arXiv subjects

Marek Gluza

Publications and source records attributed to Marek Gluza.

At least 19 recordsLinked to original sources

arXiv2025

High-fidelity regimes of resonator-mediated controlled-Z gates between quantum-dot qubits

Semiconductor double quantum dot (DQD) qubits coupled via superconducting microwave resonators provide a powerful means of long-range manipulation of the qubits' spin and charge degrees of freedom. Quantum gates can be implemented by parametrically driving the qubits while their transition frequencies are detuned from the resonator frequency. Long-range two-qubit controlled-Z (CZ) gates have been proposed for the DQD spin qubit within the rotating-wave approximation (RWA). Rapid gates demand strong coupling, but RWA breaks down when coupling strengths become significant relative to system frequencies. Therefore, understanding the errors arising from approximations used is critical for high-fidelity operation. Here, we go beyond RWA to study CZ gate fidelity for both DQD spin and charge qubits. We propose a novel parametric drive on the charge qubit that produces smaller errors and show that the fidelity of the CZ gate outperforms its spin counterpart, resulting in a much smaller fidelity loss of $0.05\%$ compared to $0.80\%$ for the spin qubit, and greater robustness against qubit dephasing and photon loss. We find that drive amplitude -- a parameter dropped in RWA -- is critical for optimizing fidelity, with the charge qubit exhibiting better tolerance to drive amplitude variations. Our results demonstrate the necessity of going beyond RWA in understanding how long-range gates can be realized in DQD qubits, with charge qubits offering considerable advantages in high-fidelity operation.

cond-mat.mes-hall↗

arXiv2025

Double-Bracket Algorithmic Cooling

Algorithmic cooling shows that it is possible to locally reduce the entropy of a qubit belonging to an isolated ensemble such as nuclear spins in molecules or nitrogen-vacancy centers in diamonds. In the same physical setting, we introduce double-bracket algorithmic cooling (DBAC), a protocol that systematically suppresses quantum coherence of pure states. DBAC achieves this by simulating quantum imaginary-time evolution through recursive unitary synthesis of Riemannian steepest-descent flows and it utilizes density-matrix exponentiation as a subroutine. This subroutine makes DBAC a concrete instance of a dynamic quantum algorithm that operates using quantum information stored in copies of the input states. Thus, the circuits of DBAC are independent of the input state, enabling the extension of algorithmic cooling from targeting entropy to quantum coherence without resorting to measurements. Akin to Nernst principle, DBAC increases the cooling performance when including more input qubits which serve as quantum instructions. Our work demonstrates that dynamic quantum algorithms are a promising route toward new protocols for foundational tasks in quantum thermodynamics.

quant-ph↗

arXiv2025

Extensive entanglement between coupled Tomonaga-Luttinger liquids in and out of equilibrium

Quantum entanglement exists in nature but is absent in classical physics, hence it fundamentally distinguishes quantum from classical theories. While entanglement is routinely observed for few-body systems, it is significantly more challenging to witness in quantum many-body systems. Here, we theoretically study entanglement between two parallel and spatially separated Tomonaga-Luttinger liquids (TLLs) partitioned along the longitudinal axis. In particular, we focus on 1D Bose gases as a realization of TLLs and investigate two experimentally relevant situations: tunnel-coupled gases at finite temperatures and after coherent splitting. In both scenarios, we analytically calculate the logarithmic negativity and identify a threshold temperature below which the system is entangled. Notably, this threshold temperature is accessible in the current and near-term 1D Bose gas experiments. Furthermore, we investigate the crossover between quantum and classical correlations in the vicinity of the threshold temperature by comparing logarithmic negativity with mutual information. We argue that the initial mutual information established by the coherent splitting is conserved in TLL dynamics, thus preventing certain generalized Gibbs ensembles from being reached during prethermalization. Moreover, both logarithmic negativity and mutual information are found to scale extensively with the subsystem's length. Although the ground-state entanglement between coupled TLLs has been predicted to be extensive, this setting is largely overlooked compared to other partitions. Our work extends the study of entanglement between coupled TLLs to finite temperatures and out-of-equilibrium regimes, and provides a strategy towards experimental detection of extensive entanglement in quantum many-body systems at finite temperatures.

