By: Neereja M. Sundaresan, Nicholas Cotaj, Yadav Prasad Kandel, Eric Lewandowski, Christian Robert Longton, Yves Martin, Jae-woong Nah, Kathryn Pooley, Martin Sandberg, Michael Scanlon, Chi Xiong, Emanuil Sashev Yanev, David Abraham, Abhinandan Antony, Vincent Arena, Nicholas Bornman, Khanh Dang, Oliver Dial, Christopher Guarino, Gabriel Haspil, Jared Hertzberg, Kentaro Heya, Swetha Kamlapurkar, Michael Karschner, George Keefe, Eric Liniger, Laura Luo, Thomas G. McConkey, David Olson, Jason Orcutt, Dmitry Ovchinnikov, Timothy Phung, Sankeerth Rajalingam, Michael Selvanayagam, William Shanks, Dongbing Shao, Abigail Shearrow, Adam Stabile, Jiri Stehlik, Joseph Suttle, Jeng-Bang Yau, Eric Zhang
Modular quantum architecture requires long-distance quantum interconnects to stitch together individual processor modules. Such interconnects, long-distance couplers or L-couplers, must support coherent quantum operation over meter-scale distances and scale to multiple connections between any two modules. Here we demonstrate four L-couplers operating between two 120-qubit IBM Nighthawk R1 superconducting qubit processors. Each L-coupler joins... more
Modular quantum architecture requires long-distance quantum interconnects to stitch together individual processor modules. Such interconnects, long-distance couplers or L-couplers, must support coherent quantum operation over meter-scale distances and scale to multiple connections between any two modules. Here we demonstrate four L-couplers operating between two 120-qubit IBM Nighthawk R1 superconducting qubit processors. Each L-coupler joins two Nighthawk lattice qubits through two frequency-tunable L-qubits, two RF-SQUID based "i2m" couplers, and 80 cm of superconducting aluminum coax. Each cable installs perpendicular to the processor surface, to enable denser connections, and is joined to the chip by an indium-to-indium room temperature pressure bond made after both modules were mounted. L-coupler modes near 5 GHz, with internal quality factors of 0.86 to 1.09e6, carry relay-based state transfer at a mean network benchmarking fidelity of 99.00%, with a best link of 99.29 +/- 0.07%. We then realize distant CZ gates between lattice qubits in separate modules at a mean fidelity of 94.75%, with a best link of 96.42 +/- 0.28%, and use them to generate entangled states across the two processors, including a demonstration of simultaneous Bell pair generation using two adjacent L-couplers. These four high-fidelity L-couplers establish a practical path to scalable quantum interconnects for modular quantum computing. less
Injection is all you need: parallel universal logic in high-rate concatenated self-dual codes
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By: Joseph Sullivan, David Amaro, Michael A. Perlin
We propose a quantum architecture that achieves addressable and parallel universal fault-tolerant logical in high-rate codes. The codes are obtained from the flexible concatenation of small-distance high-rate self-dual CSS codes. Addressable and parallel universal logic on the resulting $K$ logical qubits is injected by fault-tolerantly preparing and then consuming diverse logical $K$-qubit CSS stabilizer states and logical $\lvert H \rangle^... more
We propose a quantum architecture that achieves addressable and parallel universal fault-tolerant logical in high-rate codes. The codes are obtained from the flexible concatenation of small-distance high-rate self-dual CSS codes. Addressable and parallel universal logic on the resulting $K$ logical qubits is injected by fault-tolerantly preparing and then consuming diverse logical $K$-qubit CSS stabilizer states and logical $\lvert H \rangle^{\otimes K}$ global magic states. Flag-at-origin is used to prepare the stabilizer resource states while a concatenated cultivation protocol prepares the global magic states. These resource states are consumed by Steane-QEC or Knill-QEC teleportation gadgets, which simultaneously perform quantum error correction. Any quantum algorithm with $T$-depth $D_T$ can be executed by consuming $12D_T$ or fewer resource states. We benchmark the fault-tolerant preparation of the resource states for several two-level concatenations of the $[[k+4,k,2]]$ H codes and the Hamming $[[15,7,3]]$ code. In particular, we find that the concatenated cultivation offers at least one order of magnitude spacetime reduction compared to cultivation in the surface code. less
By: Valery, Grishin, Aryeh Lev Zabokritskiy
