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Harald Putterman

Publications and source records attributed to Harald Putterman.

16 recordsLinked to original sources
arXiv2026

When quantum thermal states look classical

At high temperature, quantum Gibbs states retain several classical features of the maximally mixed state: the absence of entanglement, the absence of magic, analyticity of the partition function, correlation decay, and algorithmic tractability. We prove new and sharp bounds showing that these features persist down to finite temperatures independent of system size, but fail at distinct inverse-temperature scales, forming a hierarchy of classical-to-quantum transitions. Our results hold for long-range Pauli interactions with bounded strength at every site. Despite such all-to-all interactions, we show that the death of entanglement occurs at constant temperature, resolving an open question of Rouze, Franca and Alhambra (STOC'25). We give a polynomial-time classical algorithm that prepares Gibbs states up to the death of entanglement transition. Notably, this is asymptotically colder than temperatures at which quantum Gibbs samplers are known to mix quickly, as well as the original separability temperature of Bakshi et al. (FOCS'24), which we improve to be tight up to constants. At asymptotically even colder temperatures, we show that the Gibbs state remains in the thermodynamic infinite-temperature phase. This leads to polynomial-time classical algorithms for estimating thermal expectations despite both entanglement and magic, and the resolution of a correlation decay conjecture of Harrow, Mehraban and Soleimanifar (STOC'20).

quant-ph↗
arXiv2026

Restrictions on non-Clifford fault tolerance and ruling out beyond-SQL quantum metrology

Quantum metrology promises a quadratic speedup over the standard quantum limit (SQL), but signal-aligned noise is expected to preclude this advantage in realistic settings. A potential route around known no-go results is to encode the sensors in a quantum code where the physical signal acts transversally as a logical gate. Understanding restrictions on transversal non-Clifford gates is therefore central to both quantum metrology and fault-tolerant quantum computation. Here, we prove such restrictions and apply them to transversal sensing. For any stabilizer code of distance $d\ge 3$ supporting a transversal logical action in level $D$ of the Clifford hierarchy, every stabilizer generating set must contain a check of weight at least $2^D$. Moreover, any $r$-level concatenated realization satisfies $r\leq \lfloor \log_2 n/D\rfloor$, forcing $r=1$ and ruling out concatenation when applied to beyond-SQL metrology. We then show that transversal single-qubit rotations by a small angle $\theta$ can only induce a nontrivial logical action on an $n$-qubit code if its checks include irreducible stabilizers of weight $\Omega(1/(n|\theta|^2))$. Here, many single-qubit errors commute with every stabilizer or logical Pauli below this weight and are only detected by a high-weight check, so their syndromes cannot be fault-tolerantly reconstructed from low-weight normalizer measurements. Since beyond-SQL transversal sensing requires $|\theta| = o(n^{-1/2})$, the weight of checks required for syndrome extraction diverges with $n$. Finally, we prove a broader metrological no-go theorem that avoids the assumptions of the quantum Cram\'{e}r-Rao bound: constant-strength signal-aligned noise rules out any asymptotic advantage over the SQL in AC or DC sensing, even with biased estimators, nonstabilizer or approximate encodings, quantum memory, intermediate measurements, or adaptive control.

quant-ph↗
arXiv2026

Bias-preserving cat-cat CNOT gate via vacuum-conditional beam-splitter

Cat qubits can exhibit strong noise bias due to their exponentially enhanced bit-flip times and only polynomially reduced phase-flip times with increasing photon number, which makes them attractive candidates for hardware-efficient quantum error correction. However, it is difficult to maintain this strong noise bias in logical operations such as CNOT gates between cats. Here, we propose a coherent CNOT gate scheme between two dissipative cats that preserves the exponential noise bias. The proposed gate relies only on unitary operations, which avoids the non-idealities associated with many existing gate schemes that rely on engineered dissipations. Assuming good component lifetimes and precise nonlinearity engineering, the proposed gate can enable logical memory in the megaquop regime (logical error rates < 10^-6) with a distance-7 repetition code consisting of 13 cat qubits.