cond-mat.quant-gas↗

arXiv2025

Grover's algorithm is an approximation of imaginary-time evolution

We reveal the power of Grover's algorithm from thermodynamic and geometric perspectives by showing that it is a product formula approximation of imaginary-time evolution (ITE), a Riemannian gradient flow on the special unitary group. This ITE formulation provides a unified perspective on Grover's algorithm, its variants and extensions to widely used quantum subroutines including amplitude amplification and oblivious amplitude amplification. Specifically, the framework explains the choice of angles in the original Grover's algorithm and $\pi/3$-algorithm. It also motivates a new $\pi/2$-algorithm, for cases a modest failure probability is acceptable, that converges faster than the $\pi/3$-algorithm without overshooting. Our analysis further provides a link between ITE and quantum signal processing, which yields a new implementation of the fixed-point quantum search algorithm. Moreover, the ITE formulation can systematically reproduce widely-used subroutines in modern quantum algorithms, such as (oblivious) amplitude amplification. These results collectively establish a deeper understanding of Grover's algorithm and suggest a potential role for thermodynamics and geometry in quantum algorithm design.

quant-ph↗

arXiv2025

Role of Riemannian geometry in double-bracket quantum imaginary-time evolution

Double-bracket quantum imaginary-time evolution (DB-QITE) is a quantum algorithm which coherently implements steps in the Riemannian steepest-descent direction for the energy cost function. DB-QITE is derived from Brockett's double-bracket flow which exhibits saddle points where gradients vanish. In this work, we perform numerical simulations of DB-QITE and describe signatures of transitioning through the vicinity of such saddle points. We provide an explicit gate count analysis using quantum compilation programmed in Qrisp.

quant-ph↗

arXiv2025

Double-bracket algorithm for quantum signal processing without post-selection

Quantum signal processing (QSP), a framework for implementing matrix-valued polynomials, is a fundamental primitive in various quantum algorithms. Despite its versatility, a potentially underappreciated challenge is that all systematic protocols for implementing QSP rely on post-selection. This can impose prohibitive costs for tasks when amplitude amplification cannot sufficiently improve the success probability. For example, in the context of ground-state preparation, this occurs when using a too poor initial state. In this work, we introduce a new formula for implementing QSP transformations of Hermitian matrices, which requires neither auxiliary qubits nor post-selection. Rather, using approximation to the exact unitary synthesis, we leverage the theory of the double-bracket quantum algorithms to provide a new quantum algorithm for QSP, termed Double-Bracket QSP (DB-QSP). The algorithm requires the energy and energetic variance of the state to be measured at each step and has a recursive structure, which leads to circuit depths that can grow super exponentially with the degree of the polynomial. With these strengths and caveats in mind, DB-QSP should be viewed as complementing the established QSP toolkit. In particular, DB-QSP can deterministically implement low-degree polynomials to "warm start" QSP methods involving post-selection.

quant-ph↗

arXiv2024

Double-bracket quantum algorithms for quantum imaginary-time evolution

Efficiently preparing approximate ground-states of large, strongly correlated systems on quantum hardware is challenging and yet nature is innately adept at this. This has motivated the study of thermodynamically inspired approaches to ground-state preparation that aim to replicate cooling processes via imaginary-time evolution. However, synthesizing quantum circuits that efficiently implement imaginary-time evolution is itself difficult, with prior proposals generally adopting heuristic variational approaches or using deep block encodings. Here, we use the insight that quantum imaginary-time evolution is a solution of Brockett's double-bracket flow and synthesize circuits that implement double-bracket flows coherently on the quantum computer. We prove that our Double-Bracket Quantum Imaginary-Time Evolution (DB-QITE) algorithm inherits the cooling guarantees of imaginary-time evolution. Concretely, each step is guaranteed to i) decrease the energy of an initial approximate ground-state by an amount proportion to the energy fluctuations of the initial state and ii) increase the fidelity with the ground-state. We provide gate counts for DB-QITE through numerical simulations in Qrisp which demonstrate scenarios where DB-QITE outperforms quantum phase estimation. Thus DB-QITE provides a means to systematically improve the approximation of a ground-state using shallow circuits.

