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.
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.
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 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.
Tensor network methods leverage the limited entanglement of quantum states to efficiently simulate many-body systems. Alternatively, Clifford circuits provide a framework for handling highly entangled stabilizer states, which have low magic and are thus also classically tractable. Clifford tensor networks combine the benefits of both approaches, exploiting Clifford circuits to reduce the classical complexity of the tensor network description of states, with promising effects on simulation approaches. We study the disentangling power of Clifford transformations acting on tensor networks, with a particular emphasis on entanglement cooling strategies. We identify regimes where exact or heuristic Clifford disentanglers are effective, explain the link between the two approaches, and characterize their breakdown as non-Clifford resources accumulate. Additionally, we prove that, beyond stabilizer settings, no Clifford operation can universally disentangle even a single qubit from an arbitrary non-Clifford rotation. Our results clarify both the capabilities and fundamental limitations of Clifford-based simulation methods.
Abstract Researchers have put a lot of effort into reducing the gap between current quantum processing units (QPU) capabilities and their potential supremacy.One approach is to keep supplementary computations in the CPU, and use QPU only for the core of the problem. In this work, we address the complexity of quantum algorithm of arbitrary quantum state initialization, an important building block of quantum data analysis and machine learning.QPUs do not outperform classical machines with existing precise initialization algorithms.Hence, many studies propose an approximate but robust quantum state initialization.Cutting a quantum state into a product of (almost) independent partitions with the help of CPU reduces the number of two-qubit gates, and correspondingly minimizes the loss of state fidelity in the quantum part of the algorithm.To find the least entangled qubits, current methods compute the singular value decomposition (SVD) for each qubit separately with CPU.In this paper, we optimize CPU usage and memory resource bottlenecks.We consider Tucker tensor decomposition as an alternative to the CPU-based SVD in a single low-entangled qubit detection task without the loss of solution quality.Both proposed methods outperform the SVD in time and memory for systems of at least ten qubits. We achieve an order faster implementation and two orders less memory usage for a system of 15 qubits.
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.