arXiv subjects

David Amaro

Publications and source records attributed to David Amaro.

At least 19 recordsLinked to original sources

arXiv2026

SyQMA: A memory-efficient, symbolic and exact universal simulator for quantum error correction

The classical simulation of universal quantum circuits is crucial both fundamentally and practically for quantum computation. We propose SyQMA, a simulator with several convenient features, particularly suited for quantum error correction (QEC). SyQMA simulates universal quantum circuits with incoherent Pauli noise and computes exact expectation values and measurement probabilities as symbolic functions of circuit parameters: rotation angles, measurement outcomes, and noise rates. This simulator can sample measurement outcomes, enabling the simulation of dynamic quantum programs where circuit composition depends on prior measurement outputs. For QEC, it performs circuit-level maximum-likelihood decoding, provides exact symbolic expressions for logical error rates, and verifies the fault distance of fault-tolerant (FT) stabiliser and magic state preparation protocols. These features are enabled by an intuitive extension of stabiliser simulators, where each non-Clifford Pauli rotation and incoherent Pauli channel is compactly represented via auxiliary qubits and a modified trace. Representing the state requires only polynomial memory and time, while computing expectation values and measurement probabilities takes exponential time in the number of non-Clifford rotations and deterministic measurements, but only polynomial memory. The FT preparation of stabiliser and magic states, including the first stage of magic state cultivation, is analysed without approximations. We also exactly convert the disjoint error probabilities of a general multi-qubit Pauli channel to independent ones, a key step for creating and sampling from detector error models. The code is publicly available and open-source.

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arXiv2026

Fast stabilizer state preparation via AI-optimized graph decimation

We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces the number of edges in the graph using two-qubit Clifford gates to produce a unitary preparation circuit. We explore various heuristic search and AI-based approaches to optimally choose Clifford gates at each step, the most sophisticated of which is a combination of reinforcement learning and Monte Carlo tree search that we call QuSynth. We apply our method to synthesize code states of various quantum error correcting codes including the 23-qubit Golay code and the 144-qubit gross code, the latter of which is significantly beyond the qubit number that is accessible to prior optimal circuit synthesis methods. We demonstrate that our techniques are capable of reducing the required two-qubit gates by up to a factor of 2.5 compared to previous approaches while retaining low circuit depth.

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arXiv2026

Fault-tolerant execution of error-corrected quantum algorithms

Scaling up quantum algorithms to tackle high-impact problems in science and industry requires quantum error correction and fault tolerance. While progress has been made in experimentally realizing error-corrected primitives, the end-to-end execution of logical quantum algorithms using only fault-tolerant (FT) components has remained out of reach. We demonstrate the FT and error-corrected execution of two quantum algorithms, the Quantum Approximate Optimization Algorithm (QAOA) and the Harrow-Hassidim-Lloyd (HHL) algorithm applied to the Poisson equation, on Quantinuum H2 and Helios trapped-ion quantum processors using the $[[7,1,3]]$ Steane code. For QAOA circuits on 5 and 6 logical qubits, we show performance improvements from increasing the number of QAOA layers and the number of $T$ gates used to approximate logical rotations, despite increased physical circuit complexity. We further show that QAOA circuits with up to 8 logical qubits and 9 logical $T$ gates perform similarly to unencoded circuits. For the largest QAOA circuits we run, with 12 logical (97 physical) qubits and 2132 physical two-qubit gates, we still observe better-than-random performance. Finally, we show that adding active QEC cycles and increasing the repeat-until-success limit of state preparation subroutines can improve the performance of a quantum algorithm, thereby demonstrating critical capabilities of scalable FT quantum computation. Our results are enabled by an FT logical $T$ gate implementation with an infidelity of $\sim 2.6(4)\times10^{-3}$ and dynamic circuits with measurement-dependent feedback. Our work demonstrates near-break-even performance of complex, error-corrected algorithmic quantum circuits using only FT components.

