arXiv subjects

Michael J. Gullans

Publications and source records attributed to Michael J. Gullans.

At least 37 records · Page 2Linked to original sources

arXiv2026

A robust phase of continuous transversal gates in quantum stabilizer codes

A quantum error correcting code protects encoded logical information against errors. Transversal gates are a naturally fault-tolerant way to manipulate logical qubits but cannot be universal themselves. Protocols such as magic state distillation are needed to achieve universality via measurements and postselection. A phase is a region of parameter space with smoothly varying large-scale statistical properties except at its boundaries. Here, we find a phase of continuously tunable logical unitaries for the surface code implemented by transversal operations and decoding that is robust against dephasing errors. The logical unitaries in this phase have an infidelity that is exponentially suppressed in the code distance compared to their rotation angles. We exploit this to design a simple fault-tolerant protocol for continuous-angle logical rotations. This lowers the overhead for applications requiring many small-angle rotations such as quantum simulation.

quant-ph↗

arXiv2026

Entangling logical qubits without physical operations

Fault-tolerant logical entangling gates are essential for scalable quantum computing, but are limited by the error rates and overheads of physical two-qubit gates and measurements. To address this limitation, we introduce phantom codes-quantum error-correcting codes that realize entangling gates between all logical qubits in a code block purely through relabelling of physical qubits during compilation, yielding perfect fidelity with no spatial or temporal overhead. We present a systematic study of such codes. First, we identify phantom codes using complementary numerical and analytical approaches. We exhaustively enumerate all $2.71 \times 10^{10}$ inequivalent CSS codes up to $n=14$ and identify additional instances up to $n=21$ via SAT-based methods. We then construct higher-distance phantom-code families using quantum Reed-Muller codes and the binarization of qudit codes. Across all identified codes, we characterize other supported fault-tolerant logical Clifford and non-Clifford operations. Second, through end-to-end noisy simulations with state preparation, full QEC cycles, and realistic physical error rates, we demonstrate scalable advantages of phantom codes over the surface code across multiple tasks. We observe a one-to-two order-of-magnitude reduction in logical infidelity at comparable qubit overhead for GHZ-state preparation and Trotterized many-body simulation tasks, given a modest preselection acceptance rate. Our work establishes phantom codes as a viable architectural route to fault-tolerant quantum computation with scalable benefits for workloads with dense local entangling structure, and introduces general tools for systematically exploring the broader landscape of quantum error-correcting codes.

quant-ph↗

arXiv2026

Electrical Interconnects for Silicon Spin Qubits

Scalable spin qubit devices will likely require long-range qubit interconnects. We propose to create such an interconnect with a resistive topgate. The topgate is positively biased, to form a channel between the two dots; an end-to-end voltage difference across the nanowire results in an electric field that propels the electron from source dot to target dot. The electron is momentum-incoherent, but not necessarily spin-incoherent; we evaluate threats to spin coherence due to spin-orbit coupling, valley physics, and nuclear spin impurities. We find that spin-orbit coupling is the dominant threat, but momentum-space motional narrowing due to frequent scattering partially protects the electron, resulting in characteristic decoherence lengths ~15 mm for plausible parameters.

cond-mat.mes-hall↗

arXiv2026

Polynomial-Time Classical Simulation of Noisy Quantum Circuits with Naturally Fault-Tolerant Gates

We construct a polynomial-time classical algorithm that samples from the output distribution of noisy geometrically local Clifford circuits with any product-state input and single-qubit measurements in any basis. Our results apply to circuits with nearest-neighbor gates on an $O(1)$-D architecture with depolarizing noise after each gate. Importantly, we assume that the circuit does not contain qubit resets or mid-circuit measurements. This class of circuits includes Clifford-magic circuits and Conjugated-Clifford circuits, which are important candidates for demonstrating quantum advantage using non-universal gates. Additionally, our results can be extended to the case of IQP circuits augmented with CNOT gates, which is another class of non-universal circuits that are relevant to current experiments. Importantly, these results do not require randomness assumptions over the circuit families considered (such as anticoncentration properties) and instead hold for every circuit in each class as long as the depth is above a constant threshold. This allows us to rule out the possibility of fault-tolerance in these circuit models. As a key technical step, we prove that interspersed noise causes a decay of long-range entanglement at depths beyond a critical threshold. To prove our results, we merge techniques from percolation theory and Pauli path analysis.

