arXiv subjects

Younes Javanmard

Publications and source records attributed to Younes Javanmard.

15 recordsLinked to original sources

arXiv2026

Biorthogonal Time-Dependent Variational Principle for Non-Hermitian Systems

We develop a biorthogonal time-dependent variational principle for real-time dynamics of non-Hermitian quantum many-body systems. Independent left and right matrix-product states obey coupled bivariational tangent-space equations whose cross-Gram matrix defines an oblique projection. A matrix-free scaled Taylor action propagates the resulting non-normal local generators without assembling dense matrices or storing a Krylov basis. We distinguish the fully coupled algorithm, which solves the cross-pairing problem and truncates the two bond bases jointly, from an efficient independently propagated approximation used for large systems. Independent truncation can make the retained left-right pairing nearly singular; overlap drift and the smallest singular value of the bond cross matrix expose this failure, while coupled truncation substantially delays it. Exact benchmarks and convergence tests validate the method. Applied to an interacting long-range non-Hermitian Ising chain, it resolves a biorthogonal dynamical quantum phase transition and shows that a weak imaginary field shifts the leading critical time from $t^{\ast}|J|=1.84$ to $1.04$.

quant-ph↗

arXiv2026

Closed Quantum Boltzmann Bridges: Coherent Revivals, Hidden Microstates, and the Emergence of Classical Two-Time Entropy Conditioning

The classical Boltzmann Bridge describes entropy histories conditioned on both an initial low-entropy macrostate and a later macrostate. Unlike the usual past-only formulation of the thermodynamic arrow, this two-time conditioning can produce entropy profiles that rise above the final entropy and then decrease toward the imposed endpoint. In this work, we formulate closed quantum analogues of the Boltzmann Bridge using macro-subspace projectors, unitary time evolution, and Boltzmann entropy defined by the dimension of coarse-grained macroscopic sectors. We first study a minimal coherent chamber-qubit model, in which each particle has only a two-state chamber degree of freedom. Although this model is the most direct quantization of the classical two-box system, its bridge entropy profile is dominated by coherent oscillations and revivals rather than classical relaxation. We then introduce a hidden-microstate bridge, in which each chamber sector contains unresolved internal degrees of freedom while the full dynamics remain unitary. Numerical experiments show that increasing the internal Hilbert-space dimension suppresses sample-dependent revival behavior and produces bridge entropy profiles whose sign structure and coarse-grained shape increasingly agree with the classical Boltzmann Bridge. We further use a Random Forest classifier to explore the parameter regime separating revival-dominated quantum behavior from classical-like coarse-grained bridge behavior. These results suggest that classical two-time-conditioned entropy behavior is not recovered by quantizing the chamber variable alone, but can emerge statistically from closed quantum.

quant-ph↗

arXiv2026

Quantum simulation of dynamical phase transitions in noisy quantum devices

Zero-noise extrapolation provides an especially useful error mitigation method for noisy intermediate-scale quantum devices. Our analysis, based on matrix product density operators, of the transverse-field Ising model with depolarizing noise, reveals both advantages and inherent problems associated with zero-noise extrapolation when simulating non-equilibrium many-body dynamics. On the one hand, interestingly, noise alters systematically the behavior of the Loschmidt echo at the dynamical phase transition times, doubling the number of non-analytic points, and hence inducing an error that, inherently, cannot be mitigated. On the other, zero-noise extrapolation may be employed to recover quantum revivals of the Loschmidt echo, which would be completely missed in the absence of mitigation, and to retrieve faithfully noise-free inter-site correlations. Our results, which are in good agreement with those obtained using quantum simulators, reveal the potential of matrix product density operators for the investigation of the performance of quantum devices with a large number of qubits and deep noisy quantum circuits.

quant-ph↗

arXiv2026

Boundary-Aware QFT Block-Encoding of Fractional Laplacians

We study the quantum Fourier transform (QFT) block-encoding of the semi-discrete fractional Laplacian on bounded domains with open, zero-extension boundary conditions. In the notation of the main construction, the target operator is the finite Toeplitz truncation $A^{(N)}_{α,h}$ obtained from the full-lattice semi-discrete operator with symbol $|ξ|^α$. A finite QFT register, however, diagonalizes circulant matrices rather than Toeplitz truncations. The native QFT circuit therefore implements a periodic surrogate $\widetilde A^{(N)}_{α,h}$, not the open-boundary operator. We identify this mismatch through an exact Toeplitz-to-circulant aliasing identity. To recover the open-boundary action, we zero-pad the state into a larger $M$-point QFT register, apply the same Fourier-symbol block-encoding, and compress back to the physical subspace. The resulting compressed block satisfies $P_{N\to M}^{\dagger}\widetilde A^{(M)}_{α,h}P_{N\to M} = A^{(N)}_{α,h}+E^{(M)}$, where $E^{(M)}$ is controlled by the tail of the semi-discrete convolution kernel. Thus, the QFT layer implements the fractional symbol, while zero-padding supplies the open-boundary geometry. The construction is an operator-compilation primitive for boundary-aware quantum simulation rather than a complete PDE solver.