quant-ph↗
arXiv2026

Fault-tolerant quantum processing of physical experiments

Quantum computers may reveal features of Nature inaccessible to conventional experiments, but manipulating raw quantum data introduces noise that degrades inference even when the processor is fault-tolerant, creating a data-input bottleneck for robust quantum learning. Here we show that quantum fault tolerance can substantially improve the sample complexity of learning from noisy experiments. We encode unknown quantum states from physical experiments into protected quantum memory, enabling fault-tolerant implementations of quantum learning algorithms otherwise degraded by errors. Using this quantum uploading procedure, we prove that noisy randomized measurement and multi-copy learning tasks can be performed exponentially faster than by any adaptive strategy that does not immediately encode physical states into error-corrected memory. These separations are not simply due to a reduced effective noise rate: they hold even when uploading is substantially noisier than the bare experimental interface, rigorously establishing immediate encoding as the optimal approach to noise-robust learning. We numerically illustrate the speedups in astronomical imaging, where quantum processing of uploaded photons locates an exoplanet obscured by a bright star using orders of magnitude fewer shots than unencoded baselines. Our results establish a robust interface between quantum computers and natural systems, enabling powerful and practical quantum-enhanced experiments.

quant-ph↗
arXiv2024

Hybrid cat-transmon architecture for scalable, hardware-efficient quantum error correction

Dissipative cat qubits are a promising physical platform for quantum computing, since their large noise bias can enable more hardware-efficient quantum error correction. In this work we theoretically study the long-term prospects of a hybrid cat-transmon quantum computing architecture where dissipative cat qubits play the role of data qubits, and error syndromes are measured using ancillary transmon qubits. The cat qubits' noise bias enables more hardware-efficient quantum error correction, and the use of transmons allows for practical, high-fidelity syndrome measurement. While correction of the dominant cat Z errors with a repetition code has recently been demonstrated in experiment, here we show how the architecture can be scaled beyond a repetition code. In particular, we propose a cat-transmon entangling gate that enables the correction of residual cat X errors in a thin rectangular surface code, so that logical error can be arbitrarily suppressed by increasing code distance. We numerically estimate logical memory performance, finding significant overhead reductions in comparison to architectures without biased noise. For example, with current state-of-the-art coherence, physical error rates of $10^{-3}$ and noise biases in the range $10^{3} - 10^{4}$ are achievable. With this level of performance, the qubit overhead required to reach algorithmically-relevant logical error rates with the cat-transmon architecture matches that of an unbiased-noise architecture with physical error rates in the range $10^{-5} - 10^{-4}$.

quant-ph↗
arXiv2024

Preserving phase coherence and linearity in cat qubits with exponential bit-flip suppression

Cat qubits, a type of bosonic qubit encoded in a harmonic oscillator, can exhibit an exponential noise bias against bit-flip errors with increasing mean photon number. Here, we focus on cat qubits stabilized by two-photon dissipation, where pairs of photons are added and removed from a harmonic oscillator by an auxiliary, lossy buffer mode. This process requires a large loss rate and strong nonlinearities of the buffer mode that must not degrade the coherence and linearity of the oscillator. In this work, we show how to overcome this challenge by coloring the loss environment of the buffer mode with a multi-pole filter and optimizing the circuit to take into account additional inductances in the buffer mode. Using these techniques, we achieve near-ideal enhancement of cat-qubit bit-flip times with increasing photon number, reaching over $0.1$ seconds with a mean photon number of only $4$. Concurrently, our cat qubit remains highly phase coherent, with phase-flip times corresponding to an effective lifetime of $T_{1,\text{eff}} \simeq 70$ $\mu$s, comparable with the bare oscillator lifetime. We achieve this performance even in the presence of an ancilla transmon, used for reading out the cat qubit states, by engineering a tunable oscillator-ancilla dispersive coupling. Furthermore, the low nonlinearity of the harmonic oscillator mode allows us to perform pulsed cat-qubit stabilization, an important control primitive, where the stabilization can remain off for a significant fraction (e.g., two thirds) of a $3~\mathrm{\mu s}$ cycle without degrading bit-flip times. These advances are important for the realization of scalable error-correction with cat qubits, where large noise bias and low phase-flip error rate enable the use of hardware-efficient outer error-correcting codes.