quant-ph↗

arXiv2026

Interacting electrons in silicon quantum interconnects

Coherent interconnects between gate-defined silicon quantum processing units are essential for scalable quantum computation and long-range entanglement. We argue that one-dimensional electron channels formed in the silicon quantum well of a Si/SiGe heterostructure exhibit strong Coulomb interactions and realize strongly interacting Luttinger liquid physics. At low electron densities, the system enters a Wigner regime characterized by dominant 4kF correlations; increasing the electron density leads to a crossover from the Wigner regime to a Friedel regime with dominant 2kF correlations. We support these results through large-scale density matrix renormalization group (DMRG) simulations of the interacting ground state under both screened and unscreened Coulomb potentials. We propose experimental signatures of the Wigner-Friedel crossover via charge transport and charge sensing in both zero- and high-magnetic field limits. We also analyze the impact of short-range correlated disorder - including random alloy fluctuations and valley splitting variations - and identify that the Wigner-Friedel crossover remains robust until disorder levels of about 400 micro eV. Finally, we show that the Wigner regime enables long-range capacitive coupling between quantum dots across the interconnect, suggesting a route to create long-range entanglement between solid-state qubits. Our results position silicon interconnects as a platform for studying Luttinger liquid physics and for enabling architectures supporting nonlocal quantum error correction and quantum simulation.

cond-mat.mes-hall↗

arXiv2025

Observation of a Fault Tolerance Threshold with Concatenated Codes

We introduce a fault-tolerant protocol for code concatenation of a generalized Shor code using a butterfly network architecture with high noise thresholds and low ancilla overhead to allow implementation on current devices. We develop a probability passing decoder using tensor networks that applies Bayesian updates to the marginal error probabilities after each layer of checks, achieving a state preparation threshold of $e_c \approx 0.089$ for erasure errors, and $\approx 0.015$ for unheralded noise. We implement our state preparation protocol on ion-trap hardware with added noise to demonstrate the threshold behavior in a real quantum device. We further theoretically test the performance of our scheme as a quantum memory and for universal quantum computation through the preparation of low-noise magic states for state distillation and $T$-gate injection.

quant-ph↗

arXiv2025

Low-depth fermion routing without ancillas

Routing is the task of permuting qubits in such a way that quantum operations can be parallelized maximally, given constraints on the hardware geometry. When simulating fermions in the Jordan-Wigner encoding with qubits, a one-dimensional nearest-neighbor-connected geometry is effectively imposed on the system, independently of the underlying hardware, which means that naively, an $O(N)$ depth routing overhead is incurred. Recently, Maskara et al. [arXiv:2509.08898] demonstrated that this routing overhead can be reduced to $O(\log N)$ by decomposing general fermion routing into $O(\log N)$ interleave permutations of depth $O(1)$, using $Θ(N)$ ancillary qubits and employing measurements and feedforward. Here, we exhibit an alternative construction that achieves the same asymptotic performance. We also generalize the result in two ways. Firstly, we show that fermion routing can be performed in depth $O(\log^2 N)$ \emph{without} ancillas, measurements, or feedforward. Secondly, we construct efficient mappings with $O(\log^2 N)$ depth between all product-preserving ternary tree fermionic encodings, thereby showing that fermion routing in any such encoding can be done efficiently. While these results assume all-to-all connectivity, they also imply upper bounds for fermion routing in devices with limited connectivity by multiplying the fermion routing depth by the worst-case qubit routing depth.

quant-ph↗

arXiv2025

Landscape of scattering universality with general dispersion relations

Universality in physics describes how disparate systems can exhibit identical low-energy behavior. Here, we reveal a rich landscape of new universal scattering phenomena governed by the interplay between an interaction and a system's density of states. We investigate one-dimensional scattering with general dispersion relations of the form $ε(k) = |k|^m$ and $ε(k) = \text{sign}(k)|k|^m$ for any real $m \geq 1$. For key models such as emitter scattering and separable potentials, we prove that the low-energy S-matrix converges to universal forms determined solely by the dispersion exponent $m$ and a few integers defining the interaction. This establishes a broad classification of new universality classes, extending far beyond the standard quadratic dispersion paradigm. Furthermore, we derive a generalized Levinson's theorem relating the total winding of the scattering phase to the number of bound states. Our findings are directly relevant to synthetic quantum systems, where engineered dispersion relations in atomic arrays and photonic crystals offer a platform to explore these universal behaviors.