quant-ph↗

arXiv2026

Quantum Markov chain Monte Carlo method with programmable quantum simulators

In this work, we present a quantum Markov chain algorithm for many-body systems that utilizes a special phase of matter known as the Many-Body Localized (MBL) phase. We show how the properties of the MBL phase enable one to address the conditions for ergodicity and sampling from distributions of quantum states. We demonstrate how to exploit the thermalized-to-localized transition to tune the acceptance rate of the Markov chain, and apply the algorithm to solve a range of combinatorial optimization problems of quadratic order and higher. The algorithm can be implemented on any quantum processing unit capable of simulating the Floquet dynamics of a one-dimensional Ising chain with nearest-neighbor interactions, providing a practical way of sampling from thermal distributions of Hamiltonians that cannot be natively implemented on the quantum hardware.

quant-ph↗

arXiv2026

Compressing Transformer Language Models via Matrix Product Operator Decomposition: A Case Study on PicoGPT

Transformer-based language models achieve strong performance across NLP tasks, but their quadratic parameter scaling with hidden dimension makes deployment on resource-constrained hardware expensive. We study Matrix Product Operator (MPO) decomposition as a principled compression method for transformers. MPO factorises weight matrices into chains of low-rank cores, with approximation quality controlled by the bond dimension chi. We replace every nn.Linear layer in PicoGPT, a GPT-2-style character-level language model with about 1M parameters, with an MPOLinear module parameterised as an MPO chain. Cores are initialised either by TT-SVD from pretrained dense weights or from random initialisation, and trained using standard PyTorch autograd without a custom backward pass. We derive balanced factorisation schemes for the five distinct weight shapes in PicoGPT and evaluate bond dimensions chi in {4, 8, 16, 32} on Tiny Shakespeare. MPO compression achieves up to 13x compression per transformer block at chi = 4. At chi = 16, the model uses 191,872 parameters instead of 1,020,224 while retaining 97.7% of baseline token accuracy (51.6% vs 52.8%). Reconstruction error follows the expected trend and is lower for three-site than two-site factorisations at the same bond dimension. The chi = 8 model gives the best accuracy per parameter, exceeding the dense baseline by 2.7x on this metric. These results show that MPO parameterisation is a practical and theoretically grounded alternative to low-rank methods and unstructured pruning for transformer compression.

cs.CL↗

arXiv2026

Coefficient-Decoupled Matrix Product Operators as an Interface to Linear-Combination-of-Unitaries Circuits

We introduce a coefficient-decoupled matrix product operator (MPO) representation for Pauli-sum operators that separates reusable symbolic operator support from a tunable coefficient bridge across a fixed bipartition. This representation provides a direct interface to linear-combination-of-unitaries (LCU) circuits: the symbolic left/right dictionaries define a static \textsc{Select} oracle that is compiled once, while coefficient updates modify only a dynamic \textsc{Prep} oracle. As a proof of concept, we construct compact state-adapted Pauli pools by sampling Pauli strings from a pretrained matrix product state (MPS), pruning them to a fixed symbolic pool, optimizing only their coefficients, and transferring the resulting weights directly to the LCU interface. The resulting workflow provides a reusable classical-to-quantum compilation strategy in which the symbolic operator structure is compiled once, and subsequent updates are confined to a low-dimensional coefficient object.

quant-ph↗

arXiv2026

Quantum search by measurements assisted by pre-trained tensor network states for Hamiltonian simulations

We present a quantum algorithm for simulating complex many-body systems and finding their ground states, combining the use of tensor networks and density matrix renormalization group (DMRG) techniques. The algorithm is based on von Neumann's measurement prescription, which serves as a conceptual building block for quantum phase estimation. We describe the implementation and simulation of the algorithm, including the estimation of resources required and the use of matrix product operators (MPOs) to represent the Hamiltonian. We highlight the potential applications of the algorithm in simulating quantum spin systems and electronic structure problems.

quant-ph↗

arXiv2024

Duality between string and computational order in symmetry-enriched topological phases

We present the first examples of topological phases of matter with uniform power for measurement-based quantum computation. This is possible thanks to a new framework for analyzing the computational properties of phases of matter that is more general than previous constructions, which were limited to short-range entangled phases in one dimension. We show that ground states of the toric code in an anisotropic magnetic field yield a natural, albeit non-computationally-universal, application of our framework. We then present a new model with topological order whose ground states are universal resources for MBQC. Both topological models are enriched by subsystem symmetries, and these symmetries protect their computational power. Our framework greatly expands the range of physical models that can be analyzed from the computational perspective.