quant-ph↗
arXiv2024

Hardware-efficient quantum error correction via concatenated bosonic qubits

In order to solve problems of practical importance, quantum computers will likely need to incorporate quantum error correction, where a logical qubit is redundantly encoded in many noisy physical qubits. The large physical-qubit overhead typically associated with error correction motivates the search for more hardware-efficient approaches. Here, using a microfabricated superconducting quantum circuit, we realize a logical qubit memory formed from the concatenation of encoded bosonic cat qubits with an outer repetition code of distance $d=5$. The bosonic cat qubits are passively protected against bit flips using a stabilizing circuit. Cat-qubit phase-flip errors are corrected by the repetition code which uses ancilla transmons for syndrome measurement. We realize a noise-biased CX gate which ensures bit-flip error suppression is maintained during error correction. We study the performance and scaling of the logical qubit memory, finding that the phase-flip correcting repetition code operates below threshold, with logical phase-flip error decreasing with code distance from $d=3$ to $d=5$. Concurrently, the logical bit-flip error is suppressed with increasing cat-qubit mean photon number. The minimum measured logical error per cycle is on average $1.75(2)\%$ for the distance-3 code sections, and $1.65(3)\%$ for the longer distance-5 code, demonstrating the effectiveness of bit-flip error suppression throughout the error correction cycle. These results, where the intrinsic error suppression of the bosonic encodings allows us to use a hardware-efficient outer error correcting code, indicate that concatenated bosonic codes are a compelling paradigm for reaching fault-tolerant quantum computation.

quant-ph↗
arXiv2023

Phonon engineering of atomic-scale defects in superconducting quantum circuits

Noise within solid-state systems at low temperatures, where many of the degrees of freedom of the host material are frozen out, can typically be traced back to material defects that support low-energy excitations. These defects can take a wide variety of microscopic forms, and for amorphous materials are broadly described using generic models such as the tunneling two-level systems (TLS) model. Although the details of TLS, and their impact on the low-temperature behavior of materials have been studied since the 1970s, these states have recently taken on further relevance in the field of quantum computing, where the limits to the coherence of superconducting microwave quantum circuits are dominated by TLS. Efforts to mitigate the impact of TLS have thus far focused on circuit design, material selection, and material surface treatment. In this work, we take a new approach that seeks to directly modify the properties of TLS through nanoscale-engineering. This is achieved by periodically structuring the host material, forming an acoustic bandgap that suppresses all microwave-frequency phonons in a GHz-wide frequency band around the operating frequency of a transmon qubit superconducting quantum circuit. For embedded TLS that are strongly coupled to the electric qubit, we measure a pronounced increase in relaxation time by two orders of magnitude when the TLS transition frequency lies within the acoustic bandgap, with the longest $T_1$ time exceeding $5$ milliseconds. Our work paves the way for in-depth investigation and coherent control of TLS, which is essential for deepening our understanding of noise in amorphous materials and advancing solid-state quantum devices.

quant-ph↗
arXiv2023

Demonstrating a long-coherence dual-rail erasure qubit using tunable transmons

Quantum error correction with erasure qubits promises significant advantages over standard error correction due to favorable thresholds for erasure errors. To realize this advantage in practice requires a qubit for which nearly all errors are such erasure errors, and the ability to check for erasure errors without dephasing the qubit. We demonstrate that a "dual-rail qubit" consisting of a pair of resonantly coupled transmons can form a highly coherent erasure qubit, where transmon $T_1$ errors are converted into erasure errors and residual dephasing is strongly suppressed, leading to millisecond-scale coherence within the qubit subspace. We show that single-qubit gates are limited primarily by erasure errors, with erasure probability $p_\text{erasure} = 2.19(2)\times 10^{-3}$ per gate while the residual errors are $\sim 40$ times lower. We further demonstrate mid-circuit detection of erasure errors while introducing $< 0.1\%$ dephasing error per check. Finally, we show that the suppression of transmon noise allows this dual-rail qubit to preserve high coherence over a broad tunable operating range, offering an improved capacity to avoid frequency collisions. This work establishes transmon-based dual-rail qubits as an attractive building block for hardware-efficient quantum error correction.