We prove a conjecture of Yu, Lai, and Oh: their rounded family of strengthened quantum Hamming bounds, which interpolates between Hamming-type bounds and the Singleton bound, holds for arbitrary exact quantum subspaces of dimension $K>1$. The result covers every integer local dimension $p\ge2$, every integer $t\ge1$, both distances $2t+1$ and $2t+2$, and every interpolation parameter $e\in\{0,\ldots,t\}$. Yu, Lai, and Oh proved these bounds f... more
We prove a conjecture of Yu, Lai, and Oh: their rounded family of strengthened quantum Hamming bounds, which interpolates between Hamming-type bounds and the Singleton bound, holds for arbitrary exact quantum subspaces of dimension $K>1$. The result covers every integer local dimension $p\ge2$, every integer $t\ge1$, both distances $2t+1$ and $2t+2$, and every interpolation parameter $e\in\{0,\ldots,t\}$. Yu, Lai, and Oh proved these bounds for pure codes and for general codes of distance three or four; the case $e=0$ contains the ordinary quantum Hamming bound for general codes, recently proved by Zhang and Chen. More generally, for $p\ge3$, we prove the inequality $Kf(0)\le p^n\mathbb{E}f(X)$, where $X\sim\operatorname{Bin}(n,1-p^{-2})$, for every real polynomial $f$ of degree at most $D$, with $2\le D<d$, that is nonnegative on $\{0,\ldots,n\}$ and positive at zero; here $n$ and $d$ are the code length and distance. less
By: Mingyuan Wang, Stefan Krastanov
Calderbank--Shor--Steane (CSS) codes support decoding and fault-tolerant logical operations through separate pure $X$ and pure $Z$ stabilizer checks. Generator choices and single-qubit Clifford transformations can obscure this structure. We give a deterministic polynomial-time algorithm that decides whether an arbitrary stabilizer code is locally Clifford-equivalent to a CSS code and constructs the required transformation and CSS checks whene... more
Calderbank--Shor--Steane (CSS) codes support decoding and fault-tolerant logical operations through separate pure $X$ and pure $Z$ stabilizer checks. Generator choices and single-qubit Clifford transformations can obscure this structure. We give a deterministic polynomial-time algorithm that decides whether an arbitrary stabilizer code is locally Clifford-equivalent to a CSS code and constructs the required transformation and CSS checks whenever such a form exists. For $m$ possibly redundant generator rows on $n$ qubits, the algorithm uses $O(mn^2+n^4)$ binary field operations. We reduce the problem to affine linear systems by characterizing local projectors that preserve the span of the binary stabilizer labels. The conversion preserves code parameters and check sparsity for quantum low-density parity-check (qLDPC) codes. We demonstrate CSS recovery and decoder reuse and resolve previously open LC-to-CSS classification questions for published code constructions. For graph states, LC-to-CSS equivalence corresponds to the existence of a bipartite graph in the local-complementation orbit. We derive a necessary-and-sufficient adjacency-matrix criterion for this property and construct such a graph whenever one exists. Our algorithm makes CSS decoding and fault-tolerant constructions accessible throughout the local Clifford equivalence classes of CSS codes. less
By: Hengzhun Chen, Zhenning Cai
We present an error-controlled framework for the quantum simulation of non-Markovian open-system dynamics in Gaussian environments. For a system coupled linearly to a Gaussian environment with zero mean, the bath's influence on the reduced dynamics is completely determined by its two-time correlation kernel. This allows us to replace the microscopic environment with an equivalent bath that has the same kernel. On a finite simulation interval,... more
We present an error-controlled framework for the quantum simulation of non-Markovian open-system dynamics in Gaussian environments. For a system coupled linearly to a Gaussian environment with zero mean, the bath's influence on the reduced dynamics is completely determined by its two-time correlation kernel. This allows us to replace the microscopic environment with an equivalent bath that has the same kernel. On a finite simulation interval, a rank-$N$ approximation of the kernel yields an effective bath of $N$ bosonic modes with time-dependent couplings to the system. To encode these modes in qubits, we first truncate each mode to its lowest $d$ occupation levels. When stronger couplings lead to large occupations, we introduce coupling dilution, which replaces each mode with several more weakly coupled copies while preserving the bath correlation kernel. This distributes excitations across more modes and trades additional modes for smaller local dimensions. We derive explicit reduced-state error bounds and establish polynomial circuit width and depth in simulation time and inverse accuracy under stated spectral-decay and coupling-regularity assumptions, provided elementary unitaries admit polynomial-cost implementations. less