quant-ph↗

arXiv2024

Simulation of a Rohksar-Kivelson ladder on a NISQ device

We present a quantum-classical algorithm to study the dynamics of the Rohksar-Kivelson plaquette ladder on NISQ devices. We show that complexity is largely reduced using gauge invariance, additional symmetries, and a crucial property associated to how plaquettes are blocked against ring-exchange in the ladder geometry. This allows for an efficient simulation of sizable plaquette ladders with a small number of qubits, well suited for the capabilities of present NISQ devices. We illustrate the procedure for ladders with simulation of up to $8$ plaquettes in an IBM-Q machine, employing scaled quantum gates.

quant-ph↗

arXiv2024

Matrix product state ansatz for the variational quantum solution of the Heisenberg model on Kagome geometries

The Variational Quantum Eigensolver (VQE) algorithm, as applied to finding the ground state of a Hamiltonian, is particularly well-suited for deployment on noisy intermediate-scale quantum (NISQ) devices. Here we utilize the VQE algorithm with a quantum circuit ansatz inspired by the Density Matrix Renormalization Group (DMRG) algorithm. To ameliorate the impact of realistic noise on the performance of the method we employ zero-noise extrapolation. We find that, with realistic error rates, our DMRG-VQE hybrid algorithm delivers good results for strongly correlated systems. We illustrate our approach with the Heisenberg model on a Kagome lattice patch and demonstrate that DMRG-VQE hybrid methods can locate, and faithfully represent the physics of, the ground state of such systems. Moreover, the parameterized ansatz circuit used in this work is low-depth and requires a reasonably small number of parameters, so is efficient for NISQ devices.

quant-ph↗

arXiv2023

Parity Quantum Optimization: Encoding Constraints

Constraints make hard optimization problems even harder to solve on quantum devices because they are implemented with large energy penalties and additional qubit overhead. The parity mapping, which has been introduced as an alternative to the spin encoding, translates the problem to a representation using only parity variables that encodes products of spin variables. In combining exchange interaction and single spin flip terms in the parity representation, constraints on sums and products of arbitrary k-body terms can be implemented without additional overhead in two-dimensional quantum systems.

quant-ph↗

arXiv2018

Accessing eigenstate spin-glass order from reduced density matrices

Many-body localized phases may not only be characterized by their ergodicity breaking, but can also host ordered phases such as the many-body localized spin-glass (MBL-SG). The MBL-SG is challenging to access in a dynamical measurement and therefore experimentally since the conventionally used Edwards-Anderson order parameter is a two-point correlation function in time. In this work, we show that many-body localized spin-glass order can also be detected from two-site reduced density matrices, which we use to construct an eigenstate spin-glass order parameter. We find that this eigenstate spin-glass order parameter captures spin-glass phases in random Ising chains both in many-body eigenstates as well as in the nonequilibrium dynamics from a local in time measurement. We discuss how our results can be used to observe MBL-SG order within current experiments in Rydberg atoms and trapped ion systems.

cond-mat.str-el↗

arXiv2018

Sharp entanglement thresholds in the logarithmic negativity of disjoint blocks in the transverse-field Ising chain

Entanglement has developed into an essential concept for the characterization of phases and phase transitions in ground states of quantum many-body systems. In this work, we use the logarithmic negativity to study the spatial entanglement structure in the transverse-field Ising chain both in the ground state and at nonzero temperatures. Specifically, we investigate the entanglement between two disjoint blocks as a function of their separation, which can be viewed as the entanglement analog of a spatial correlation function. We find sharp entanglement thresholds at a critical distance beyond which the logarithmic negativity vanishes exactly and thus the two blocks become unentangled, which holds even in the presence of long-ranged quantum correlations, i.e., at the system's quantum critical point. Using Time-Evolving Block Decimation (TEBD), we explore this feature as a function of temperature and size of the two blocks and present a simple model to describe our numerical observations.

cond-mat.str-el↗

arXiv2016

Interaction-tuned Anderson versus Mott localization

Disorder or sufficiently strong interactions can render a metallic state unstable causing it to turn into an insulating one. Despite the fact that the interplay of these two routes to a vanishing conductivity has been a central research topic, a unifying picture has not emerged so far. Here, we establish that the two-dimensional Falicov-Kimball model, one of the simplest lattice models of strong electron correlation does allow for the study of this interplay. In particular, we show that this model at particle-hole symmetry possesses three distinct thermodynamic insulating phases and exhibits Anderson localization. The previously reported metallic phase is identified as a finite-size feature due to the presence of weak localization. We characterize these phases by their electronic density of states, staggered occupation, conductivity, and the generalized inverse participation ratio. The implications of our findings for other strongly correlated systems are discussed.

cond-mat.str-el↗