arXiv subjects

Alessandro Ciani

Publications and source records attributed to Alessandro Ciani.

At least 19 recordsLinked to original sources

arXiv2026

Analytical Series Expansion for Efficient Gradient Evaluation in Multi-Qubit Optimal Control

The open-loop optimization of quantum dynamics using gradient-based quantum optimal control methods involves calculating the time-ordered propagator and its gradient. In this Letter, we present a unifying framework for gradient-based quantum optimal control with respect to any general pulse parameterization by deriving the formal solution from first principles. For the case of unitary propagators, we derive a series expansion involving time-independent commutators and time-dependent coefficients, significantly reducing the number of matrix exponentials needed to compute the gradient. The expansion highlights the connection between derivatives of the propagator and operator evolution in the Heisenberg picture. The method is particularly suited for simulating optimal control tasks in quantum systems with local interactions, which is a common situation in large multi-qubit platforms. We compare the computational cost required for the series with the Gradient Optimization of Analytic conTrols (GOAT) method, and, focusing on the problem of preparation of a GHZ state, demonstrate more than an order of magnitude speedup for a qubit ladder and a chain geometry.

quant-ph↗

arXiv2026

Quantum Simulation of Strongly Correlated Fermion-Phonon Models in Circuit QED

Gate-based digital quantum simulations offer an exciting new paradigm for studying the many-body physics of strongly correlated systems. In this context, electron-phonon models are challenging for qubit-only quantum simulators, as bosonic degrees of freedom require costly finite-dimensional encodings. Here, we elaborate on an alternative approach based on a digital-analog circuit QED architecture, where fermions are encoded in transmon qubits while bosons are represented directly by microwave resonators. The central building block of this framework is a qubit-resonator Rabi gate that emulates strong electron-phonon coupling and can be implemented through a sequence of resonant Jaynes-Cummings gates interleaved with layers of single-qubit rotations. Using this Rabi gate as the fundamental unitary operation, we construct quantum circuits for the Hubbard-Holstein and Yukawa-Sachdev-Ye-Kitaev models, which describe, respectively, strongly correlated electrons coupled to phonons and phonon-mediated interactions among Majorana fermions. We further demonstrate how nonclassical phonon physics and signatures of quantum chaos in these models can be probed through circuit simulations, and develop measurement and variational protocols tailored to near-term superconducting quantum hardware.

quant-ph↗

arXiv2025

Quantum oracles for the finite element method

In order to assess potential advantages of quantum algorithms that require quantum oracles as subroutines, the careful evaluation of the overall complexity of the oracles themselves is crucial. This study examines the quantum routines required for the implementation of oracles used in the block-encoding of the $N \times N$ stiffness and mass matrices, which typically emerge in the finite element analysis of elastic structures. Starting from basic quantum adders, we show how to construct the necessary oracles, which require the calculation of polynomials, square root and the implementation of conditional operations. We propose quantum subroutines based on fixed-point arithmetic that, given an $r$-qubit register, construct the oracle using $\mathcal{O}((K + L + N_{\mathrm{geo}} + N_{\mathrm{D}}) r)$ ancilla qubits and have a $\mathcal{O}((K + L)r^2 + \log_2(N_{\mathrm{geo}} + N_{\mathrm{D}}))$ runtime, with $K$ the order at which we truncate the polynomials, $L$ the number of iterations in the Newton-Raphson subroutine for the square root, while $N_{\mathrm{geo}}$ and $N_{\mathrm{D}}$ are the number of hypercuboids used to approximate the geometry and the boundary, respectively. Since in practice $r$ scales as $r = \mathcal{O}(\log_2 N)$, and assuming that the other parameters are fixed independently of $N$, this shows that the oracles, while still costly in practice, do not endanger potential polynomial or exponential advantages in $N$.

