arXiv subjects

J. Ignacio Cirac

Publications and source records attributed to J. Ignacio Cirac.

At least 37 records · Page 2Linked to original sources

arXiv2026

Quasi-Adiabatic Processing of Thermal States

We investigate the performance of an adiabatic evolution protocol when initialized from a Gibbs state at finite temperature. Specifically, we identify the diagonality of the final state in the energy eigenbasis, as well as the difference in energy and in energy variance with respect to the ideal adiabatic limit as key benchmarks for success and introduce metrics to quantify the off-diagonal contributions. Provided these benchmarks converge to their ideal adiabatic values, we argue that thermal expectation values of observables can be recovered, in accordance with the eigenstate thermalization hypothesis. For the transverse-field Ising model, we analytically establish that these benchmarks converge polynomially in both the quasi-adiabatic evolution time $T$ and system size. We perform numerical studies on non-integrable systems and find close quantitative agreement for the off-diagonality metrics, along with qualitatively similar behavior in the energy convergence.

quant-ph↗

arXiv2026

Compiling Quantum Regular Language States

State preparation compilers for quantum computers typically sit at two extremes: general-purpose routines that treat the target as an opaque amplitude vector, and bespoke constructions for a handful of well-known state families. We ask whether a compiler can instead accept simple, structure-aware specifications while providing predictable resource guarantees. We answer this by designing and implementing a quantum state-preparation compiler for regular language states (RLS): uniform superpositions over bitstrings accepted by a regular description, and their complements. Users describe the target state via (i) a finite set of bitstrings, (ii) a regular expression, or (iii) a deterministic finite automaton (DFA), optionally with a complement flag. By translating the input to a DFA, minimizing it, and mapping it to an optimal matrix product state (MPS), the compiler obtains an intermediate representation (IR) that exposes and compresses hidden structure. The efficient DFA representation and minimization offloads expensive linear algebra computation in exchange of simpler automata manipulations. The combination of the regular-language frontend and this IR gives concise specifications not only for RLS but also for their complements that might otherwise require exponentially large state descriptions. This enables state preparation of an RLS or its complement with the same asymptotic resources and compile time. We outline two hardware-aware backends: SeqRLSP, which yields linear-depth, ancilla-free circuits for linear nearest-neighbor architectures via sequential generation, and TreeRLSP, which achieves logarithmic depth on all-to-all connectivity via a tree tensor network. We prove depth and gate-count bounds scaling with the system size and the state's maximal Schmidt rank, and we give explicit compile-time bounds that expose the benefit of our approach. We implement and evaluate the pipeline.

quant-ph↗

arXiv2026

Efficient Characterization of Coherent and Correlated Low-Degree Noise in Layers of Gates

We present a quantum process-tomography protocol based on a low-degree ansatz for the quantum channel, i.e. when it can be expressed as a fixed-degree polynomial in terms of Pauli operators. We demonstrate how to perform tomography of such channels with a logarithmic amount of effort relative to the size of the system, by employing random state preparation and measurements in the Pauli basis. We extend the applicability of the protocol to channels consisting of a layer of quantum gates with a polylogarithmic number of non-Clifford gates, followed by a low-degree noise channel. Rather than inverting the layer of quantum gates on the hardware-which would introduce additional errors-we instead carry out the inversion in classical postprocessing, while adding to the sample complexity a factor at most polynomial in system size. Numerical simulations support our theoretical findings and demonstrate the feasibility of our method.

quant-ph↗

arXiv2026

Quantum Circuits for Matrix-Product Unitaries

Matrix-product unitaries (MPUs) are many-body unitary operators that, as a consequence of their tensor-network structure, preserve the entanglement area law in 1D systems. However, it is unknown how to implement an MPU as a quantum circuit since the individual tensors describing the MPU are not unitary. In this Letter, we show that a large class of MPUs can be implemented with a polynomial-depth quantum circuit. For an $N$-site MPU built from a repeated bulk tensor with open boundary, we explicitly construct a quantum circuit of polynomial depth $T = O(N^α)$ realizing the MPU, where the constant $α$ depends only on the bulk and boundary tensor and not the system size $N$. We show that this class includes nontrivial unitaries that generate long-range entanglement and, in particular, contains a large class of unitaries constructed from representations of $C^*$-weak Hopf algebras. Furthermore, we also adapt our construction to nonuniform translationally-varying MPUs and show that they can be implemented by a circuit of depth $O(N^β \, \mathrm{poly}\, D)$ where $β\le 1 + \log_2 \sqrt{D}/ s_{\min}$, with $D$ being the bond dimension and $s_{\min}$ the smallest nonzero Schmidt value of the normalized Choi state corresponding to the MPU.

