Simulating strongly correlated many-body quantum systems using Quantum Tensor Networks (QTNs) is fundamentally constrained by entanglement growth and the resulting computational requirements. This research presents an empirical optimization framework for two-qubit boundary disentanglers parameterized in SU(4), using an unconstrained coordinate-descent search over local unitary rotations. The proposed approach achieves an 87.75% reduction in bipartite von Neumann entanglement entropy, from 2.0000 to 0.2450 bits. The resulting Schmidt spectrum enables a 50% bond-dimension truncation to χ = 2, with a reported state fidelity of 99.85%. The optimized four-qubit circuit was compiled using Qiskit 2.5.2 for IBM Quantum's 156-qubit Heron r2 processor (ibm_fez) and executed on physical quantum hardware using 1,024 measurement shots. The compiled circuit has a depth of 36, with 9 native CZ gates and 46 single-qubit SX/RZ gates. The reported measurement results show over 88.6% probability mass concentration in the theoretical Schmidt eigenspaces. This work investigates the practical potential of boundary disentanglement for reducing tensor-network representation costs and supporting the simulation of strongly entangled quantum systems on near-term superconducting quantum hardware.
Simulating strongly correlated many-body quantum systems using Quantum Tensor Networks (QTNs) is fundamentally constrained by entanglement growth and the resulting computational requirements. This research presents an empirical optimization framework for two-qubit boundary disentanglers parameterized in SU(4), using an unconstrained coordinate-descent search over local unitary rotations. The proposed approach achieves an 87.75% reduction in bipartite von Neumann entanglement entropy, from 2.0000 to 0.2450 bits. The resulting Schmidt spectrum enables a 50% bond-dimension truncation to χ = 2, with a reported state fidelity of 99.85%. The optimized four-qubit circuit was compiled using Qiskit 2.5.2 for IBM Quantum's 156-qubit Heron r2 processor (ibm_fez) and executed on physical quantum hardware using 1,024 measurement shots. The compiled circuit has a depth of 36, with 9 native CZ gates and 46 single-qubit SX/RZ gates. The reported measurement results show over 88.6% probability mass concentration in the theoretical Schmidt eigenspaces. This work investigates the practical potential of boundary disentanglement for reducing tensor-network representation costs and supporting the simulation of strongly entangled quantum systems on near-term superconducting quantum hardware.
Entanglement is a key bottleneck limiting the efficiency of tensor-network and quantum simulations of molecular electronic structures. Here, we systematically assess and extend Clifford disentanglers as a structure-preserving approach to entanglement reduction: they can modify the entanglement structure of qubit wavefunctions while retaining the Pauli-string form of qubit Hamiltonians. To enable a practical search over Clifford transformations, we classify Clifford operators by their action on the Schmidt spectrum across a bipartition, reducing the two- and four-qubit search spaces to 20 and 91392 representatives, respectively. Embedded in an iterative Clifford-augmented matrix product state framework, these transformations reduce the energy errors at fixed bond dimension for the molecular test cases studied and mitigate the dependence on orbital orderings and fermion-to-qubit mappings. We further show that Clifford disentanglers can also benefit quantum simulations such as the shallow-circuit variational quantum eigensolver calculations. Together, these results establish Clifford disentanglers as a useful structure-preserving entanglement-engineering tool for tensor-network and quantum simulations of molecular electronic structure, while also clarifying their correlation dependence and motivating future developments.
We develop a quantum circuit synthesis method for preparing a class of tensor network states. The scheme applies to states tractable with belief propagation (BP), a tensor network gauging scheme which recently allowed for classical simulations at large scales. The problem is reduced to independent, strictly local, classical variational optimizations: each nearest-neighbor two-qubit "disentangler" gate minimizes the entropy defined on an edge. Disentanglers drive the state to a product state and their Hermitian conjugate prepares the target. Each disentangling layer has depth at most z+1 (with z the maximal number of nearest neighbors per site), the optimization has no barren plateaus, and the bond dimension stays bounded. As a demonstration, with only 3-5 disentangling layers we prepare a 102-qubit tree tensor network encoding a 17-dimensional normal distribution and the transverse-field Ising model ground states on a 64- to 127-qubit heavy-hex lattice with fidelities of order 0.9−0.999. The method opens new possibilities for quantum applications by transferring classical tensor network states onto hardware.