physics.atom-ph↗

arXiv2025

Non-Clifford Gates are Required for Long-Term Memory

We show that all Clifford circuits under interspersed depolarizing noise lose memory of their input exponentially quickly, even when given access to a constant supply of fresh qubits in arbitrary states. This is somewhat surprising given the result of Aharonov et al. [STOC1997] which gives a fault-tolerant protocol for general quantum circuits using a supply of fresh qubits. Our result shows that such a protocol is impossible using only Clifford gates demonstrating that non-Clifford gates are fundamentally required to store information for long periods of time.

quant-ph↗

arXiv2025

Single-Shot Universality in Quantum LDPC Codes via Code-Switching

Code-switching is a powerful technique in quantum error correction that allows one to leverage the complementary strengths of different codes to achieve fault-tolerant universal quantum computation. However, existing code-switching protocols that encapsulate recent generalized lattice surgery approaches often either require many rounds of measurements to ensure fault-tolerance or suffer from low code rates. We present a single-shot, universal protocol that uses code-switching between high-rate quantum codes to perform fault-tolerant quantum computation. To our best knowledge, our work contains the first universal fault-tolerant quantum computation protocol that achieves what we term single-shot universality on high-rate codes that is characterized by (i) single-shot error correction, (ii) single-shot state preparation, as well as (iii) universal logical gates and logical measurements with constant depth circuits. We achieve this feat with single-shot code-switching between constant-rate 2D hypergraph product (HGP) codes and high-rate 3D HGP codes that can be viewed as a generalization of Bombin's dimensional jump for color codes and Hillmann et al.'s single-shot lattice surgery for higher-dimensional topological codes. In addition, we prove the fault-tolerance of our code-switching protocol under both the adversarial and local-stochastic noise models. We introduce a vastly simpler recipe to construct high-rate 3D HGP codes with transversal CCZ gates that grants immense flexibility in the choice of expander graphs and local codes, allowing us to expand the search space for codes with good parameters and interesting logical gates. Our work opens an alternative path towards universal fault-tolerant quantum computation with low space-time overhead by circumventing the need for magic state distillation.

quant-ph↗

arXiv2025

Error correction phase transition in noisy random quantum circuits

In this work, we study the task of encoding logical information via a noisy quantum circuit. It is known that at superlogarithmic depth, the output of any noisy circuit without reset gates or intermediate measurements becomes indistinguishable from the maximally mixed state, implying that all input information is destroyed. This raises the question of whether there is a low-depth regime where information is preserved as it is encoded into an error-correcting codespace by the circuit. When considering noisy random encoding circuits, our numerical simulations show that there is a sharp phase transition at a critical depth of order $p^{-1}$, where $p$ is the noise rate, such that below this depth threshold quantum information is preserved, whereas after this threshold it is lost. Furthermore, we rigorously prove that this is the best achievable trade-off between depth and noise rate for any noisy circuit encoding a constant rate of information. Thus, random circuits are optimal noisy encoders in this sense.

quant-ph↗

arXiv2025

Dynamically generated concatenated codes and their phase diagrams

We formulate code concatenation as the action of a unitary quantum circuit on an expanding tree geometry and find that for certain classes of gates, applied identically at each node, a binary tree circuit encodes a single logical qubit with code distance that grows exponentially in the depth of the tree. When there is noise in the bulk or at the end of this encoding circuit, the system undergoes a phase transition between a coding phase, where an optimal decoder can successfully recover logical information, and a non-coding phase. Leveraging the tree structure, we combine the formalism of "tensor enumerators" from quantum coding theory with standard recursive techniques for classical spin models on the Bethe lattice to explore these phases. In the presence of bulk errors, the coding phase is a type of spin glass, characterized by a distribution of failure probabilities. When the errors are heralded, the recursion relation is exactly solvable, giving us an analytic handle on the phase diagram.

