arXiv subjects

Fernando G. S. L. Brandão

Publications and source records attributed to Fernando G. S. L. Brandão.

At least 19 recordsLinked to original sources

arXiv2026

Cavity-mediated cross-cross-resonance gate

We propose a cavity-mediated gate between two transmon qubits or other nonlinear superconducting elements. The gate is realized by driving both qubits at a frequency that is near-resonant with the frequency of the cavity. Since both qubits are subject to a cross-resonant drive, we call this gate a cross-cross-resonance gate. In close analogy with gates between trapped-ion qubits, in phase space, the state of the cavity makes a circle whose area depends on the state of the two qubits, realizing a controlled-phase gate. We propose two schemes for canceling the dominant error, which is the qubit-cavity dispersive coupling. We also show that this cross-cross-resonance gate allows one to realize simultaneous gates between multiple pairs of qubits coupled via the same metamaterial composed of an array of coupled cavities or other linear mediators.

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arXiv2026

Solving Sparse SDPs in Sublinear Time: A Classical Algorithm Inspired by the Quantum OR Lemma

We give the first sublinear-time classical solvers for sparse semidefinite programs in the bounded-radius regime, without low-rank assumptions or Frobenius norm dependence on the constraint matrices. For constant precision and bounded primal and dual radii, prior quantum algorithms of Brandão et al. (2019) and van Apeldoorn and Gilyén (2019) achieved $\widetilde{O}(\sqrt{n}+\sqrt{m})$ dependence on matrix dimension $n$ and constraint number $m$. Compared with the $\widetilde{O}(mn)$ runtime of existing classical methods, this suggests a quartic quantum speedup when $m \approx n$. Beyond a usual Grover speedup, this separation relies on the Quantum OR lemma, whose sample-reuse mechanism decouples the cost of Gibbs-state preparation from constraint search. We show that this reuse mechanism is classically realizable for sparse SDPs. Our main technical contribution is a classical procedure for simultaneously estimating many expectation values with respect to a sparse Hamiltonian's Gibbs state. This combines randomized Lánczos filtering with an efficient sampling-based estimator. We also introduce a stochastic online-learning framework for SDP solving, substantially improving accuracy-dependence over standard oracle-based MMWU approaches. Let $s$ denote the the input matrix sparsity and $γ:=Rr/\varepsilon$ capture dependence on the primal $(R)$ and dual $(r)$ radii as well as target accuracy $(\varepsilon)$. When $γ^2\leq\min\{m,n/s\}$, our solver runs in time $\widetilde{O}\left(nsγ^{4.5}+msγ^2\right)$. For $γ=O(1)$, this is $\widetilde{O}\left((n+m)s\right)$ and sublinear in the $O(mns)$ input size. Similar to the quantum algorithms, this matches known lower bounds with respect to $m$ and $n$, up to logarithmic factors. This implies that, with respect to dimensions $m$ and $n$, there is no super-quadratic quantum advantage for generic sparse SDP solving.

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arXiv2026

Readout-induced degradation of transmon lifetimes: interplay of TLSs and qubit spectral reshaping

Measurement backaction degrades dispersive readout of superconducting qubits even at modest drive strengths, often via the reduction of qubit lifetimes during readout. In this work, we theoretically and experimentally study this degradation and show how it can result from the interplay between detuned two-level systems (TLSs) and a drive-renormalized qubit spectrum. For modest to strong readout, the qubit emission spectrum becomes non-Lorentzian and depends sensitively on the readout drive frequency (even when measurement rate is fixed). We combine the readout-modified qubit emission spectrum with time-dependent perturbation theory to predict qubit lifetimes in the presence of a TLS bath. Master equation simulations and experimental measurements on a frequency-tunable transmon confirm these predictions quantitatively. In particular, we find that driving at the resonator frequency associated with the qubit ground state yields the narrowest qubit emission spectrum and the least lifetime degradation for a fixed measurement rate, providing a practical guideline for optimizing readout protocols in future quantum processors.

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arXiv2026

Suppressing errors in analog logical rotation gates via balanced fusion

There have been a number of recent proposals to use analog logical rotations in early fault-tolerant quantum algorithms. Existing proposals implement a logical rotation by angle $ϕ$, with error $O(pϕ)$, where $p$ is the physical error rate. While this is not fault-tolerant, if $ϕ$ is sufficiently small the logical error rate can be suppressed. In this work, we introduce and analyze the `balanced fusion' technique for improving the error scaling of analog logical rotations to $O(p ϕ^{1.5})$, without having to resort to fallback synthesis. Balanced fusion is enabled by an improved analysis of the accumulation of coherent error terms in analog logical rotations. Our techniques improve the viability of analog logical rotations for small rotation angles as an alternative to cultivation-powered rotation synthesis.