quant-ph↗

arXiv2025

Uniform matrix product states with a boundary

Canonical forms are central to the analytical understanding of tensor network states, underpinning key results such as the complete classification of one-dimensional symmetry-protected topological phases within the matrix product state (MPS) framework. Yet, the established theory applies only to uniform MPS with periodic boundary conditions, leaving many physically relevant states beyond its reach. Here we introduce a generalized canonical form for uniform MPS with a boundary matrix, thus extending the analytical MPS framework to a more general setting of wider physical significance. This canonical form reveals that any such MPS can be represented as a block-invertible matrix product operator acting on a structured class of algebraic regular language states that capture its essential long-range and scale-invariant features. Our construction builds on new algebraic results of independent interest that characterize the span and algebra generated by non-semisimple sets of matrices, including a generalized quantum Wielandt's inequality that gives an explicit upper bound on the blocking length at which the fixed-length span stabilizes to an algebra. Together, these results establish a unified theoretical foundation for uniform MPS with boundaries, bridging the gap between periodic and arbitrary-boundary settings, and providing the basis for extending key analytical and classification results of matrix product states to a much broader class of states and operators.

quant-ph↗

arXiv2025

Estimating ground-state properties in quantum simulators with global control

Accurately determining ground-state properties of quantum many-body systems remains one of the major challenges of quantum simulation. In this work, we present a protocol for estimating the ground-state energy using only global time evolution under a target Hamiltonian. This avoids the need for controlled operations that are typically required in conventional quantum phase estimation and extends the algorithm applicability to analog simulators. Our method extracts energy differences from measurements of the Loschmidt echo over an initial ground-state approximation, combines them with direct energy measurements, and solves a set of equations to infer the individual eigenenergies. We benchmark this protocol on free-fermion systems, showing orders-of-magnitude precision gains over direct energy measurements on the initial state, with accuracy improving rapidly with initial-state fidelity and persisting for hundreds of modes. We further demonstrate applicability to the 2D Ising and Fermi-Hubbard models and show that the approach extends naturally to other observables such as order parameters. Finally, we analyze the effect of experimental imperfections and propose error-mitigation strategies. These results establish a practical route to compute physically relevant quantities with high precision using globally controlled quantum simulators.

quant-ph↗

arXiv2025

Parent Lindbladians for Matrix Product Density Operators

Understanding quantum phases of matter is a fundamental goal in physics. For pure states, the representatives of phases are the ground states of locally interacting Hamiltonians, which are also renormalization fixed points (RFPs). These RFP states are exactly described by tensor networks. Extending this framework to mixed states, matrix product density operators (MPDOs) which are RFPs are believed to encapsulate mixed-state phases of matter in one dimension, where non-trivial topological phases have already been shown to exist. However, to better motivate the physical relevance of those states, and in particular the physical relevance of the recently found non-trivial phases, it remains an open question whether such MPDO RFPs can be realized as steady states of local Lindbladians. In this work, we resolve this question by analytically constructing parent Lindbladians for MPDO RFPs. These Lindbladians are local, frustration-free, and exhibit minimal steady-state degeneracy. Interestingly, we find that parent Lindbladians possess a rich structure that distinguishes them from their Hamiltonian counterparts. In particular, we uncover an intriguing connection between the non-commutativity of the Lindbladian terms and the fact that the corresponding MPDO RFP belongs to a non-trivial phase.

quant-ph↗

arXiv2025

Dynamical complexity of non-Gaussian many-body systems with dissipation

We characterize the dynamical state of many-body bosonic and fermionic many-body models with inter-site Gaussian couplings, on-site non-Gaussian interactions and local dissipation comprising incoherent particle loss, particle gain, and dephasing. We first establish that, for fermionic systems, if the dephasing noise is larger than the non-Gaussian interactions, irrespective of the Gaussian coupling strength, the system state is a convex combination of Gaussian states at all times. Furthermore, for bosonic systems, we show that if the particle loss and particle gain rates are larger than the Gaussian inter-site couplings, the system remains in a separable state at all times. Building on this characterization, we establish that at noise rates above a threshold, there exists a classical algorithm that can efficiently sample from the system state of both the fermionic and bosonic models. Finally, we show that, unlike fermionic systems, bosonic systems can evolve into states that are not convex-Gaussian even when the dissipation is much higher than the on-site non-Gaussianity. Similarly, unlike bosonic systems, fermionic systems can generate entanglement even with noise rates much larger than the inter-site couplings.