quant-ph↗

arXiv2025

Fault-tolerant hyperbolic Floquet quantum error correcting codes

A central goal in quantum error correction is to reduce the overhead of fault-tolerant quantum computing by increasing noise thresholds and reducing the number of physical qubits required to sustain a logical qubit. We introduce a potential path towards this goal based on a family of dynamically generated quantum error correcting codes that we call "hyperbolic Floquet codes.'' These codes are defined by a specific sequence of non-commuting two-body measurements arranged periodically in time that stabilize a topological code on a hyperbolic manifold with negative curvature. We focus on a family of lattices for $n$ qubits that, according to our prescription that defines the code, provably achieve a finite encoding rate $(1/8+2/n)$ while still requiring only two-body measurements. Similar to hyperbolic surface codes, the distance of the code at each time-step scales at most logarithmically in $n$. The family of lattices we choose indicates that this scaling is achievable in practice. We develop and benchmark an efficient matching-based decoder that provides evidence of a threshold near 0.1% in a phenomenological noise model and 0.25% in an entangling measurements noise model. Utilizing weight-two check operators and a qubit connectivity of 3, one of our hyperbolic Floquet codes uses 400 physical qubits to encode 52 logical qubits with a code distance of 8, i.e., it is a $[[400,52,8]]$ code. At small error rates, comparable logical error suppression to this code requires 5x as many physical qubits (1924) when using the honeycomb Floquet code with the same noise model and decoder.

quant-ph↗

arXiv2025

Emergent unitary designs for encoded qubits from coherent errors and syndrome measurements

Unitary $k$-designs are distributions of unitary gates that match the Haar distribution up to its $k$-th statistical moment. They are a crucial resource for randomized quantum protocols. However, their implementation on encoded logical qubits is nontrivial due to the need for magic gates, which can require a large resource overhead. In this work, we propose an efficient approach to generate unitary designs for encoded qubits in surface codes by applying local unitary rotations ("coherent errors") on the physical qubits followed by syndrome measurement and error correction. We prove that under some conditions on the coherent errors (notably including all single-qubit unitaries) and on the error correcting code, this process induces a unitary transformation of the logical subspace. We numerically show that the ensemble of logical unitaries (indexed by the random syndrome outcomes) converges to a unitary design in the thermodynamic limit, provided the density or strength of coherent errors is above a finite threshold. This "unitary design" phase transition coincides with the code's coherent error threshold under optimal decoding. Furthermore, we propose a classical algorithm to simulate the protocol based on a "staircase" implementation of the surface code encoder and decoder circuits. This enables a mapping to a 1+1D monitored circuit, where we observe an entanglement phase transition (and thus a classical complexity phase transition of the decoding algorithm) coinciding with the aforementioned unitary design phase transition. Our results provide a practical way to realize unitary designs on encoded qubits, with applications including quantum state tomography and benchmarking in error correcting codes.

quant-ph↗

arXiv2025

Automorphism gadgets in homological product codes

The homological product is a general-purpose recipe that forges new quantum codes from arbitrary classical or quantum input codes, often providing enhanced error-correcting properties. When the input codes are classical linear codes, it is also known as the hypergraph product. We investigate structured homological product codes that admit logical operations arising from permutation symmetries in their input codes. We present a broad theoretical framework that characterizes the logical operations resulting from these underlying automorphisms. In general, these logical operations can be performed by a combination of physical qubit permutations and a subsystem circuit. In special cases related to symmetries of the input Tanner graphs, logical operations can be performed solely through qubit permutations. We further demonstrate that these "automorphism gadgets" can possess inherent fault-tolerant properties such as effective distance preservation, assuming physical permutations are free. Finally, we survey the literature of classical linear codes with rich automorphism structures and show how various classical code families fit into our framework. Complementary to other fault-tolerant gadgets for homological product codes, our results further advance the search for practical fault tolerance beyond topological codes in platforms capable of long-range connectivity.