quant-ph↗

arXiv2025

Bridging wire and gate cutting with ZX-calculus

Quantum circuit cutting refers to a series of techniques that allow one to partition a quantum computation on a large quantum computer into several quantum computations on smaller devices. This usually comes at the price of a sampling overhead, that is quantified by the $1$-norm of the associated decomposition. The applicability of these techniques relies on the possibility of finding decompositions of the ideal, global unitaries into quantum operations that can be simulated onto each sub-register, which should ideally minimize the $1$-norm. In this work, we show how these decompositions can be obtained diagrammatically using ZX-calculus expanding on the work of Ufrecht et al. [arXiv:2302.00387]. The central idea of our work is that since in ZX-calculus only connectivity matters, it should be possible to cut wires in ZX-diagrams by inserting known decompositions of the identity in standard quantum circuits. We show how, using this basic idea, many of the gate decompositions known in the literature can be re-interpreted as an instance of wire cuts in ZX-diagrams. Furthermore, we obtain improved decompositions for multi-qubit controlled-Z (MCZ) gates with $1$-norm equal to $3$ for any number of qubits and any partition, which we argue to be optimal. Our work gives new ways of thinking about circuit cutting that can be particularly valuable for finding decompositions of large unitary gates. Besides, it sheds light on the question of why exploiting classical communication decreases the 1-norm of a wire cut but does not do so for certain gate decompositions. In particular, using wire cuts with classical communication, we obtain gate decompositions that do not require classical communication.

quant-ph↗

arXiv2024

Non-Markovian Ensemble Propagation

Open quantum systems are ubiquitous in nature and central to quantum technologies. A common description of their dynamics is given by the celebrated Lindblad master equation, which can be generalized to the non-Markovian scenario. In this work, we introduce the Non-Markovian Ensemble Propagation (NMEP) method, which extends the Monte Carlo Wave-Function (MCWF) method to the non-Markovian case in a simple and general manner. We demonstrate its accuracy and effectiveness in a selection of examples, and compare the results with either analytic expressions or direct numerical integration of the master equation.

quant-ph↗

arXiv2024

A methodical approach to evaluate the potential of Quantum Computing for Manufacturing Simulations

In this paper, a methodical approach to evaluate the potential of quantum computing for manufacturing simulation, using the example of multi-axis milling of thin-walled aerospace components, is discussed. A developed approach for identifying bottlenecks in manufacturing simulations, for which the application of quantum computing potentially provides a speed-up or increase in accuracy, is presented. Moreover, indicators of quantum computing suitability and feasibility are defined with the main objective of identifying whether a manufacturing simulation bottleneck is suitable for quantum computing applications. First results of testing a hybrid routine as an application approach for the milling dynamics simulation on quantum machines are presented.

quant-ph↗

arXiv2024

Calculating response functions of coupled oscillators using quantum phase estimation

We study the problem of estimating frequency response functions of systems of coupled, classical harmonic oscillators using a quantum computer. The functional form of these response functions can be mapped to a corresponding eigenproblem of a Hermitian matrix $H$, thus suggesting the use of quantum phase estimation. Our proposed quantum algorithm operates in the standard $s$-sparse, oracle-based query access model. For a network of $N$ oscillators with maximum norm $\lVert H \rVert_{\mathrm{max}}$, and when the eigenvalue tolerance $\varepsilon$ is much smaller than the minimum eigenvalue gap, we use $\mathcal{O}(\log(N s \lVert H \rVert_{\mathrm{max}}/\varepsilon)$ algorithmic qubits and obtain a rigorous worst-case query complexity upper bound $\mathcal{O}(s \lVert H \rVert_{\mathrm{max}}/(\delta^2 \varepsilon) )$ up to logarithmic factors, where $\delta$ denotes the desired precision on the coefficients appearing in the response functions. Crucially, our proposal does not suffer from the infamous state preparation bottleneck and can as such potentially achieve large quantum speedups compared to relevant classical methods. As a proof-of-principle of exponential quantum speedup, we show that a simple adaptation of our algorithm solves the random glued-trees problem in polynomial time. We discuss practical limitations as well as potential improvements for quantifying finite size, end-to-end complexities for application to relevant instances.

quant-ph↗

arXiv2024

Quantum Computing Enhanced Service Ecosystem for Simulation in Manufacturing

Quantum computing (QC) and machine learning (ML), taken individually or combined into quantum-assisted ML (QML), are ascending computing paradigms whose calculations come with huge potential for speedup, increase in precision, and resource reductions. Likely improvements for numerical simulations in engineering imply the possibility of a strong economic impact on the manufacturing industry. In this project report, we propose a framework for a quantum computing-enhanced service ecosystem for simulation in manufacturing, consisting of various layers ranging from hardware to algorithms to service and organizational layers. In addition, we give insight into the current state of the art of applications research based on QC and QML, both from a scientific and an industrial point of view. We further analyse two high-value use cases with the aim of a quantitative evaluation of these new computing paradigms for industrially-relevant settings.