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arXiv2026

A Berry-Esseen Bound for Quantum Lattice Systems

It is expected that the statistical fluctuations of local observables in large quantum systems obey the central limit theorem, and approximate a normal distribution as their size grows. Here, we prove a version of the Berry-Esseen theorem for quantum lattice systems, which strengthens that central limit theorem by providing a rigorous convergence estimate towards the normal distribution for large but finite system size. Given a local quantum Hamiltonian on $N$ particles and a quantum state with a finite correlation length, the result states that the measurement of local observables such as the energy follows a normal distribution, up to an error scaling as $\mathcal{O}\left(N^{-\frac{1}{2}} \text{polylog}(N)\right)$, which is optimal up to logarithmic factors.

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arXiv2026

Fast, High-Fidelity Erasure Detection of Dual-Rail Qubits with Symmetrically Coupled Readout

Erasure qubits are a promising platform for implementing hardware-efficient quantum error correction. Realizing the error-correction advantages of this encoding requires frequent mid-circuit erasure checks that are fast, high-fidelity, and scalable. Here, we realize erasure detection with a hardware-efficient circuit consisting of a single readout resonator dispersively and symmetrically coupled to both transmons of a dual-rail qubit. We use this circuit to demonstrate single-shot erasure detection in 384 ns with minimal impact on the dual-rail logical manifold, achieving a residual error per check of $6.0(2) \times 10^{-4}$, with only $8(3) \times 10^{-5}$ induced dephasing per check, and an erasure error per check of $2.54(1)\times 10^{-2}$. The high degree of matched dispersive readout coupling ($χ$-matching) within the dual-rail qubit code space also allows us to realize a new modality: time-continuous erasure detection performed in parallel with single-qubit gates. Here we achieve a median $7.2 \times 10^{-5}$ error per gate with $< 1 \times 10^{-5}$ error induced by erasure detection. This demonstrates a reduction in erasure detection overhead as well as a crucial ingredient for soft information quantum error correction. Together, these results establish symmetrically coupled dispersive readout as a fast, hardware-efficient, and scalable component for erasure-based quantum error correction using transmon dual-rail qubits.

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arXiv2026

Mind the gap: Achieving a super-Grover quantum speedup by jumping to the end

We present a quantum algorithm that has rigorous runtime guarantees for several families of binary optimization problems, including Quadratic Unconstrained Binary Optimization (QUBO), Ising spin glasses ($p$-spin model), and $k$-local constraint satisfaction problems ($k$-CSP). We show that either (a) the algorithm finds the optimal solution in time $O^*(2^{(0.5-c)n})$ for an $n$-independent constant $c$, a $2^{cn}$ advantage over Grover's algorithm; or (b) there are sufficiently many low-cost solutions such that classical random guessing produces a $(1-η)$ approximation to the optimal cost value in sub-exponential time for arbitrarily small choice of $η$. Additionally, we show that for a large fraction of random instances from the $k$-spin model and for any sufficiently close-to-regular, fully satisfiable (or slightly frustrated) $k$-CSP formula, statement (a) is the case. The algorithm and its analysis is largely inspired by Hastings' short-path algorithm [$\textit{Quantum}$ $\textbf{2}$ (2018) 78].

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arXiv2025

The Fast for the Curious: How to accelerate fault-tolerant quantum applications

We evaluate strategies for reducing the run time of fault-tolerant quantum computations, targeting practical utility in scientific or industrial workflows. Delivering a technology with broad impact requires scaling devices, while also maintaining acceptable run times for computations. Optimizing logical clock speed may require moving beyond current strategies, and adopting methods that trade faster run time for increased qubit counts or engineering complexity. We discuss how the co-design of hardware, fault tolerance, and algorithmic subroutines can reduce run times. We illustrate a selection of these topics with resource estimates for simulating the Fermi-Hubbard model.