quant-ph↗

arXiv2024

Strategies for optimizing double-bracket quantum algorithms

Recently double-bracket quantum algorithms have been proposed as a way to compile circuits for approximating eigenstates. Physically, they consist of appropriately composing evolutions under an input Hamiltonian together with diagonal evolutions. Here, we present strategies to optimize the choice of the double-bracket evolutions to enhance the diagonalization efficiency. This can be done by finding optimal generators and durations of the evolutions. We present numerical results regarding the preparation of double-bracket iterations, both in ideal cases where the algorithm's setup provides analytical convergence guarantees and in more heuristic cases, where we use an adaptive and variational approach to optimize the generators of the evolutions. As an example, we discuss the efficacy of these optimization strategies when considering a spin-chain Hamiltonian as the target. To propose algorithms that can be executed starting today, fully aware of the limitations of the quantum technologies at our disposal, we finally present a selection of diagonal evolution parametrizations that can be directly compiled into CNOTs and single-qubit rotation gates. We discuss the advantages and limitations of this compilation and propose a way to take advantage of this approach when used in synergy with other existing methods.

quant-ph↗

arXiv2024

Double-bracket quantum algorithms for high-fidelity ground state preparation

Ground state preparation is a central application for quantum computers but remains challenging in practice. In this work, we quantitatively investigate the performance and gate counts of double-bracket quantum algorithms (DBQAs) for ground state preparation. We propose a practical strategy in which DBQAs refine initial state preparation circuits, and we compile them for Heisenberg chains using controlled-Z and single-qubit gates. Warm-started DBQAs consistently improve both the energy and ground-state fidelity relative to the initial states provided by variational ans\"atze, indicating that DBQAs offer an effective unitary synthesis method. To demonstrate compatibility with near-term hardware, we executed a proof-of-concept example on IBM devices. With error mitigation, we observed a statistically significant improvement over the corresponding warm-start circuit. Furthermore, numerical emulations for the same system size indicate that executing DBQAs on Quantinuum's hardware could achieve similar cost-function gains without requiring error mitigation. These findings suggest that DBQAs are a promising approach for enhancing ground-state approximations on near-term quantum devices.

quant-ph↗

arXiv2024

Measurement of total phase fluctuation in cold-atomic quantum simulators

Studying the dynamics of quantum many-body systems is often constrained by the limitations in probing relevant observables, especially in continuous systems. A powerful method to gain information about such systems is the reconstruction of local currents from the continuity equation. We show that this approach can be used to extract the total phase fluctuation of adjacent Bose gases. We validate our technique numerically and demonstrate its effectiveness by analyzing data from selected experiments simulating 1D quantum field theories through the phase difference of two parallel 1D Bose gases. This analysis reveals the previously hidden sector of the sum mode of the phase, which is important for studying long-time thermalization and out-of-equilibrium dynamics of the system. Our method is general and can be applied to other cold atom systems with spatial phase gradients, thereby expanding the scope and capabilities of cold-atomic quantum simulators.

cond-mat.quant-gas↗

arXiv2024

High-Fidelity CZ Gates in Double Quantum Dot -- Circuit QED Systems Beyond the Rotating-Wave Approximation

