei Ye and Wen-Long Ma
We propose a general method to characterize classical
stochastic noise causing
qubit dephasing through repetitive Ramsey interferometry measurements (RIMs) on the
qubit. Compared to filter-function-based spectroscopy, our method with simpler pulse control is less constrained by probe coherence time and can directly detect arbitrary-order correlation functions of quasistatic noise processes. We show that each RIM with a short
evolution time and suitably chosen control pulses directly samples the noise field and the $n$-point correlations of the RIM outcomes are proportional to the $n$-point correlation functions of the noise processes. We demonstrate the method numerically for two representative cases: an Ornstein-Uhlenbeck Gaussian process and a non-Gaussian ensemble of two-level fluctuators. While practical constraints such as readout contrast and sampling cost persist, our method offers a direct route to quasistatic classical noise spectroscopy across diverse platforms.
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