By: Shiroman Prakash, K. L. Ramya
We construct short triorthogonal codes for qudits of odd prime dimension by generalizing doubling, which combines a triorthogonal code with a code admitting a transversal phase gate, and raises the distance by up to two. This gives codes with parameters $[[28,1,4]]_3$, $[[37,1,5]]_3$, $[[72,1,6]]_3$, $[[118,1,8]]_3$, $[[33,1,5]]_5$ and $[[20,1,4]]_7$, each shorter than the cyclic, concatenated and Reed-Muller codes of the same distance, and a... more
We construct short triorthogonal codes for qudits of odd prime dimension by generalizing doubling, which combines a triorthogonal code with a code admitting a transversal phase gate, and raises the distance by up to two. This gives codes with parameters $[[28,1,4]]_3$, $[[37,1,5]]_3$, $[[72,1,6]]_3$, $[[118,1,8]]_3$, $[[33,1,5]]_5$ and $[[20,1,4]]_7$, each shorter than the cyclic, concatenated and Reed-Muller codes of the same distance, and a doubling construction of the $[[15,1,3]]_3$ code. When the columns of a generator matrix are regarded as charged points, triorthogonality becomes the vanishing of multipole moments up to octupole order, and doubling becomes a double layer of opposite charges; this picture explains why inputs with nontrivial coefficients can give shorter codes. We also show by exhaustive search that the shortest codes of distance three have length $11$ for $p=5$ and length $7$ for $p=7$. Combined with high-rate distance-two codes, the new codes reduce the cost of qutrit magic state distillation by up to an order of magnitude in regimes with high input noise. less
4 SciCasts by .
By: Zuo Wang, Paul M. Schindler, Modesto Orozco-Ruiz, Nguyen H. Le, Florian Mintert, Marin Bukov
The Renormalization Group (RG) establishes relations between effective descriptions of physical systems at different scales; in Hamiltonian RG, these relations induce a flow in the space of Hamiltonians. In direct correspondence, we design an RG framework for quantum control by constructing a flow in the space of time-dependent Hamiltonians. A prescribed control subspace, selected to contain only experimentally accessible terms, forms the fix... more
The Renormalization Group (RG) establishes relations between effective descriptions of physical systems at different scales; in Hamiltonian RG, these relations induce a flow in the space of Hamiltonians. In direct correspondence, we design an RG framework for quantum control by constructing a flow in the space of time-dependent Hamiltonians. A prescribed control subspace, selected to contain only experimentally accessible terms, forms the fixed-point manifold, while the flow preserves the target unitary and monotonically reduces the Hamiltonian weight outside this subspace. Exploiting the freedom in constructing the flow, we introduce flow-equation engineering to enhance the versatility of the framework for diverse control problems, including time-periodic and open-interval smooth protocols with prescribed endpoints. We provide two disparate applications to exhibit the utility of our approach: (i) Nonperturbative Floquet engineering beyond the regime of validity of high-frequency expansions, which we demonstrate by constructing an implementable time-periodic protocol for the Haldane model; (ii) Accessible fast-forward driving from unit-fidelity counterdiabatic evolution, which we showcase for large transverse-field Ising chains away from the adiabatic regime by compressing the long-range multibody adiabatic gauge potential into the original time-dependent Ising control schedules. Our control RG framework reveals a unifying perspective on Hamiltonian engineering and unitary quantum control, and can serve as an organizing principle behind seemingly disparate nonequilibrium quantum dynamics. less
By: Connor Lenihan, Kripa Panchagnula, Luca Erhart, Jem Guhit, Carlo A. Gaggioli, Gabriel Greene-Diniz, Gabriel Laude, Megan Cerys Rowe, Fabian Finger, Pranav Kalidindi, Enrico Rinaldi, Mikko Muuronen, Chandrika Mulakala, Thomas M. Soini, Elvira Shishenina, David Muñoz Ramo, David Zsolt Manrique
Accurate modelling of chemical reaction rates requires precise correlated energy differences. Quantum computing offers a potential route to their determination, but extracting energies from quantum-prepared states can demand prohibitive sampling. We demonstrate measurement-efficient correlated energy estimation using an electronically challenging H$_2$DBB--Ru model derived from a Ru-functionalized hafnium metal-organic framework relevant to r... more