quant-ph↗
arXiv2021

Stabilizing a Bosonic Qubit using Colored Dissipation

Protected qubits such as the 0-$\pi$ qubit, and bosonic qubits including cat qubits and GKP qubits offer advantages for fault-tolerance. Some of these protected qubits (e.g., 0-$\pi$ qubit and Kerr cat qubit) are stabilized by Hamiltonians which have (near-)degenerate ground state manifolds with large energy-gaps to the excited state manifolds. Without dissipative stabilization mechanisms the performance of such energy-gap-protected qubits can be limited by leakage to excited states. Here, we propose a scheme for dissipatively stabilizing an energy-gap-protected qubit using colored (i.e., frequency-selective) dissipation without inducing errors in the ground state manifold. Concretely we apply our colored dissipation technique to Kerr cat qubits and propose colored Kerr cat qubits which are protected by an engineered colored single-photon loss. When applied to the Kerr cat qubits our scheme significantly suppresses leakage-induced bit-flip errors (which we show are a limiting error mechanism) while only using linear interactions. Beyond the benefits to the Kerr cat qubit we also show that our frequency-selective loss technique can be applied to a broader class of protected qubits.

quant-ph↗
arXiv2021

Exponential suppression of bit or phase flip errors with repetitive error correction

Realizing the potential of quantum computing will require achieving sufficiently low logical error rates. Many applications call for error rates in the $10^{-15}$ regime, but state-of-the-art quantum platforms typically have physical error rates near $10^{-3}$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits so that errors can be detected and corrected. Logical errors are then exponentially suppressed as the number of physical qubits grows, provided that the physical error rates are below a certain threshold. QEC also requires that the errors are local and that performance is maintained over many rounds of error correction, two major outstanding experimental challenges. Here, we implement 1D repetition codes embedded in a 2D grid of superconducting qubits which demonstrate exponential suppression of bit or phase-flip errors, reducing logical error per round by more than $100\times$ when increasing the number of qubits from 5 to 21. Crucially, this error suppression is stable over 50 rounds of error correction. We also introduce a method for analyzing error correlations with high precision, and characterize the locality of errors in a device performing QEC for the first time. Finally, we perform error detection using a small 2D surface code logical qubit on the same device, and show that the results from both 1D and 2D codes agree with numerical simulations using a simple depolarizing error model. These findings demonstrate that superconducting qubits are on a viable path towards fault tolerant quantum computing.

quant-ph↗
arXiv2020

Building a fault-tolerant quantum computer using concatenated cat codes

We present a comprehensive architectural analysis for a proposed fault-tolerant quantum computer based on cat codes concatenated with outer quantum error-correcting codes. For the physical hardware, we propose a system of acoustic resonators coupled to superconducting circuits with a two-dimensional layout. Using estimated physical parameters for the hardware, we perform a detailed error analysis of measurements and gates, including CNOT and Toffoli gates. Having built a realistic noise model, we numerically simulate quantum error correction when the outer code is either a repetition code or a thin rectangular surface code. Our next step toward universal fault-tolerant quantum computation is a protocol for fault-tolerant Toffoli magic state preparation that significantly improves upon the fidelity of physical Toffoli gates at very low qubit cost. To achieve even lower overheads, we devise a new magic-state distillation protocol for Toffoli states. Combining these results together, we obtain realistic full-resource estimates of the physical error rates and overheads needed to run useful fault-tolerant quantum algorithms. We find that with around 1,000 superconducting circuit components, one could construct a fault-tolerant quantum computer that can run circuits which are currently intractable for classical computers. Hardware with 18,000 superconducting circuit components, in turn, could simulate the Hubbard model in a regime beyond the reach of classical computing.

