Loading data into quantum computers is a key bottleneck that threatens end-to-end quantum advantage. Quantum-circuit compilers for structured states like matrix product states (MPS) are a critical enabler to manage this in quantum chemistry, finance, and many-body quantum simulation. Approximate preparation of MPS typically relies on layered sequential staircases of nearest-neighbour gates. We present Adaptive State Preparation by Iterative Removal of Entanglement (ASPIRE), an algorithm that approximately compiles state-preparation circuits by selecting gates based on the state's underlying entanglement geometry and the available connectivity of the target quantum processor. Our protocol scores candidate qubit pairs on the removability of their entanglement and identifies layers of parallelised long-ranged gates that remove the most entanglement. We demonstrate our protocol empirically across a range of settings, illustrating its success for preparing Hamiltonian ground states and multivariate amplitude-encoded functions, and accounting for qubit connectivity, hardware noise, and both NISQ and early fault-tolerant settings. Throughout, ASPIRE typically achieves higher fidelities and shallower circuits than existing methods for states with long-ranged entanglement, even when classical optimisation is accounted for. Our investigation positions ASPIRE as a competitive, resource-frugal state-preparation protocol, with particular promise for applications tolerant to imperfect fidelity such as preparation of guide states for quantum phase estimation.
Loading data into quantum computers is a key bottleneck that threatens end-to-end quantum advantage. Quantum-circuit compilers for structured states like matrix product states (MPS) are a critical enabler to manage this in quantum chemistry, finance, and many-body quantum simulation. Approximate preparation of MPS typically relies on layered sequential staircases of nearest-neighbour gates. We present Adaptive State Preparation by Iterative Removal of Entanglement (ASPIRE), an algorithm that approximately compiles state-preparation circuits by selecting gates based on the state's underlying entanglement geometry and the available connectivity of the target quantum processor. Our protocol scores candidate qubit pairs on the removability of their entanglement and identifies layers of parallelised long-ranged gates that remove the most entanglement. We demonstrate our protocol empirically across a range of settings, illustrating its success for preparing Hamiltonian ground states and multivariate amplitude-encoded functions, and accounting for qubit connectivity, hardware noise, and both NISQ and early fault-tolerant settings. Throughout, ASPIRE typically achieves higher fidelities and shallower circuits than existing methods for states with long-ranged entanglement, even when classical optimisation is accounted for. Our investigation positions ASPIRE as a competitive, resource-frugal state-preparation protocol, with particular promise for applications tolerant to imperfect fidelity such as preparation of guide states for quantum phase estimation.
Quantum state preparation represents a critical bottleneck for a broad class of quantum algorithms. In this work, we introduce the Schmidt Spectrum Optimisation (SSO) algorithm as an efficient and scalable approach for preparing quantum states described by Matrix Product States (MPS). The SSO algorithm employs a preparation-by-disentangling strategy by optimising circuit layers of two-qubit gates to progressively remove entanglement from a target state. Each circuit layer is computed sequentially and efficiently on a classical computer using tensor network optimisation techniques. Once the target state has been successfully disentangled, a quantum state-preparation circuit is formed by reversing the sequence of optimised disentangling layers. Across benchmarks including random MPS and MPS approximations to the ground-states of local Hamiltonians, we find that the SSO algorithm significantly improves upon prior variational and disentangling-based approaches, highlighting its potential as a scalable framework for quantum state preparation.
Preparing arbitrary quantum states requires exponential resources. Matrix Product States (MPS) admit more efficient constructions, particularly when accuracy is traded for circuit complexity. Existing approaches to MPS preparation mostly rely on heuristic circuits that are deterministic but quickly saturate in accuracy, or on variational optimization methods that reach high fidelities but scale poorly. This work introduces an end-to-end MPS preparation framework that combines the strengths of both strategies within a single pipeline. Heuristic staircase-like and brick wall disentangler circuits provide warm-start initializations for variational optimization, enabling high-fidelity state preparation for large systems. Target MPSs are either specified as physical quantum states or constructed from classical datasets via amplitude encoding, using step-by-step singular value decompositions or tensor cross interpolation. The framework incorporates entanglement-based qubit reordering, reformulated as a quadratic assignment problem, and low-level optimizations that reduce depths by up to 50% and CNOT counts by 33%. We evaluate the full pipeline on datasets of varying complexity across systems of 19-50 qubits and identify trade-offs between fidelity, gate count, and circuit depth. Optimized brick wall circuits typically achieve the lowest depths, while the optimized staircase-like circuits minimize gate counts. Overall, our results provide principled and scalable protocols for preparing MPSs as quantum circuits, supporting utility-scale applications on near-term quantum devices.