Accurate modelling of chemical reaction rates requires precise correlated energy differences. Quantum computing offers a potential route to their determination, but extracting energies from quantum-prepared states can demand prohibitive sampling. We demonstrate measurement-efficient correlated energy estimation using an electronically challenging H$_2$DBB--Ru model derived from a Ru-functionalized hafnium metal-organic framework relevant to radiodynamic and photodynamic therapies. The mixed estimator combines a quantum-prepared target with sparse multiconfiguration references and recovers ground-state corrections using magnitude-only compute-uncompute measurements. Analytical variance estimates predict 1.6 mHa precision with a few hundred shots, about 100 times fewer than the single-determinant formulation and three orders of magnitude fewer than optimized Hamiltonian-term sampling. With approximate targets, it reaches comparable accuracy using simpler state preparation than direct expectation-value estimation. Emulator and trapped-ion experiments on Quantinuum Helios validate the approach up to (10,10), including a 50-qubit circuit combining AI-assisted state preparation with error detection, providing a measurement-efficient route to correlated energy differences for challenging chemical problems. less
By: Alexander Chansky
Counterdiabatic (CD) driving suppresses the excitations of fast protocols by adding an auxiliary Hamiltonian, but in many-body and topological systems the exact CD term is generally non-local and multi-body. We study this obstruction for Thouless pumping in the Rice-Mele model, first without and then with interactions. For noninteracting fermions, the exact CD term of the pump is non-local, but the variational framework of Sels and Polkovniko... more
Counterdiabatic (CD) driving suppresses the excitations of fast protocols by adding an auxiliary Hamiltonian, but in many-body and topological systems the exact CD term is generally non-local and multi-body. We study this obstruction for Thouless pumping in the Rice-Mele model, first without and then with interactions. For noninteracting fermions, the exact CD term of the pump is non-local, but the variational framework of Sels and Polkovnikov yields accurate nearest-neighbor approximations. For the spinful Rice-Mele chain with onsite and nearest-neighbor repulsion, in the regime where the competition of the two interactions stabilizes quantized pumping, this approach fails: the infinite-temperature variational action only penalizes the CD amplitudes, and the resulting two-parameter nearest-neighbor term does not prevent the pump from breaking down when the cycle time is reduced from $50/t$ to $2/t$. We trace the failure to the structure of the exact many-body gauge potential, whose amplitude for each hop depends on the interaction energy that the hop costs. Resolving the nearest-neighbor currents by this energy, and fixing the coefficients with a ground-state-weighted action, gives a local ansatz with 14 coefficients that keeps the interacting pump quantized for cycle times $T=2/t$ and $T=1/t$, with an accuracy per site that does not degrade between rings of 8 and 12 sites. less
By: César Hernando de la Fuente, Joonas Majaniemi, Evert van Nieuwenburg, Felix Frohnert
Correlated decoding improves matching and clustering surface-code decoders by reweighting one decoding subgraph conditioned on the other's correction. We show that standard reweighting can cause correlated decoders to fail on size-$(d-1)/2$ fault configurations that a distance-$d$ code should correct, reducing error suppression deep below threshold. Under circuit-level noise, a single first-pass edge can discount several correlated edges, eve... more
Correlated decoding improves matching and clustering surface-code decoders by reweighting one decoding subgraph conditioned on the other's correction. We show that standard reweighting can cause correlated decoders to fail on size-$(d-1)/2$ fault configurations that a distance-$d$ code should correct, reducing error suppression deep below threshold. Under circuit-level noise, a single first-pass edge can discount several correlated edges, even though their joint occurrence requires additional independent faults, so the decoder favors an over-discounted correction. Regularizing the reweighting rule restores the nominal distance scaling and a clear correlated-decoding advantage. less
By: Riccardo Molteni, Minjun Jeon, Paolo Braccia, Abhinav Deshpande, Vedran Dunjko, Liang Jiang, Su-un Lee, Swarnadeep Majumder, Javier Robledo Moreno, Parthasarathy Suryanarayanan, Kunal Sharma