quant-ph↗
arXiv2020

Observation of separated dynamics of charge and spin in the Fermi-Hubbard model

Strongly correlated quantum systems give rise to many exotic physical phenomena, including high-temperature superconductivity. Simulating these systems on quantum computers may avoid the prohibitively high computational cost incurred in classical approaches. However, systematic errors and decoherence effects presented in current quantum devices make it difficult to achieve this. Here, we simulate the dynamics of the one-dimensional Fermi-Hubbard model using 16 qubits on a digital superconducting quantum processor. We observe separations in the spreading velocities of charge and spin densities in the highly excited regime, a regime that is beyond the conventional quasiparticle picture. To minimize systematic errors, we introduce an accurate gate calibration procedure that is fast enough to capture temporal drifts of the gate parameters. We also employ a sequence of error-mitigation techniques to reduce decoherence effects and residual systematic errors. These procedures allow us to simulate the time evolution of the model faithfully despite having over 600 two-qubit gates in our circuits. Our experiment charts a path to practical quantum simulation of strongly correlated phenomena using available quantum devices.

quant-ph↗
arXiv2020

Creating and manipulating a Laughlin-type $\nu=1/3$ fractional quantum Hall state on a quantum computer with linear depth circuits

Here we present an efficient quantum algorithm to generate an equivalent many-body state to Laughlin's $\nu=1/3$ fractional quantum Hall state on a digitized quantum computer. Our algorithm only uses quantum gates acting on neighboring qubits in a quasi-one-dimensional setting, and its circuit depth is linear in the number of qubits, i.e., the number of Landau orbitals in the second quantized picture. We identify correlation functions that serve as signatures of the Laughlin state and discuss how to obtain them on a quantum computer. We also discuss a generalization of the algorithm for creating quasiparticles in the Laughlin state. This paves the way for several important studies, including quantum simulation of nonequilibrium dynamics and braiding of quasiparticles in quantum Hall states.

cond-mat.str-el↗
arXiv2020

Quantum Approximate Optimization of Non-Planar Graph Problems on a Planar Superconducting Processor

We demonstrate the application of the Google Sycamore superconducting qubit quantum processor to combinatorial optimization problems with the quantum approximate optimization algorithm (QAOA). Like past QAOA experiments, we study performance for problems defined on the (planar) connectivity graph of our hardware; however, we also apply the QAOA to the Sherrington-Kirkpatrick model and MaxCut, both high dimensional graph problems for which the QAOA requires significant compilation. Experimental scans of the QAOA energy landscape show good agreement with theory across even the largest instances studied (23 qubits) and we are able to perform variational optimization successfully. For problems defined on our hardware graph we obtain an approximation ratio that is independent of problem size and observe, for the first time, that performance increases with circuit depth. For problems requiring compilation, performance decreases with problem size but still provides an advantage over random guessing for circuits involving several thousand gates. This behavior highlights the challenge of using near-term quantum computers to optimize problems on graphs differing from hardware connectivity. As these graphs are more representative of real world instances, our results advocate for more emphasis on such problems in the developing tradition of using the QAOA as a holistic, device-level benchmark of quantum processors.

quant-ph↗
arXiv2020

Hartree-Fock on a superconducting qubit quantum computer

As the search continues for useful applications of noisy intermediate scale quantum devices, variational simulations of fermionic systems remain one of the most promising directions. Here, we perform a series of quantum simulations of chemistry the largest of which involved a dozen qubits, 78 two-qubit gates, and 114 one-qubit gates. We model the binding energy of ${\rm H}_6$, ${\rm H}_8$, ${\rm H}_{10}$ and ${\rm H}_{12}$ chains as well as the isomerization of diazene. We also demonstrate error-mitigation strategies based on $N$-representability which dramatically improve the effective fidelity of our experiments. Our parameterized ansatz circuits realize the Givens rotation approach to non-interacting fermion evolution, which we variationally optimize to prepare the Hartree-Fock wavefunction. This ubiquitous algorithmic primitive corresponds to a rotation of the orbital basis and is required by many proposals for correlated simulations of molecules and Hubbard models. Because non-interacting fermion evolutions are classically tractable to simulate, yet still generate highly entangled states over the computational basis, we use these experiments to benchmark the performance of our hardware while establishing a foundation for scaling up more complex correlated quantum simulations of chemistry.

quant-ph↗