Semiconductor double quantum dot (DQD) qubits coupled via superconducting microwave resonators provide a powerful means of long-range manipulation of the qubits' spin and charge degrees of freedom. Quantum gates can be implemented by parametrically driving the qubits while their transition frequencies are detuned from the resonator frequency. Long-range two-qubit CZ gates have been proposed for the DQD spin qubit within the rotating-wave approximation (RWA). Rapid gates demand strong coupling, but RWA breaks down when coupling strengths become significant relative to system frequencies. Therefore, understanding the detrimental impact of time-dependent terms ignored by RWA is critical for high-fidelity operation. Here, we go beyond RWA to study CZ gate fidelity for both DQD spin and charge qubits. We propose a novel parametric drive on the charge qubit that produces fewer time-dependent terms and show that it outperforms its spin counterpart. We find that drive amplitude - a parameter dropped in RWA - is critical for optimizing fidelity and map out high-fidelity regimes. Our results demonstrate the necessity of going beyond RWA in understanding how long-range gates can be realized in DQD qubits, with charge qubits offering considerable advantages in high-fidelity operation.

cond-mat.mes-hall↗

arXiv2024

Double-bracket quantum algorithms for diagonalization

This work proposes double-bracket iterations as a framework for obtaining diagonalizing quantum circuits. Their implementation on a quantum computer consists of interlacing evolutions generated by the input Hamiltonian with diagonal evolutions which can be chosen variationally. No qubit overheads or controlled-unitary operations are needed but the method is recursive which makes the circuit depth grow exponentially with the number of recursion steps. To make near-term implementations viable, the proposal includes optimization of diagonal evolution generators and of recursion step durations. Indeed, thanks to this numerical examples show that the expressive power of double-bracket iterations suffices to approximate eigenstates of relevant quantum models with few recursion steps. Compared to brute-force optimization of unstructured circuits double-bracket iterations do not suffer from the same trainability limitations. Moreover, with an implementation cost lower than required for quantum phase estimation they are more suitable for near-term quantum computing experiments. More broadly, this work opens a pathway for constructing purposeful quantum algorithms based on so-called double-bracket flows also for tasks different from diagonalization and thus enlarges the quantum computing toolkit geared towards practical physics problems.

quant-ph↗

arXiv2024

Quantum Dynamic Programming

We introduce a quantum extension of dynamic programming, a fundamental computational method that efficiently solves recursive problems using memory. Our innovation lies in showing how to coherently generate recursion step unitaries by using memorized intermediate quantum states. Quantum dynamic programming achieves an exponential reduction in circuit depth for a broad class of fixed-point quantum recursions, though this comes at the cost of increased circuit width. Interestingly, the trade-off becomes more favourable when the initial state is pure. By hybridizing our approach with a conventional memoryless one, we can flexibly balance circuit depth and width to optimize performance on quantum devices with fixed hardware constraints. Finally, we showcase applications of quantum dynamic programming to several quantum recursions, including a variant of Grover's search, quantum imaginary-time evolution, and a new protocol for obliviously preparing a quantum state in its Schmidt basis.

quant-ph↗

arXiv2024

Systematic analysis of relative phase extraction in one-dimensional Bose gases interferometry

Spatially resolved relative phase measurement of two adjacent 1D Bose gases is enabled by matter-wave interference upon free expansion. However, longitudinal dynamics is typically ignored in the analysis of experimental data. We provide an analytical formula showing a correction to the readout of the relative phase due to longitudinal expansion and mixing with the common phase. We numerically assess the error propagation to the estimation of the gases' physical quantities such as correlation functions and temperature. Our work characterizes the reliability and robustness of interferometric measurements, directing us to the improvement of existing phase extraction methods necessary to observe new physical phenomena in cold-atomic quantum simulators.

cond-mat.quant-gas↗

arXiv2022

Experimental Observation of Curved Light-Cones in a Quantum Field Simulator

We investigate signal propagation in a quantum field simulator of the Klein-Gordon model realized by two strongly coupled parallel one-dimensional quasi-condensates. By measuring local phononic fields after a quench, we observe the propagation of correlations along sharp light-cone fronts. If the local atomic density is inhomogeneous, these propagation fronts are curved. For sharp edges, the propagation fronts are reflected at the system's boundaries. By extracting the space-dependent variation of the front velocity from the data, we find agreement with theoretical predictions based on curved geodesics of an inhomogeneous metric. This work extends the range of quantum simulations of non-equilibrium field dynamics in general spacetime metrics.