Machine learning is widely regarded as a promising application in which quantum computing could offer a computational advantage. However, general quantum machine learning models with provable guarantees on performance, trainability, and efficient inference remain limited. In this work, we introduce quantum Hamiltonian embeddings, a supervised learning framework in which a classical training dataset is encoded into a single effective, paramete... more
Machine learning is widely regarded as a promising application in which quantum computing could offer a computational advantage. However, general quantum machine learning models with provable guarantees on performance, trainability, and efficient inference remain limited. In this work, we introduce quantum Hamiltonian embeddings, a supervised learning framework in which a classical training dataset is encoded into a single effective, parameterized Hamiltonian. Training optimizes the parameters of this data-dependent Hamiltonian, whose approximate ground state defines the classification rule. Once the ground state has been approximated using a quantum algorithm, inference can be performed either classically using a classical representation of the learned state, or with a quantum representation of the state. We establish efficient methods for gradient estimation and prove favorable generalization guarantees. Furthermore, under standard cryptographic assumptions, we show that Hamiltonian embeddings can realize hypothesis functions beyond the reach of efficient classical algorithms. We then demonstrate the framework at scale on IBM Heron processors using a standard benchmark dataset. Together, these results establish Hamiltonian embeddings as a new framework for quantum machine learning, combining theoretical guarantees with a path for experimental investigations at scale on quantum hardware. less
Quantum algorithms for optimal control: large-scale finite-horizon linear-quadratic regulation
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By: Xiajie Huang, Cristina Álvarez Yuste, Nikita Guseynov, Nana Liu, Javier González-Conde
We develop quantum algorithms for optimal control over a prescribed finite time interval (finite horizon), focusing on continuous-time linear-quadratic regulation (LQR). This foundational control problem often requires solving a nonlinear matrix Riccati equation, which can be costly for large systems and long control durations on conventional classical solvers. We instead work directly with the state-costate optimality equations, reformulatin... more
We develop quantum algorithms for optimal control over a prescribed finite time interval (finite horizon), focusing on continuous-time linear-quadratic regulation (LQR). This foundational control problem often requires solving a nonlinear matrix Riccati equation, which can be costly for large systems and long control durations on conventional classical solvers. We instead work directly with the state-costate optimality equations, reformulating the LQR problem as a multiple-shooting linear system. Importantly, we prove a condition-number bound for the system that is independent of the horizon, under stabilizability and detectability assumptions. By incorporating the initial and final conditions into a single linear system, we can solve the subsequent linear system more efficiently with a quantum linear systems subroutine. For a given initial state, our quantum algorithms return classical estimates of the optimal cost and the optimal control inputs at a selected time, without constructing a Riccati solution operator. Given sparse-matrix block-encodings, an initial-state preparation oracle and a fixed number of control inputs, the query and gate complexities scale polylogarithmically with system size and control duration, provided that sparsity, relevant norms, and stability parameters are bounded. The dependence on the target error is inverse-linear up to logarithmic factors. We establish the required bounds uniformly in system size and duration for a family of damped mass-spring chains with two endpoint controls. Numerical experiments support the analysis. less
By: Atta ur Rahman, Muhammad Noman, Ying-Jian Zhu, Jia-Xin Peng, Saeed Haddadi
Tests of gravity-mediated entanglement aim to determine whether two massive objects in spatial superposition can become entangled through their mutual gravitational interaction. In an ideal model, the two objects are often treated as pointlike branches, but real wave packets have a finite width and are also exposed to dephasing and residual non-gravitational forces. We study these effects in a two-branch gravitational cat-state model with Gau... more