quant-ph↗

arXiv2025

Error Mitigation Thresholds in Noisy Random Quantum Circuits

Extracting useful information from noisy near-term quantum simulations requires error mitigation strategies. A broad class of these strategies rely on precise characterization of the noise source. We study the robustness of probabilistic error cancellation and tensor network error mitigation when the noise is imperfectly characterized. We adapt an Imry-Ma argument to predict the existence of a threshold in the robustness of these error mitigation methods for random spatially local circuits in spatial dimensions $D \geq 2$: noise characterization disorder below the threshold rate allows for error mitigation up to times that scale with the number of qubits. For one-dimensional circuits, by contrast, mitigation fails at an $\mathcal{O}(1)$ time for any imperfection in the characterization of disorder. As a result, error mitigation is only a practical method for sufficiently well-characterized noise. We discuss further implications for tests of quantum computational advantage, fault-tolerant probes of measurement-induced phase transitions, and quantum algorithms in near-term devices.

quant-ph↗

arXiv2025

Fault-tolerant fermionic quantum computing

Simulating the dynamics of electrons and other fermionic particles in quantum chemistry, materials science, and high-energy physics is one of the most promising applications of fault-tolerant quantum computers. However, the overhead in mapping time evolution under fermionic Hamiltonians to qubit gates renders this endeavor challenging. We introduce fermionic fault-tolerant quantum computing, a framework which removes this overhead altogether. Using native fermionic operations we first construct a repetition code which corrects phase errors only. Within a fermionic color code, which corrects for both phase and loss errors, we then realize a universal fermionic gate set, including transversal fermionic Clifford gates. Interfacing with qubit color codes we introduce qubit-fermion fault-tolerant computation, which allows for qubit-controlled fermionic time evolution, a crucial subroutine in state-of-the-art quantum algorithms. As an application, we consider simulating crystalline materials, finding an exponential improvement in circuit depth for a single time step from $\mathcal{O}(N)$ to $\mathcal{O}(\log(N))$ with respect to lattice site number $N$ while retaining a site count of $\tilde{\mathcal{O}}(N)$, implying a linear-in-$N$ end-to-end gate depth for simulating materials, as opposed to quadratic in previous approaches. We also introduce a fermion-inspired qubit algorithm with $O(\mathrm{log}(N)$ depth, but a prohibitive number of additional ancilla qubits. We show how our framework can be implemented in neutral atoms, overcoming the apparent inability of neutral atoms to implement non-number-conserving gates. Our work opens the door to fermion-qubit fault-tolerant quantum computation in platforms with native fermions such as neutral atoms, quantum dots and donors in silicon, with applications in quantum chemistry, material science, and high-energy physics.

quant-ph↗

arXiv2025

Architectural mechanisms of a universal fault-tolerant quantum computer

Quantum error correction (QEC) is believed to be essential for the realization of large-scale quantum computers. However, due to the complexity of operating on the encoded `logical' qubits, understanding the physical principles for building fault-tolerant quantum devices and combining them into efficient architectures is an outstanding scientific challenge. Here we utilize reconfigurable arrays of up to 448 neutral atoms to implement all key elements of a universal, fault-tolerant quantum processing architecture and experimentally explore their underlying working mechanisms. We first employ surface codes to study how repeated QEC suppresses errors, demonstrating 2.14(13)x below-threshold performance in a four-round characterization circuit by leveraging atom loss detection and machine learning decoding. We then investigate logical entanglement using transversal gates and lattice surgery, and extend it to universal logic through transversal teleportation with 3D [[15,1,3]] codes, enabling arbitrary-angle synthesis with logarithmic overhead. Finally, we develop mid-circuit qubit re-use, increasing experimental cycle rates by two orders of magnitude and enabling deep-circuit protocols with dozens of logical qubits and hundreds of logical teleportations with [[7,1,3]] and high-rate [[16,6,4]] codes while maintaining constant internal entropy. Our experiments reveal key principles for efficient architecture design, involving the interplay between quantum logic and entropy removal, judiciously using physical entanglement in logic gates and magic state generation, and leveraging teleportations for universality and physical qubit reset. These results establish foundations for scalable, universal error-corrected processing and its practical implementation with neutral atom systems.

quant-ph↗