We aim to rigorously address how local noise affects classical simulability of quantum dynamics benchmarked by tensor-network methods. Using operator entanglement entropy (OEE), we prove the following: (1) For single-qubit depolarizing noise on arbitrary circuits, tensor networks with poly(n) bond dimension suffice for fixed absolute Hilbert-Schmidt error after $\order{1}$ depth, while relative error demands $\order{\log n}$ depth; and this bound is optimal. (2) For single-qubit depolarizing noise on 1D local circuits, the existence of whole-trajectory error-bounded matrix product operator (MPO) of poly(n) bond dimension at all depths. (3) For general single-qubit noise in 1D brickwall circuits, random two-design gates with contraction coefficient c<1/3 yield an $\order{1}$ OEE plateau with probability 1−Te−Ω(n), while arbitrary gates with c<1/48 give $\order{\log n}$ OEE in the worst case. (4) In higher dimensions, these bounds yield uniform-in-depth poly(n) average boundary-bond dimensions for projected entangled pair operators~(PEPO) across every cut -- under depolarizing noise at either absolute or relative accuracy, and under general noise with strong contraction at absolute accuracy. Our results establish a rigorous connection between certain noise models, circuit types, and their classical simulability.
Many recent tensor network algorithms apply unitary operators to parts of a tensor network in order to reduce entanglement. However, many of the previously used iterative algorithms to minimize entanglement can be slow. We introduce an approximate, fast, and simple algorithm to optimize disentangling unitary tensors. Our algorithm is asymptotically faster than previous iterative algorithms and often results in a residual entanglement entropy that is within 10 to 40% of the minimum. For certain input tensors, our algorithm returns an optimal solution. When disentangling order-4 tensors with equal bond dimensions, our algorithm achieves an entanglement spectrum where nearly half of the singular values are zero. We further validate our algorithm by showing that it can efficiently disentangle random 1D states of qubits.
Quantum computing faces challenges such as noise, short coherence time, and limited qubit connections. These challenges worsen as quantum circuits become more complex. One major issue is the increasing depth of quantum circuits. This research proposes an optimization framework targeting depth and gate count reduction in quantum circuits, specifically for Noisy Intermediate-Scale Quantum (NISQ) devices. The proposed approach combines unitary merging of single-qubit gates, CNOT cancellation, gate commuting, and rotation gate rewriting strategies. Consecutive gates acting on the same qubit, such asRx(θ1)⋅Rx(θ2), are algebraically merged into a single rotation, while pairs of redundant CNOT gates are eliminated based on gate identity relations. The technique is implemented using Qiskit and validated across five diverse circuits including complex, random, and multi-qubit configurations. Experimental results show an average depth reduction of 33.33% and gate count reduction of 32.14%, with runtime improvement of up to 25%. For instance, an input circuit with a depth of 7 and gate count of 11 was reduced to a depth of 2 and 4 gates. All optimized circuits preserve functional correctness with a fidelityF≥0.99. High-resolution circuit diagrams are presented to visually demonstrate improvements before and after optimization. Additionally, global phase shifts such aseiπ/4are preserved or analytically characterized where relevant. This work enhances the viability of quantum computations on near-term hardware and opens pathways for future AI-driven quantum optimizations.
We report the multi-system physical benchmarking of non-equilibrium quantum hydrodynamic transport, extreme-depth variational circuits, and three-dimensional biomolecular tensor fields across three commercial 156-qubit IBM Heron superconducting transmon processors: ibm_fez, ibm_marrakesh, and ibm_kingston. Utilizing Qiskit 2.x and native two-qubit Controlled-Z (CZ) pulse primitives with tunable couplers, we execute fourteen consecutive production workloads spanning circuit depths up to 547 gate cycles, on-chip transmon registrations up to 100 active physical qubits (Project APEX-HYDRO, Job dateauqhcrkc73du2gr0; 840 native CZ gates), and full-chip macroscopic entanglement across all 156 transmon sites. In our landmark 100-qubit hydrodynamic benchmark on ibm_kingston, we physically measure non-equilibrium wavepacket spreading on a connected heavy-hexagonal transmon subgraph, observing Kardar-Parisi-Zhang (KPZ) superdiffusive transport with dynamical critical exponent z = 1.52 ± 0.04 in the integrable 1D regime (lambda=0), crossing over to conventional diffusion (z = 1.98 ± 0.05) upon introducing heavy-hex transverse cross-couplers (lambda=0.5). We prove that classical Matrix Product State (MPS) simulations truncate at quench time t* ≈ 2.12 hbar/J for bond dimensions chi <= 128, demonstrating an operational quantum advantage boundary on superconducting silicon. Concurrently, we achieve sustained variational coherence across 29 entangling layers (435 native CZ gates, Depth 547) in 1.12 seconds on-chip (Job dat840jojkfs738qag4g), and simulate 3D anisotropic stress tensors derived from AlphaFold3 biomolecular coordinates across 64 qubits on ibm_fez. All 14 production workloads completed with a 100.0% execution reliability, establishing quantitative design rules for utility-scale superconducting quantum simulation.