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arXiv2026

Computing with many encoded logical qubits beyond break-even

High-rate quantum error correcting (QEC) codes encode many logical qubits in a given number of physical qubits, making them promising candidates for quantum computation. Implementing high-rate codes at a scale that both frustrates classical computing and improves performance by encoding requires both high fidelity gates and long-range qubit connectivity -- both of which are offered by trapped-ion quantum computers. Here, we demonstrate computations that outperform their unencoded counterparts in the high-rate $[[ k+2,\, k,\, 2 ]]$ iceberg quantum error detecting (QED) and $[[ (k_2 + 2)(k_1 + 2),\, k_2k_1,\, 4 ]]$ two-level concatenated iceberg QEC codes, using the 98-qubit Quantinuum Helios trapped-ion quantum processor. Utilizing new gadgets for encoded operations, we realize this "beyond break-even" performance with reasonable postselection rates across a range of fault-tolerant (FT) and partially-fault-tolerant (pFT) component and application benchmarks with between $48$ and $94$ logical qubits. These benchmarks include FT state preparation and measurement, QEC cycle benchmarking, logical gate benchmarking, GHZ state preparation, and a pFT quantum simulation of the three-dimensional $XY$ model of quantum magnetism. Additionally, we illustrate that postselection rates can be suppressed by increasing the code distance via concatenation. Our results represent state-of-the-art logical component and state fidelities and provide evidence that high-rate QED/QEC codes are viable on contemporary quantum computers for near-term beyond-classical-scale computation.

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arXiv2026

Digital signatures with classical shadows on near-term quantum computers

Quantum mechanics provides cryptographic primitives whose security is grounded in hardness assumptions independent of those underlying classical cryptography. However, existing proposals require low-noise quantum communication and long-lived quantum memory, capabilities which remain challenging to realize in practice. In this work, we introduce a quantum digital signature scheme that operates with only classical communication, using the classical shadows of states produced by random circuits as public keys. We provide theoretical and numerical evidence supporting the conjectured hardness of learning the private key (the circuit) from the public key (the shadow). A key technical ingredient enabling our scheme is an improved state-certification primitive that achieves higher noise tolerance and lower sample complexity than prior methods. We realize this certification by designing a high-rate error-detecting code tailored to our random-circuit ensemble and experimentally generating shadows for 32-qubit states using circuits with $\geq 80$ logical ($\geq 582$ physical) two-qubit gates, attaining 0.90 $\pm$ 0.01 fidelity. With increased number of measurement samples, our hardware-demonstrated primitives realize a proof-of-principle quantum digital signature, demonstrating the near-term feasibility of our scheme.

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arXiv2025

Flag at origin: a modular fault-tolerant preparation for CSS codes

Fault-tolerant (FT) preparation of diverse logical stabilizer states in quantum error-correcting (QEC) codes is essential for FT computation. Existing constructions of these FT circuits are often constrained by classical computational resources or result in unnecessarily large quantum circuits. This work introduces a modular construction for FT preparation circuits in CSS codes of arbitrary distance, yielding significantly more resource-efficient circuits than previous approaches, especially for the largest codes studied. The key insight is that in bipartite CX circuits used to prepare CSS states, $X$ errors propagate in one direction across the qubit partition, while $Z$ errors propagate in the opposite direction. By appending $X$-detecting flag gadgets to the first partition and $Z$-detecting flag gadgets to the second, the circuit becomes FT. To manage the associated overhead, we propose an algorithm that discovers optimal (or near-optimal) flag gadgets at any distance. These gadgets are reusable across different QEC codes and FT subroutines, such as flag-based QEC. We estimate the logical state preparation error using subset-sampling Monte Carlo simulations at the circuit level, combined with approximate maximum-likelihood look-up table decoding. On Quantinuum's H2-1 device, preparation of the $\lvert\bar{0}\rangle$ state in the [[23,1,7]] Golay code achieves a logical SPAM error rate of $3.3_{-2.4}^{+8.6} \times 10^{-4}$ with an acceptance rate of $47.23(86)\%$. This surpasses (within $95\%$ confidence intervals) the minimum SPAM error rate of $6.0(1.6) \times 10^{-4}$ for a physical $\lvert 0\rangle$, as well as the best previously demonstrated logical state preparations.

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arXiv2025

Breaking even with magic: demonstration of a high-fidelity logical non-Clifford gate

Encoding quantum information to protect it from errors is essential for performing large-scale quantum computations. Performing a universal set of quantum gates on encoded states demands a potentially large resource overhead and minimizing this overhead is key for the practical development of large-scale fault-tolerant quantum computers. We propose and experimentally implement a magic-state preparation protocol to fault-tolerantly prepare a pair of logical magic states in a [[6,2,2]] quantum error-detecting code using only eight physical qubits. Implementing this protocol on H1-1, a 20 qubit trapped-ion quantum processor, we prepare magic states with experimental infidelity $7^{+3}_{-1}\times 10^{-5}$ with a $14.8^{+1}_{-1}\%$ discard rate and use these to perform a fault-tolerant non-Clifford gate, the controlled-Hadamard (CH), with logical infidelity $\leq 2.3^{+9}_{-9}\times 10^{-4}$. Notably, this significantly outperforms the unencoded physical CH infidelity of $10^{-3}$. Through circuit-level stabilizer simulations, we show that this protocol can be self-concatenated to produce extremely high-fidelity magic states with low space-time overhead in a [[36,4,4]] quantum error correcting code, with logical error rates of $6\times 10^{-10}$ ($5\times 10^{-14}$) at two-qubit error rate of $10^{-3}$ ($10^{-4}$) respectively.