quant-ph↗

arXiv2023

Lecture Notes on Quantum Electrical Circuits

During the last 30 years, stimulated by the quest to build superconducting quantum processors, a theory of quantum electrical circuits has emerged and this theory goes under the name of circuit quantum electrodynamics or circuit-QED. The goal of the theory is to provide a quantum description of the most relevant degrees of freedom. The central objects to be derived and studied are the Lagrangian and the Hamiltonian governing these degrees of freedom. Central concepts in classical network theory such as impedance and scattering matrices can be used to obtain the Hamiltonian and Lagrangian description for the lossless (linear) part of the circuits. Methods of analysis, both classical and quantum, can also be developed for nonreciprocal circuits. These lecture notes aim at giving a pedagogical overview of this subject for theoretically-oriented Master or PhD students in physics and electrical engineering, as well as Master and PhD students who work on experimental superconducting quantum devices and wish to learn more theory.

quant-ph↗

arXiv2023

Emergence of noise-induced barren plateaus in arbitrary layered noise models

In variational quantum algorithms the parameters of a parameterized quantum circuit are optimized in order to minimize a cost function that encodes the solution of the problem. The barren plateau phenomenon manifests as an exponentially vanishing dependence of the cost function with respect to the variational parameters, and thus hampers the optimization process. We discuss how, and in which sense, the phenomenon of noise-induced barren plateaus emerges in parameterized quantum circuits with a layered noise model. Previous results have shown the existence of noise-induced barren plateaus in the presence of local Pauli noise [arXiv:2007.14384]. We extend these results analytically to arbitrary completely-positive trace preserving maps in two cases: 1) when a parameter-shift rule holds, 2) when the parameterized quantum circuit at each layer forms a unitary $2$-design. The second example shows how highly expressive unitaries give rise not only to standard barren plateaus [arXiv:1803.11173], but also to noise-induced ones. In the second part of the paper, we study numerically the emergence of noise-induced barren plateaus in QAOA circuits focusing on the case of MaxCut problems on $d$-regular graphs and amplitude damping noise.

quant-ph↗

arXiv2023

Homological Quantum Rotor Codes: Logical Qubits from Torsion

We formally define homological quantum rotor codes which use multiple quantum rotors to encode logical information. These codes generalize homological or CSS quantum codes for qubits or qudits, as well as linear oscillator codes which encode logical oscillators. Unlike for qubits or oscillators, homological quantum rotor codes allow one to encode both logical rotors and logical qudits in the same block of code, depending on the homology of the underlying chain complex. In particular, a code based on the chain complex obtained from tessellating the real projective plane or a M\"{o}bius strip encodes a qubit. We discuss the distance scaling for such codes which can be more subtle than in the qubit case due to the concept of logical operator spreading by continuous stabilizer phase-shifts. We give constructions of homological quantum rotor codes based on 2D and 3D manifolds as well as products of chain complexes. Superconducting devices being composed of islands with integer Cooper pair charges could form a natural hardware platform for realizing these codes: we show that the $0$-$\pi$-qubit as well as Kitaev's current-mirror qubit -- also known as the M\"{o}bius strip qubit -- are indeed small examples of such codes and discuss possible extensions.

quant-ph↗

arXiv2022

Microwave-activated gates between a fluxonium and a transmon qubit

We propose and analyze two types of microwave-activated gates between a fluxonium and a transmon qubit, namely a cross-resonance (CR) and a CPHASE gate. The large frequency difference between a transmon and a fluxonium makes the realization of a two-qubit gate challenging. For a medium-frequency fluxonium qubit, the transmon-fluxonium system allows for a cross-resonance effect mediated by the higher levels of the fluxonium over a wide range of transmon frequencies. This allows one to realize the cross-resonance gate by driving the fluxonium at the transmon frequency, mitigating typical problems of the cross-resonance gate in transmon-transmon chips related to frequency targeting and residual ZZ coupling. However, when the fundamental frequency of the fluxonium enters the low-frequency regime below 100 MHz, the cross-resonance effect decreases leading to long gate times. For this range of parameters, a fast microwave CPHASE gate can be implemented using the higher levels of the fluxonium. In both cases, we perform numerical simulations of the gate showing that a gate fidelity above 99% can be obtained with gate times between 100 and 300 ns. Next to a detailed gate analysis, we perform a study of chip yield for a surface code lattice of fluxonia and transmons interacting via the proposed cross-resonance gate. We find a much better yield as compared to a transmon-only architecture with the cross-resonance gate as native two-qubit gate.