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arXiv2025

Quantum algorithms: A survey of applications and end-to-end complexities

The anticipated applications of quantum computers span across science and industry, ranging from quantum chemistry and many-body physics to optimization, finance, and machine learning. Proposed quantum solutions in these areas typically combine multiple quantum algorithmic primitives into an overall quantum algorithm, which must then incorporate the methods of quantum error correction and fault tolerance to be implemented correctly on quantum hardware. As such, it can be difficult to assess how much a particular application benefits from quantum computing, as the various approaches are often sensitive to intricate technical details about the underlying primitives and their complexities. Here we present a survey of several potential application areas of quantum algorithms and their underlying algorithmic primitives, carefully considering technical caveats and subtleties. We outline the challenges and opportunities in each area in an "end-to-end" fashion by clearly defining the problem being solved alongside the input-output model, instantiating all "oracles," and spelling out all hidden costs. We also compare quantum solutions against state-of-the-art classical methods and complexity-theoretic limitations to evaluate possible quantum speedups. The survey is written in a modular, wiki-like fashion to facilitate navigation of the content. Each primitive and application area is discussed in a standalone section, with its own bibliography of references and embedded hyperlinks that direct to other relevant sections. This structure mirrors that of complex quantum algorithms that involve several layers of abstraction, and it enables rapid evaluation of how end-to-end complexities are impacted when subroutines are altered.

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arXiv2025

A distillation-teleportation protocol for fault-tolerant QRAM

We present a protocol for fault-tolerantly implementing the logical quantum random access memory (QRAM) operation, given access to a specialized, noisy QRAM device. For coherently accessing classical memories of size $2^n$, our protocol consumes only $\mathrm{poly}(n)$ fault-tolerant quantum resources (logical gates, logical qubits, quantum error correction cycles, etc.), avoiding the need to perform active error correction on all $Ω(2^n)$ components of the QRAM device. This is the first rigorous conceptual demonstration that a specialized, noisy QRAM device could be useful for implementing a fault-tolerant quantum algorithm. In fact, the fidelity of the device can be as low as $1/\mathrm{poly}(n)$. The protocol queries the noisy QRAM device $\mathrm{poly}(n)$ times to prepare a sequence of $n$-qubit QRAM resource states, which are moved to a general-purpose $\mathrm{poly}(n)$-size processor to be encoded into a QEC code, distilled, and fault-tolerantly teleported into the computation. To aid this protocol, we develop a new gate-efficient streaming version of quantum purity amplification that matches the optimal sample complexity in a wide range of parameters and is therefore of independent interest. The exponential reduction in fault-tolerant quantum resources comes at the expense of an exponential quantity of purely classical complexity: each of the $n$ iterations of the protocol requires adaptively updating the $2^n$-size classical dataset and providing the noisy QRAM device with access to the updated dataset at the next iteration. While our protocol demonstrates that QRAM is more compatible with fault-tolerant quantum computation than previously thought, the need for significant classical computational complexity exposes potentially fundamental limitations to realizing a truly $\mathrm{poly}(n)$-cost fault-tolerant QRAM.

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arXiv2025

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 $T_{1,\text{eff}} \simeq 70$ $μ$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 $3~\mathrm{μs}$ 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.

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arXiv2025

On a gap in the proof of the generalised quantum Stein's lemma and its consequences for the reversibility of quantum resources

We show that the proof of the generalised quantum Stein's lemma [Brandão & Plenio, Commun. Math. Phys. 295, 791 (2010)] is not correct due to a gap in the argument leading to Lemma III.9. Hence, the main achievability result of Brandão & Plenio is not known to hold. This puts into question a number of established results in the literature, in particular the reversibility of quantum entanglement [Brandão & Plenio, Commun. Math. Phys. 295, 829 (2010); Nat. Phys. 4, 873 (2008)] and of general quantum resources [Brandão & Gour, Phys. Rev. Lett. 115, 070503 (2015)] under asymptotically resource non-generating operations. We discuss potential ways to recover variants of the newly unsettled results using other approaches.

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arXiv2025

Myths around quantum computation before full fault tolerance: What no-go theorems rule out and what they don't

In this perspective article, we revisit and critically evaluate prevailing viewpoints on the capabilities and limitations of near-term quantum computing and its potential transition toward fully fault-tolerant quantum computing. We examine theoretical no-go results and their implications, addressing misconceptions about the practicality of quantum error mitigation techniques and variational quantum algorithms. By emphasizing the nuances of error scaling, circuit depth, and algorithmic feasibility, we highlight viable near-term applications and synergies between error mitigation and early fault-tolerant architectures. Our discussion explores strategies for addressing current challenges, such as barren plateaus in variational circuits and the integration of quantum error mitigation and quantum error correction techniques. We aim to underscore the importance of continued innovation in hardware and algorithmic design to bridge the gap between theoretical potential and practical utility, paving the way for meaningful quantum advantage in the era of late noisy intermediate scale and early fault-tolerant quantum devices.

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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 $10^{-5} - 10^{-4}$.