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arXiv2025

Quantum Error-Corrected Computation of Molecular Energies

We present the first demonstration of an end-to-end pipeline with quantum error correction (QEC) for a quantum computation of the electronic structure of molecular systems. We calculate the ground-state energy of molecular hydrogen, using quantum phase estimation (QPE) on qubits encoded with the $[[7,1,3]]$ color code on Quantinuum H2-2. We obtain improvements in computational fidelity by (1) introducing several partially fault-tolerant (FT) techniques for the Clifford+$R_{Z}$ (arbitrary-angle single-qubit rotation) gate set, and (2) integrating Steane QEC gadgets for real-time error correction. In particular, the latter enhances the QPE circuits' performance despite the complexity of the extra QEC circuitry. The encoded circuits contain up to 1585 (546) fixed and 7202 (1702) conditional physical two-qubit gates (mid-circuit measurements), and $\sim$3900 ($\sim$760) total operations are applied on average. The energy $E$ is experimentally estimated to within $E - E_{\mathrm{FCI}} = 0.001(13)$ hartree, where $E_{\mathrm{FCI}}$ denotes the exact ground state energy within the given basis set. Additionally, we conduct numerical simulations with tunable noise parameters to identify the dominant sources of noise. We find that orienting the QEC protocols towards higher memory noise protection is the most promising avenue to improve our experimental results.

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arXiv2025

Iceberg Beyond the Tip: Co-Compilation of a Quantum Error Detection Code and a Quantum Algorithm

The rapid progress in quantum hardware is expected to make them viable tools for the study of quantum algorithms in the near term. The timeline to useful algorithmic experimentation can be accelerated by techniques that use many noisy shots to produce an accurate estimate of the observable of interest. One such technique is to encode the quantum circuit using an error detection code and discard the samples for which an error has been detected. An underexplored property of error-detecting codes is the flexibility in the circuit encoding and fault-tolerant gadgets, which enables their co-optimization with the algorthmic circuit. However, standard circuit optimization tools cannot be used to exploit this flexibility as optimization must preserve the fault-tolerance of the gadget. In this work, we focus on the $[[k+2, k, 2]]$ Iceberg quantum error detection code, which is tailored to trapped-ion quantum processors. We design new flexible fault-tolerant gadgets for the Iceberg code, which we then co-optimize with the algorithmic circuit for the quantum approximate optimization algorithm (QAOA) using tree search. By co-optimizing the QAOA circuit and the Iceberg gadgets, we achieve an improvement in QAOA success probability from $44\%$ to $65\%$ and an increase in post-selection rate from $4\%$ to $33\%$ at 22 algorithmic qubits, utilizing 330 algorithmic two-qubit gates and 744 physical two-qubit gates on the Quantinuum H2-1 quantum computer, compared to the previous state-of-the-art hardware demonstration. Furthermore, we demonstrate better-than-unencoded performance for up to 34 algorithmic qubits, employing 510 algorithmic two-qubit gates and 1140 physical two-qubit gates.

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arXiv2024

Performance of Quantum Approximate Optimization with Quantum Error Detection

Quantum algorithms must be scaled up to tackle real-world applications. Doing so requires overcoming the noise present on today's hardware. The quantum approximate optimization algorithm (QAOA) is a promising candidate for scaling up, due to its modest resource requirements and documented asymptotic speedup over state-of-the-art classical algorithms for some problems. However, achieving better-than-classical performance with QAOA is believed to require fault tolerance. In this paper, we demonstrate a partially fault-tolerant implementation of QAOA using the $[[k+2,k,2]]$ ``Iceberg'' error detection code. We observe that encoding the circuit with the Iceberg code improves the algorithmic performance as compared to the unencoded circuit for problems with up to $20$ logical qubits on a trapped-ion quantum computer. Additionally, we propose and calibrate a model for predicting the code performance. We use this model to characterize the limits of the Iceberg code and extrapolate its performance to future hardware with improved error rates. In particular, we show how our model can be used to determine the necessary conditions for QAOA to outperform the Goemans-Williamson algorithm on future hardware. To the best of our knowledge, our results demonstrate the largest universal quantum computing algorithm protected by partially fault-tolerant quantum error detection on practical applications to date, paving the way towards solving real-world applications with quantum computers.