Tests of gravity-mediated entanglement aim to determine whether two massive objects in spatial superposition can become entangled through their mutual gravitational interaction. In an ideal model, the two objects are often treated as pointlike branches, but real wave packets have a finite width and are also exposed to dephasing and residual non-gravitational forces. We study these effects in a two-branch gravitational cat-state model with Gaussian wave packets. The Newtonian interaction is averaged over the finite wave-packet width, and spatially correlated dephasing is included phenomenologically. We then ask a practical question: when does the generated state remain useful rather than merely entangled? To answer this, we examine Bell violation, teleportation fidelity, coherent information, Fisher information, and state distinguishability. We find finite parameter windows where the same state is Bell-nonlocal and teleportation-useful, but these windows shrink as the wave packets become broader or the dephasing becomes stronger. We also show that a residual electrostatic branch interaction can coherently cancel the gravitational nonlocal phase and strongly suppress the operational signal. The results identify finite-width and electrostatic tolerance boundaries that should be considered in future tests of gravity-mediated entanglement. less
By: Mathieu Féchant, Phillip Lenhard, Nicolas Gosling, Ritika Dhundhwal, Denis Bénâtre, Wolfgang Wernsdorfer, Thomas Reisinger, Ioan M. Pop
Understanding the microscopic environment of superconducting qubits is a central challenge for quantum technologies. Parasitic two-level systems (TLSs) of various microscopic origins are ubiquitous and limit qubit performance through decoherence, frequency drifts, and leakage. Recently, long-lived TLSs with lifetimes exceeding those of state-of-the-art qubits have been shown to induce correlated qubit dynamics, with direct implications for qu... more
Understanding the microscopic environment of superconducting qubits is a central challenge for quantum technologies. Parasitic two-level systems (TLSs) of various microscopic origins are ubiquitous and limit qubit performance through decoherence, frequency drifts, and leakage. Recently, long-lived TLSs with lifetimes exceeding those of state-of-the-art qubits have been shown to induce correlated qubit dynamics, with direct implications for quantum error correction. Here, we perform wide-band quantum-jump correlation spectroscopy on flux-tunable transmon qubits and identify microscopic degrees of freedom that outlive the qubit by orders of magnitude. Pump-probe measurements at varying detunings from these objects reveal intrinsic lifetimes exceeding one second. Their weak coupling to the qubit, in the kilohertz range, is consistent with positional defects described by the standard tunneling model, without excluding other microscopic origins such as magnetic spin impurities or trapped quasiparticles. More broadly, these results establish superconducting qubits as a sensitive probe of exceptionally long-lived microscopic degrees of freedom and open a route toward their controlled access and functionalization. less
By: Yifei Wang, Yingfei Gu
Classical simulation of magic state factories, including distillation, cultivation, and code switching, is challenging because of their substantial non-Clifford content. We introduce $\texttt{magna}$ (magic-state-factory assessment via global network algebra), a classical simulator that simulates such protocols as cheaply as Clifford circuits. $\texttt{magna}$ expresses the figures of merit of a protocol, namely the acceptance rate and the fi... more
Classical simulation of magic state factories, including distillation, cultivation, and code switching, is challenging because of their substantial non-Clifford content. We introduce $\texttt{magna}$ (magic-state-factory assessment via global network algebra), a classical simulator that simulates such protocols as cheaply as Clifford circuits. $\texttt{magna}$ expresses the figures of merit of a protocol, namely the acceptance rate and the fidelity of the accepted states, as tensor networks, which it reduces globally by exploiting a structural correspondence with transversal gates on quantum codes. $\texttt{magna}$ further supports feedforward conditioned on arbitrary functions of mid-circuit measurement outcomes, including decoder outputs. We simulate Bravyi--Haah distillation with up to 100 output magic states at a cost that does not grow exponentially in the number of outputs, and achieve state-of-the-art sampling times for distance-5 magic state cultivation on both color codes and RP$^2$ surface codes. Finally, we validate nonlinear feedforward on a logical-level distillation protocol with 15 rounds of decoder-dependent feedforward. $\texttt{magna}$ aims to contribute to the key infrastructure for the large-scale evaluation and optimization of magic state factories. less