quant-ph↗

arXiv2021

Error mitigation and quantum-assisted simulation in the error corrected regime

A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations to a universal set by the addition of `magic' quantum states. In this context, we develop a general framework to discuss the value of the available, non-ideal magic resources, relative to those ideally required. We single out a quantity, the Quantum-assisted Robustness of Magic (QRoM), which measures the overhead of simulating the ideal resource with the non-ideal ones through quasiprobability-based methods. This extends error mitigation techniques, originally developed for Noisy Intermediate Scale Quantum (NISQ) devices, to the case where qubits are logically encoded. The QRoM shows how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit and enables the construction of explicit protocols, interpolating between classical simulation and an ideal quantum computer.

quant-ph↗

arXiv2020

Stoquasticity in circuit QED

We analyze whether circuit-QED Hamiltonians are stoquastic focusing on systems of coupled flux qubits: we show that scalable sign-problem free path integral Monte Carlo simulations can typically be performed for such systems. Despite this, we corroborate the recent finding [arXiv:1903.06139] that an effective, non-stoquastic qubit Hamiltonian can emerge in a system of capacitively coupled flux qubits. We find that if the capacitive coupling is sufficiently small, this non-stoquasticity of the effective qubit Hamiltonian can be avoided if we perform a canonical transformation prior to projecting onto an effective qubit Hamiltonian. Our results shed light on the power of circuit-QED Hamiltonians for the use of quantum adiabatic computation and the subtlety of finding a representation which cures the sign problem in these systems

quant-ph↗

arXiv2020

Hardware-Encoding Grid States in a Non-Reciprocal Superconducting Circuit

We present a circuit design composed of a non-reciprocal device and Josephson junctions whose ground space is doubly degenerate and the ground states are approximate codewords of the Gottesman-Kitaev-Preskill (GKP) code. We determine the low-energy dynamics of the circuit by working out the equivalence of this system to the problem of a single electron confined in a two-dimensional plane and under the effect of strong magnetic field and of a periodic potential. We find that the circuit is naturally protected against the common noise channels in superconducting circuits, such as charge and flux noise, implying that it can be used for passive quantum error correction. We also propose realistic design parameters for an experimental realization and we describe possible protocols to perform logical one- and two-qubit gates, state preparation and readout.

quant-ph↗

arXiv2018

Hamiltonian quantum computing with superconducting qubits

We consider how the Hamiltonian Quantum Computing scheme introduced in [arXiv:1509.01278] can be implemented using a 2D array of superconducting transmon qubits. We show how the scheme requires the engineering of strong attractive cross-Kerr and weak flip-flop or hopping interactions and we detail how this can be achieved. Our proposal uses a new electric circuit for obtaining the attractive cross-Kerr coupling between transmons via a dipole-like element. We discuss and numerically analyze the forward motion and execution of the computation and its dependence on coupling strengths and their variability. We extend [arXiv:1509.01278] by explicitly showing how to construct a direct Toffoli gate, thus establishing computational universality via the Hadamard and Toffoli gate or via controlled-Hadamard, Hadamard and CNOT.

quant-ph↗

arXiv2018

Equation of motion approach to black-box quantization: taming the multi-mode Jaynes-Cummings model

An accurate modeling of a Josephson junction that is embedded in an arbitrary environment is of crucial importance for qubit design. We present a formalism to obtain a Lindblad master equation that describes the evolution of the system. As the qubit degrees of freedom oscillate with a well-defined frequency $\omega_q$, the environment only has to be modeled close to this frequency. Different from alternative approaches, we show that this goal can be achieved by modeling the environment with only few degrees of freedom. We treat the example of a transmon qubit coupled to a stripline resonator. We derive the parameters of a dissipative single-mode Jaynes-Cummings model starting from first principles. We show that the leading contribution of the off-resonant modes is a correlated decay process involving both the qubit and the resonator mode. In particular, our results show that the effect of the off-resonant modes in the multi-mode Jaynes-Cummings model is perturbative in $1/ \omega_q$.

cond-mat.mes-hall↗

arXiv2017

Three-qubit direct dispersive parity measurement with Tunable Coupling Qubits

We consider the direct three-qubit parity measurement scheme with two measurement resonators, using circuit quantum electrodynamics to analyze its functioning for several different types of superconducting qubits. We find that for the most common, transmon-like qubit, the presence of additional qubit-state dependent coupling terms of the two resonators hinders the possibility of performing the direct parity measurement. We show how this problem can be solved by employing the Tunable Coupling Qubit (TCQ) in a particular designed configuration. In this case, we effectively engineer the original model Hamiltonian by cancelling the harmful terms. We further develop an analysis of the measurement in terms of information gains and provide some estimates of the typical parameters for optimal operation with TCQs.

quant-ph↗