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arXiv2024

Performance analysis of a filtering variational quantum algorithm

Even a minor boost in solving combinatorial optimization problems can greatly benefit multiple industries. Quantum computers, with their unique information processing capabilities, hold promise for delivering such enhancements. The Filtering Variational Quantum Eigensolver (F-VQE) is a variational hybrid quantum algorithm designed to solve combinatorial optimization problems on existing quantum computers with limited qubit number, connectivity, and fidelity. In this work we employ Instantaneous Quantum Polynomial circuits as our parameterized quantum circuits. We propose a hardware-efficient implementation that respects limited qubit connectivity and show that they halve the number of circuits necessary to evaluate the gradient with the parameter-shift rule. To assess the potential of this protocol in the context of combinatorial optimization, we conduct extensive numerical analysis. We compare the performance against three classical baseline algorithms on weighted MaxCut and the Asymmetric Traveling Salesperson Problem (ATSP). We employ noiseless simulators for problems encoded on 13 to 29 qubits, and up to 37 qubits on the IBMQ real quantum devices. The ATSP encoding employed reduces the number of qubits and avoids the need of constraints compared to the standard QUBO / Ising model. Despite some observed positive signs, we conclude that significant development is necessary for a practical advantage with F-VQE.

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arXiv2022

Protecting Expressive Circuits with a Quantum Error Detection Code

A successful quantum error correction protocol would allow quantum computers to run algorithms without suffering from the effects of noise. However, fully fault-tolerant quantum error correction is too resource intensive for existing quantum computers. In this context we develop a quantum error detection code for implementations on existing trapped-ion computers. By encoding $k$ logical qubits into $k+2$ physical qubits, this code presents fault-tolerant state initialisation and syndrome measurement circuits that can detect any single-qubit error. It provides a universal set of local and global logical rotations that have physical support on only two qubits. A high-fidelity -- though non fault-tolerant -- compilation of this universal gate set is possible thanks to the two-qubit physical rotations present in trapped-ion computers with all-to-all connectivity. Given the particular structure of the logical operators, we nickname it the Iceberg code. We demonstrate the protection of circuits of 8 logical qubits with up to 256 layers, saturate the logical quantum volume of $2^8$, and show the positive effect of increasing the frequency of syndrome measurements within the circuit. These results illustrate the practical usefulness of the Iceberg code to protect expressive circuits on existing trapped-ion quantum computers.

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arXiv2022

Exploring the neighborhood of 1-layer QAOA with Instantaneous Quantum Polynomial circuits

We embed 1-layer QAOA circuits into the larger class of parameterized Instantaneous Quantum Polynomial circuits to produce an improved variational quantum algorithm for solving combinatorial optimization problems. The use of analytic expressions to find optimal parameters classically makes our protocol robust against barren plateaus and hardware noise. The average overlap with the ground state scales as $\mathcal{O}(2^{-0.31 N})$ with the number of qubits $N$ for random Sherrington-Kirkpatrick (SK) Hamiltonians of up to 29 qubits, a polynomial improvement over 1-layer QAOA. Additionally, we observe that performing variational imaginary time evolution on the manifold approximates low-temperature pseudo-Boltzmann states. Our protocol outperforms 1-layer QAOA on the recently released Quantinuum H2 trapped-ion quantum hardware and emulator, where we obtain an average approximation ratio of $0.985$ across 312 random SK instances of 7 to 32 qubits, from which almost $44\%$ are solved optimally using 4 to 1208 shots per instance.

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arXiv2022

A case study of variational quantum algorithms for a job shop scheduling problem

Combinatorial optimization models a vast range of industrial processes aiming at improving their efficiency. In general, solving this type of problem exactly is computationally intractable. Therefore, practitioners rely on heuristic solution approaches. Variational quantum algorithms are optimization heuristics that can be demonstrated with available quantum hardware. In this case study, we apply four variational quantum heuristics running on IBM's superconducting quantum processors to the job shop scheduling problem. Our problem optimizes a steel manufacturing process. A comparison on 5 qubits shows that the recent filtering variational quantum eigensolver (F-VQE) converges faster and samples the global optimum more frequently than the quantum approximate optimization algorithm (QAOA), the standard variational quantum eigensolver (VQE), and variational quantum imaginary time evolution (VarQITE). Furthermore, F-VQE readily solves problem sizes of up to 23 qubits on hardware without error mitigation post processing.