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arXiv2024

End-to-end resource analysis for quantum interior point methods and portfolio optimization

We study quantum interior point methods (QIPMs) for second-order cone programming (SOCP), guided by the example use case of portfolio optimization (PO). We provide a complete quantum circuit-level description of the algorithm from problem input to problem output, making several improvements to the implementation of the QIPM. We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm, including constant factors. The resource counts we find depend on instance-specific parameters, such as the condition number of certain linear systems within the problem. To determine the size of these parameters, we perform numerical simulations of small PO instances, which lead to concrete resource estimates for the PO use case. Our numerical results do not probe large enough instance sizes to make conclusive statements about the asymptotic scaling of the algorithm. However, already at small instance sizes, our analysis suggests that, due primarily to large constant pre-factors, poorly conditioned linear systems, and a fundamental reliance on costly quantum state tomography, fundamental improvements to the QIPM are required for it to lead to practical quantum advantage.

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arXiv2024

Efficient Unitary T-designs from Random Sums

Unitary $T$-designs play an important role in quantum information, with diverse applications in quantum algorithms, benchmarking, tomography, and communication. Until now, the most efficient construction of unitary $T$-designs for $n$-qudit systems has been via random local quantum circuits, which have been shown to converge to approximate $T$-designs in the diamond norm using $O(T^{5+o(1)} n^2)$ quantum gates. In this work, we provide a new construction of $T$-designs via random matrix theory using $\tilde{O}(T^2 n^2)$ quantum gates. Our construction leverages two key ideas. First, in the spirit of central limit theorems, we approximate the Gaussian Unitary Ensemble (GUE) by an i.i.d. sum of random Hermitian matrices. Second, we show that the product of just two exponentiated GUE matrices is already approximately Haar random. Thus, multiplying two exponentiated sums over rather simple random matrices yields a unitary $T$-design, via Hamiltonian simulation. A central feature of our proof is a new connection between the polynomial method in quantum query complexity and the large-dimension ($N$) expansion in random matrix theory. In particular, we show that the polynomial method provides exponentially improved bounds on the high moments of certain random matrix ensembles, without requiring intricate Weingarten calculations. In doing so, we define and solve a new type of moment problem on the unit circle, asking whether a finite number of equally weighted points, corresponding to eigenvalues of unitary matrices, can reproduce a given set of moments.

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arXiv2023

Quantum Thermal State Preparation

Preparing ground states and thermal states is essential for simulating quantum systems on quantum computers. Despite the hope for practical quantum advantage in quantum simulation, popular state preparation approaches have been challenged. Monte Carlo-style quantum Gibbs samplers have emerged as an alternative, but prior proposals have been unsatisfactory due to technical obstacles rooted in energy-time uncertainty. We introduce simple continuous-time quantum Gibbs samplers that overcome these obstacles by efficiently simulating Nature-inspired quantum master equations (Lindbladians). In addition, we construct the first provably accurate and efficient algorithm for preparing certain purified Gibbs states (called thermal field double states in high-energy physics) of rapidly thermalizing systems; this algorithm also benefits from a quantum walk speedup. Our algorithms' costs have a provable dependence on temperature, accuracy, and the mixing time (or spectral gap) of the relevant Lindbladian. We complete the first rigorous proof of finite-time thermalization for physically derived Lindbladians by developing a general analytic framework for nonasymptotic secular approximation and approximate detailed balance. Given the success of classical Markov chain Monte Carlo (MCMC) algorithms and the ubiquity of thermodynamics, we anticipate that quantum Gibbs sampling will become indispensable in quantum computing.

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arXiv2023

Preparing random states and benchmarking with many-body quantum chaos

Producing quantum states at random has become increasingly important in modern quantum science, with applications both theoretical and practical. In particular, ensembles of such randomly-distributed, but pure, quantum states underly our understanding of complexity in quantum circuits and black holes, and have been used for benchmarking quantum devices in tests of quantum advantage. However, creating random ensembles has necessitated a high degree of spatio-temporal control, placing such studies out of reach for a wide class of quantum systems. Here we solve this problem by predicting and experimentally observing the emergence of random state ensembles naturally under time-independent Hamiltonian dynamics, which we use to implement an efficient, widely applicable benchmarking protocol. The observed random ensembles emerge from projective measurements and are intimately linked to universal correlations built up between subsystems of a larger quantum system, offering new insights into quantum thermalization. Predicated on this discovery, we develop a fidelity estimation scheme, which we demonstrate for a Rydberg quantum simulator with up to 25 atoms using fewer than 10^4 experimental samples. This method has broad applicability, as we show for Hamiltonian parameter estimation, target-state generation benchmarking, and comparison of analog and digital quantum devices. Our work has implications for understanding randomness in quantum dynamics, and enables applications of this concept in a much wider context.

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