quant-ph↗

arXiv2025

Optical lattice quantum simulator of dynamics beyond Born-Oppenheimer

Here, we propose a platform based on ultra-cold fermionic molecules trapped in optical lattices to simulate nonadiabatic effects, as they appear in certain molecular dynamical problems. The idea consists of a judicious choice of two rotational states as the simulated electronic or nuclear degrees of freedom, in which their dipolar interactions induce the required attractive or repulsive interactions between them. We benchmark our proposal by studying the scattering of an electron or a proton against a hydrogen atom, showing the effect of electronic exchange and inelastic ionization as the mass ratio between the simulated nuclei and electrons -- a tunable experimental parameter in our simulator -- becomes comparable. These benchmarks illustrate how the simulator can qualitatively emulate phenomena like those appearing in molecular dynamical problems even if the simulated interaction occurs in two-dimensions with a dipolar scaling. Beyond the molecular implementation proposed here, our proposal can be readily extrapolated to other atomic platforms, e.g., based on fermionic Rydberg atoms.

cond-mat.quant-gas↗

arXiv2025

Noise robustness of problem-to-simulator mappings for quantum many-body physics

Simulating quantum dynamics on digital or analog quantum simulators often requires ``problem-to-simulator" mappings such as trotterization, floquet-magnus expansion or perturbative expansions. When the simulator is noiseless, it is well understood that these problem-to-simulator mappings can be made as accurate as desired at the expense of simulator run-time. However, precisely because the simulator has to be run for a longer time to increase its accuracy, it is expected that noise in the quantum simulator catastrophically effects the simulator output. We show that, contrary to this expectation, these mappings remain stable to noise when considering the task of simulating dynamics of local observables in quantum lattice models. Specifically, we prove that in all of these mappings, local observables can be determined to a system-size independent, precision that scales sublinearly with the noise-rate in the simulator. Our results provide theoretical evidence that quantum simulators can be used for solving problems in many-body physics without or with modest error correction.

quant-ph↗

arXiv2025

Hardware-efficient quantum phase estimation via local control

Quantum phase estimation plays a central role in quantum simulation as it enables the study of spectral properties of many-body quantum systems. Most variants of the phase estimation algorithm require the application of the global unitary evolution conditioned on the state of one or more auxiliary qubits, posing a significant challenge for current quantum devices. In this work, we present an approach to quantum phase estimation that uses only locally controlled operations, resulting in a significantly reduced circuit depth. At the heart of our approach are efficient routines to measure the complex phase of the expectation value of the time-evolution operator, the so-called Loschmidt echo, for both circuit dynamics and Hamiltonian dynamics. By tracking changes in the phase during the dynamics, the routines trade circuit depth for an increased sampling cost and classical postprocessing. Our approach does not rely on reference states and is applicable to any efficiently preparable state, regardless of its correlations. We provide a comprehensive analysis of the sample complexity and illustrate the results with numerical simulations. Our methods offer a practical pathway for measuring spectral properties in large many-body quantum systems using current quantum devices.

quant-ph↗

arXiv2025

Optimizing digital quantum simulation of open quantum lattice models

Many-body systems arising in condensed matter physics and quantum optics inevitably couple to the environment and need to be modelled as open quantum systems. While near-optimal algorithms have been developed for simulating many-body quantum dynamics, algorithms for their open system counterparts remain less well investigated. We address the problem of simulating geometrically local many-body open quantum systems interacting with a stationary Gaussian environment. Under a smoothness assumption on the system-environment interaction, we develop near-optimal algorithms that, for a model with $N$ spins and evolution time $t$, attain a simulation error $δ$ in the system-state with $\mathcal{O}(Nt(Nt/δ)^{o(1)})$ gates, $\mathcal{O}(t(Nt/δ)^{o(1)})$ parallelized circuit depth and $\tilde{\mathcal{O}}(N(Nt/δ)^{o(1)})$ ancillas. We additionally show that, if only simulating local observables is of interest, then the circuit depth of the digital algorithm can be chosen to be independent of the system size $N$. This provides theoretical evidence for the utility of these algorithms for simulating physically relevant models, where typically local observables are of interest, on pre-fault tolerant devices. Finally, for the limiting case of Markovian dynamics with commuting jump operators, we propose two algorithms based on sampling a Wiener process and on a locally dilated Hamiltonian construction, respectively. These algorithms reduce the asymptotic gate complexity on $N$ compared to currently available algorithms in terms of the required number of geometrically local gates.

quant-ph↗

arXiv2025

Matrix product states as thin torus limits of conformal correlators

We introduce one-parameter families of spin chain ansatz wavefunctions constructed from chiral conformal field theory correlators on a torus, with the modular parameter $τ$ serving as the deformation parameter. In the cylinder limit $τ\to\infty$, these wavefunctions reduce to infinite dimensional matrix product states. In contrast, in the thin torus limit $τ\to0$, they become finite bond dimension matrix product states (MPS). Focusing on families derived from the SU(2)$_1$ and SU(2)$_2$ Wess-Zumino-Witten models, we show that in the thin torus limit they reproduce known MPS ground states, such as those of the Majumdar-Ghosh and AKLT spin chains.