Abstract Preparing arbitrary quantum states requires exponential resources. Matrix product states (MPS) admit more efficient constructions, particularly when accuracy is traded for circuit complexity. Existing approaches to MPS preparation mostly rely on heuristic circuits that are deterministic but quickly saturate in accuracy, or on variational optimization methods that reach high fidelities but scale poorly. This work introduces an end-to-end MPS preparation framework that combines the strengths of both strategies within a single pipeline. Heuristic staircase-like and brick wall disentangler circuits provide warm-start initializations for variational optimization, enabling high-fidelity state preparation for large systems. Target MPSs are either specified as physical quantum states or constructed from classical datasets via amplitude encoding, using step-by-step singular value decompositions or tensor cross interpolation. The framework incorporates entanglement-based qubit reordering, reformulated as a quadratic assignment problem, and low-level optimizations that reduce depths by up to 50 % and CNOT counts by 33 % . We evaluate the full pipeline on datasets of varying complexity across systems of 19–50 qubits and identify trade-offs between fidelity, gate count, and circuit depth. Optimized brick wall circuits typically achieve the lowest depths, while the optimized staircase-like circuits minimize gate counts. Overall, our results provide principled and scalable protocols for preparing MPSs as quantum circuits, supporting utility-scale applications on near-term quantum devices.
Quantum state preparation is a fundamental component of quantum algorithms, particularly in quantum machine learning and data processing, where classical data must be encoded efficiently into quantum states. Existing amplitude encoding techniques often rely on recursive bipartitions or tensor decompositions, which either lead to deep circuits or lack practical guidance for circuit construction. In this work, we introduce Tucker Iterative Quantum State Preparation (Q-Tucker), a novel method that adaptively constructs shallow, deterministic quantum circuits by exploiting the global entanglement structure of target states. Building upon the Tucker decomposition, our method factors the target quantum state into a core tensor and mode-specific operators, enabling direct decompositions across multiple subsystems.
Preparing matrix product states (MPSs) on quantum computers is an essential routine in the simulation of many-body physics. However, widely used schemes based on staircase circuits are often too deep to execute on current hardware. Here, we demonstrate that MPSs with short-range correlations can be prepared with shallow circuits by leveraging heuristics from approximate quantum compiling (AQC). We achieve this with ADAPT-AQC, an adaptive-ansatz preparation algorithm, and introduce a generalized initialization procedure for the existing AQC-Tensor algorithm. We first compare these methods for the task of preparing a molecular electronic structure ground state. We then use them to prepare an antiferromagnetic (AFM) ground state of the 50-site Heisenberg XXZ spin chain near the AFM-XY phase boundary. Through the execution of circuits with up to 59 depth and 1251 gates, we perform a global quench and observe the relaxation of magnetic ordering in a parameter regime previously inaccessible due to deep ground-state preparation circuits. Our results demonstrate how the integration of quantum and classical resources can push the boundary of what can be studied on quantum computers.
Adaptive quantum circuits, which combine local unitary gates, midcircuit measurements, and feedforward operations, have recently emerged as a promising avenue for efficient state preparation, particularly on near-term quantum devices limited to shallow-depth circuits. Matrix product states (MPS) comprise a significant class of many-body entangled states, efficiently describing the ground states of one-dimensional gapped local Hamiltonians and finding applications in a number of recent quantum algorithms. Recently, it has been shown that the Affleck-Kennedy-Lieb-Tasaki state—a paradigmatic example of an MPS—can be exactly prepared with an adaptive quantum circuit of constant depth, an impossible feat with local unitary gates alone due to its nonzero correlation length [Smith , PRX Quantum 4, 020315 (2023)]. In this work, we broaden the scope of this approach and demonstrate that a diverse class of MPS can be exactly prepared using constant-depth adaptive quantum circuits, outperforming theoretically optimal preparation with unitary circuits. We show that this class includes short- and long-ranged entangled MPS, symmetry-protected topological (SPT) and symmetry-broken states, MPS with finite Abelian, non-Abelian, and continuous symmetries, resource states for MBQC, and families of states with tunable correlation length. Moreover, we illustrate the utility of our framework for designing constant-depth sampling protocols, such as for random MPS or for generating MPS in a particular SPT phase. We present sufficient conditions for particular MPS to be preparable in constant time, with global on-site symmetry playing a pivotal role. Altogether, this work demonstrates the immense promise of adaptive quantum circuits for efficiently preparing many-body entangled states and provides explicit algorithms that outperform known protocols to prepare an essential class of states. Published by the American Physical Society 2024