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arXiv:2403.03283 · Quantum

Deterministic Bethe state preparation

David Raveh, Rafael I. Nepomechie

Published Oct 24, 2024• 14 citations
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Abstract

We present an explicit quantum circuit that prepares an arbitrary U ( 1 ) -eigenstate on a quantum computer, including the exact eigenstates of the spin- 1 / 2 X X Z quantum spin chain with either open or closed boundary conditions. The algorithm is deterministic, does not require ancillary qubits, and does not require QR decompositions. The circuit prepares such an L -qubit state with M down-spins using ( L M ) − 1 multi-controlled rotation gates and 2 M ( L − M ) CNOT-gates.

DOI
10.22331/q-2024-10-24-1510

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We present a deterministic framework for preparing an arbitrary three-qubit pure state. To leverage entanglement structure in the state-preparation task, we classify three-qubit pure states into five types with respect to a 1∣21|21∣2 bipartition. Given a target state specified by its amplitudes, we provide concrete criteria and concurrence-based tests that determine its type. For each type, we derive an explicit circuit template composed of elementary single-qubit rotations and CNOT gates, with gate parameters determined systematically from the Schmidt decomposition. The full construction is described step by step from the target amplitudes, with no procedural ambiguity. As an application, we further group frequently encountered three-qubit pure states in quantum information into four classes and provide an explicit circuit for each class. Compared with prior approaches, our circuits are designed for practical use: they admit a direct algorithmic instantiation, use only CNOT gates between adjacent qubits, and for certain classes achieve smaller gate counts and circuit depth.
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