quant-ph↗

arXiv2025

Quantum algorithms for cooling: a simple case study

Preparation of low-energy quantum many-body states has a wide range of applications in quantum information processing and condensed matter physics. Quantum cooling algorithms offer a promising alternative to other methods based, for instance, on variational and adiabatic principles, or on dissipative state preparation. In this work, we investigate a set of cooling algorithms in a simple, solvable fermionic model which allows us to identify the mechanisms which underlie the cooling process and, also, those which prevent it. We derive analytical expressions for the cooling dynamics, steady states, and cooling rates in the weak coupling limit. We find that multi-frequency and randomized cycle strategies can significantly enhance the performance of the quantum algorithm and circumvent some of the obstacles. We also analyze the effects of noise and evaluate the conditions under which cooling remains feasible. Furthermore, we present optimized cooling protocols that can significantly enhance cooling performance in the presence of noise. Additionally, we compare cooling and dissipative state preparation and show that, in the model analyzed here, cooling generally achieves lower energies and is more resilient to noise.

quant-ph↗

arXiv2025

Learning mixed quantum states in large-scale experiments

We present and test a protocol to learn the matrix-product operator (MPO) representation of an experimentally prepared quantum state. The protocol takes as an input classical shadows corresponding to local randomized measurements, and outputs the tensors of a MPO which maximizes a suitably-defined fidelity with the experimental state. The tensor optimization is carried out sequentially, similarly to the well-known density matrix renormalization group algorithm. Our approach is provably efficient under certain technical conditions which are expected to be met in short-range correlated states and in typical noisy experimental settings. Under the same conditions, we also provide an efficient scheme to estimate fidelities between the learned and the experimental states. We experimentally demonstrate our protocol by learning entangled quantum states of up to $N = 96$ qubits in a superconducting quantum processor. Our method upgrades classical shadows to large-scale quantum computation and simulation experiments.

quant-ph↗

arXiv2025

Efficient tensor network simulation of multi-emitter non-Markovian systems

We present a numerical method to simulate a system of multiple emitters coupled to a non-interacting bath, in any parameter regime. Our method relies on a Block Lanczos transformation that maps the whole system onto a strip geometry, whose width is given by the number of emitters. Utilizing the spatial symmetries of the problem and identifying the relevant range of energies of the bath we achieve a more efficient simulation, which we perform using tensor network techniques. As a demonstration, we study the collective emission from multiple emitters coupled to a square lattice of bosons and observe how the departure from Markovianity as coupling strength and emitter number is increased prevents collective radiation. We also simulate the dynamic preparation of an excitation in a bound state from a multi-excitation initial state. Our work opens new possibilities for the systematic exploration of non-Markovian effects in the dynamics and equilibrium properties of multi-emitter systems. Furthermore, it can easily be extended to other setups, including finite bath temperature or impurities coupled to fermionic environments.

quant-ph↗

arXiv2025

Quantum Simulation of Dynamical Response Functions of Equilibrium States

The computation of dynamical response functions is central to many problems in condensed matter physics. Owing to the rapid growth of quantum correlations following a quench, classical methods face significant challenges even if an efficient description of the equilibrium state is available. Quantum computing offers a promising alternative. However, existing approaches often assume access to the equilibrium state, which may be difficult to prepare in practice. In this work, we present a method that circumvents this by using energy filter techniques, enabling the computation of response functions and other dynamical properties in both microcanonical and canonical ensembles. Our approach only requires the preparation of states that have significant weight at the desired energy. The dynamical response functions are then reconstructed from measurements after quenches of varying duration by classical postprocessing. We illustrate the algorithm numerically by applying it to compute the dynamical conductivity of a free-fermion model, which unveils the energy-dependent localization properties of the model.

quant-ph↗

arXiv2025

Effects of retardation on many-body superradiance in chiral waveguide QED

We study the superradiant decay of a chain of atoms coupled to a chiral waveguide, focusing on the regime of non-negligible photon propagation time. Using an exact master equation description which accounts for delay effects, we obtain evidence to suggest that competition between collective decay and retardation leads to the emergence of an effective maximum number of atoms able to contribute to the superradiant dynamics, resulting in a plateau of the peak emission rate. To develop this analysis further, we investigate the inter-atomic correlations to find features consistent with the formation of individual superradiant domains. Moreover, we find that retardation can also result in persistent oscillatory atomic dynamics accompanied by a periodic sequence of emission bursts.

quant-ph↗