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arXiv2022

Filtering variational quantum algorithms for combinatorial optimization

Current gate-based quantum computers have the potential to provide a computational advantage if algorithms use quantum hardware efficiently. To make combinatorial optimization more efficient, we introduce the Filtering Variational Quantum Eigensolver (F-VQE) which utilizes filtering operators to achieve faster and more reliable convergence to the optimal solution. Additionally we explore the use of causal cones to reduce the number of qubits required on a quantum computer. Using random weighted MaxCut problems, we numerically analyze our methods and show that they perform better than the original VQE algorithm and the Quantum Approximate Optimization Algorithm (QAOA). We also demonstrate the experimental feasibility of our algorithms on a Honeywell trapped-ion quantum processor.

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arXiv2020

Scalable characterization of localizable entanglement in noisy topological quantum codes

Topological quantum error correcting codes have emerged as leading candidates towards the goal of achieving large-scale fault-tolerant quantum computers. However, quantifying entanglement in these systems of large size in the presence of noise is a challenging task. In this paper, we provide two different prescriptions to characterize noisy stabilizer states, including the surface and the color codes, in terms of localizable entanglement over a subset of qubits. In one approach, we exploit appropriately constructed entanglement witness operators to estimate a witness-based lower bound of localizable entanglement, which is directly accessible in experiments. In the other recipe, we use graph states that are local unitary equivalent to the stabilizer state to determine a computable measurement-based lower bound of localizable entanglement. If used experimentally, this translates to a lower bound of localizable entanglement obtained from single-qubit measurements in specific bases to be performed on the qubits outside the subsystem of interest. Towards computing these lower bounds, we discuss in detail the methodology of obtaining a local unitary equivalent graph state from a stabilizer state, which includes a new and scalable geometric recipe as well as an algebraic method that applies to general stabilizer states of arbitrary size. Moreover, as a crucial step of the latter recipe, we develop a scalable graph-transformation algorithm that creates a link between two specific nodes in a graph using a sequence of local complementation operations. We develop open-source Python packages for these transformations, and illustrate the methodology by applying it to a noisy topological color code, and study how the witness and measurement-based lower bounds of localizable entanglement varies with the distance between the chosen qubits.

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arXiv2019

Design and Experimental Performance of Local Entanglement Witness Operators

Entanglement is a central concept in quantum information and a key resource for many quantum protocols. In this work we propose and analyze a class of entanglement witnesses that detect the presence of entanglement in subsystems of experimental multi-qubit stabilizer states. The witnesses we propose can be decomposed into sums of Pauli operators and can be efficiently evaluated by either two measurement settings only or at most a number of measurements that only depends on the size of the subsystem of interest. We provide two constructive methods to design the local witness operators, the first one based on the local unitary equivalence between graph and stabilizer states, and the second one based on sufficient and necessary conditions that the respective set of constituent Pauli operators needs to fulfill. We theoretically establish the noise tolerance of the proposed witnesses and benchmark their practical performance by analyzing the local entanglement structure of an experimental seven-qubit quantum error correction code.

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arXiv2019

Analytical percolation theory for topological color codes under qubit loss

Quantum information theory has shown strong connections with classical statistical physics. For example, quantum error correcting codes like the surface and the color code present a tolerance to qubit loss that is related to the classical percolation threshold of the lattices where the codes are defined. Here we explore such connection to study analytically the tolerance of the color code when the protocol introduced in [Phys. Rev. Lett. $\textbf{121}$, 060501 (2018)] to correct qubit losses is applied. This protocol is based on the removal of the lost qubit from the code, a neighboring qubit, and the lattice edges where these two qubits reside. We first obtain analytically the average fraction of edges $ r(p) $ that the protocol erases from the lattice to correct a fraction $ p $ of qubit losses. Then, the threshold $ p_c $ below which the logical information is protected corresponds to the value of $ p $ at which $ r(p) $ equals the bond-percolation threshold of the lattice. Moreover, we prove that the logical information is protected if and only if the set of lost qubits does not include the entire support of any logical operator. The results presented here open a route to an analytical understanding of the effects of qubit losses in topological quantum error codes.

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