cond-mat.quant-gas↗

arXiv2022

Boundary theories of critical matchgate tensor networks

Key aspects of the AdS/CFT correspondence can be captured in terms of tensor network models on hyperbolic lattices. For tensors fulfilling the matchgate constraint, these have previously been shown to produce disordered boundary states whose site-averaged ground state properties match the translation-invariant critical Ising model. In this work, we substantially sharpen this relationship by deriving disordered local Hamiltonians generalizing the critical Ising model whose ground and low-energy excited states are accurately represented by the matchgate ansatz without any averaging. We show that these Hamiltonians exhibit multi-scale quasiperiodic symmetries captured by an analytical toy model based on layers of the hyperbolic lattice, breaking the conformal symmetries of the critical Ising model in a controlled manner. We provide a direct identification of correlation functions of ground and low-energy excited states between the disordered and translation-invariant models and give numerical evidence that the former approaches the latter in the large bond dimension limit. This establishes tensor networks on regular hyperbolic tilings as an effective tool for the study of conformal field theories. Furthermore, our numerical probes of the bulk parameters corresponding to boundary excited states constitute a first step towards a tensor network bulk-boundary dictionary between regular hyperbolic geometries and critical boundary states.

quant-ph↗

arXiv2022

Mechanisms for the emergence of Gaussian correlations

We comprehensively investigate two distinct mechanisms leading to memory loss of non-Gaussian correlations after switching off the interactions in an isolated quantum system undergoing out-of-equilibrium dynamics. The first mechanism is based on spatial scrambling and results in the emergence of locally Gaussian steady states in large systems evolving over long times. The second mechanism, characterized as `canonical transmutation', is based on the mixing of a pair of canonically conjugate fields, one of which initially exhibits non-Gaussian fluctuations while the other is Gaussian and dominates the dynamics, resulting in the emergence of relative Gaussianity even at finite system sizes and times. We evaluate signatures of the occurrence of the two candidate mechanisms in a recent experiment that has observed Gaussification in an atom-chip controlled ultracold gas and elucidate evidence that it is canonical transmutation rather than spatial scrambling that is responsible for Gaussification in the experiment. Both mechanisms are shown to share the common feature that the Gaussian correlations revealed dynamically by the quench are already present though practically inaccessible at the initial time. On the way, we present novel observations based on the experimental data, demonstrating clustering of equilibrium correlations, analyzing the dynamics of full counting statistics, and utilizing tomographic reconstructions of quantum field states. Our work aims at providing an accessible presentation of the potential of atom-chip experiments to explore fundamental aspects of quantum field theories in quantum simulations.

quant-ph↗

arXiv2022

Breaking of Huygens-Fresnel principle in inhomogeneous Tomonaga-Luttinger liquids

Tomonaga-Luttinger liquids (TLLs) can be used to effectively describe one-dimensional quantum many-body systems such as ultracold atoms, charges in nanowires, superconducting circuits, and gapless spin chains. Their properties are given by two parameters, the propagation velocity and the Luttinger parameter. Here we study inhomogeneous TLLs where these are promoted to functions of position and demonstrate that they profoundly affect the dynamics: In general, besides curving the light cone, we show that propagation is no longer ballistically localized to the light-cone trajectories, different from standard homogeneous TLLs. Specifically, if the Luttinger parameter depends on position, the dynamics features pronounced spreading into the light cone, which cannot be understood via a simple superposition of waves as in the Huygens-Fresnel principle. This is the case for ultracold atoms in a parabolic trap, which serves as our main motivation, and we discuss possible experimental observations in such systems.

cond-mat.stat-mech↗