By: Tai-Hsuan Yang, Andrew D. Kim, Akash Vijay, Jong Yeon Lee
Quantum low-density parity-check (qLDPC) codes have a canonical mixed state---the normalized projector onto the code space---that lies at the intersection of quantum error correction and quantum many-body physics, yet the stability of its information-theoretic structure under local noise remains poorly understood. Recent progress on mixed-state phases of matter has identified the spatial decay of conditional mutual information (CMI) $I(A:C|B)... more
Quantum low-density parity-check (qLDPC) codes have a canonical mixed state---the normalized projector onto the code space---that lies at the intersection of quantum error correction and quantum many-body physics, yet the stability of its information-theoretic structure under local noise remains poorly understood. Recent progress on mixed-state phases of matter has identified the spatial decay of conditional mutual information (CMI) $I(A:C|B)$ as a key diagnostic of such stability, analogous to the role of the spectral gap for quantum ground states. We prove that, for the normalized code-projector state of a $\mathbb{Z}_d$ qLDPC stabilizer code under local Pauli noise, the CMI across a buffer $B$ separating $A$ from $C$ decays exponentially with the width of $B$ in two complementary noise regimes independent of system size. At weak noise, this holds for full-system tripartitions, where correlations between the two sides require an error cluster to cross the buffer, an exponentially unlikely event. At strong noise, exponential decay holds whenever the buffer supports no logical operator, since correlations can persist only along rare chains of buffer qudits that remain informative. Under an additional space-uniformity assumption, we establish the robustness of Levin--Wen topological entropy. On finite-dimensional lattices of size $n$, the weak-noise bound further implies a constant-layer quasi-local Petz recovery channel of range $O(\poly(\log n)/\varepsilon)$ that recovers the noiseless state within trace-distance error $\varepsilon$. Both CMI bounds apply to general qLDPC interaction graphs, including geometries where such constant-depth quasi-local recovery need not exist. Thus, the exponential decay of the noise-induced CMI provides a general criterion for mixed-state phase stability. less
By: Andi Gu, Alek H. Kemeny, Susanne F. Yelin, Mikhail D. Lukin
Significant efforts are currently being directed toward the implementation of large-scale quantum information processors, but realizing useful quantum advantage also requires the development of efficient quantum algorithms. While for many practical problems the dominant resource costs are associated with a small set of computational primitives, optimizing them in the quantum setting presents unique challenges, including a reversibility constr... more
Significant efforts are currently being directed toward the implementation of large-scale quantum information processors, but realizing useful quantum advantage also requires the development of efficient quantum algorithms. While for many practical problems the dominant resource costs are associated with a small set of computational primitives, optimizing them in the quantum setting presents unique challenges, including a reversibility constraint absent from ordinary classical computation. Here we introduce an evolutionary framework in which large language models (LLMs) propose circuit designs and an independent evaluator verifies and scores them. We apply this framework to tasks spanning numerical computation, chemistry, optimization, quantum simulation, and number theory. In seven of the eight tasks, the discovered circuits significantly reduce both Toffoli and qubit counts relative to the state of the art. In the eighth, the search discovers a new reversible architecture for prime-field modular inversion. By handling reversibility differently, the architecture makes divsteps -- a classical algorithm previously impractical for reversible integer arithmetic -- viable and substantially improves the Toffoli-qubit trade-off for modular inversion. These results open the door for evaluator-guided LLM co-design of new algorithmic structures for quantum computation. less