Finite Imaginary-Time Evolution for Polynomial Unconstrained Binary Optimization
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arXiv
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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866909003782553600 |
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| author | Kim, Jaehee Kim, Juhyeon Lee, Gwonhak Baek, Kyunghyun Park, Daniel K. Bang, Jeongho Huh, Joonsuk |
| author_facet | Kim, Jaehee Kim, Juhyeon Lee, Gwonhak Baek, Kyunghyun Park, Daniel K. Bang, Jeongho Huh, Joonsuk |
| contents | Imaginary-time evolution is a standard primitive for ground-state preparation but is nonunitary, precluding direct quantum implementation. We develop Finite Imaginary-Time Evolution (FinITE), a finite-beta construction for diagonal Pauli-Z cost Hamiltonians arising from polynomial unconstrained binary optimization (PUBO) instances, including QUBO and HUBO cases. FinITE uses the linear-combination-of-unitaries (LCU) framework to implement a scaled imaginary-time propagator. The commuting Pauli-Z structure makes termwise block-encodings compose without product-formula error, and higher-order Pauli-Z terms are handled directly without quadratization. The structure yields an exact finite-beta identity between the LCU success probability and the ground-subspace fidelity. Combined with a gap-based fidelity lower bound, the identity yields a closed-form sufficient imaginary-time threshold beta-star for a chosen target fidelity. The threshold depends on estimates of the spectral gap and the initial ground-subspace overlap. Because the LCU success event is flagged by a known ancilla outcome, we integrate fixed-point amplitude amplification with an explicit query-complexity bound. Statevector simulations verify the identity on a five-vertex MaxCut (QUBO) and an eight-qubit cubic HUBO instance, and shot-based simulations on the MaxCut instance illustrate the predicted finite-beta threshold and amplification procedure. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_27482 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finite Imaginary-Time Evolution for Polynomial Unconstrained Binary Optimization Kim, Jaehee Kim, Juhyeon Lee, Gwonhak Baek, Kyunghyun Park, Daniel K. Bang, Jeongho Huh, Joonsuk Quantum Physics Imaginary-time evolution is a standard primitive for ground-state preparation but is nonunitary, precluding direct quantum implementation. We develop Finite Imaginary-Time Evolution (FinITE), a finite-beta construction for diagonal Pauli-Z cost Hamiltonians arising from polynomial unconstrained binary optimization (PUBO) instances, including QUBO and HUBO cases. FinITE uses the linear-combination-of-unitaries (LCU) framework to implement a scaled imaginary-time propagator. The commuting Pauli-Z structure makes termwise block-encodings compose without product-formula error, and higher-order Pauli-Z terms are handled directly without quadratization. The structure yields an exact finite-beta identity between the LCU success probability and the ground-subspace fidelity. Combined with a gap-based fidelity lower bound, the identity yields a closed-form sufficient imaginary-time threshold beta-star for a chosen target fidelity. The threshold depends on estimates of the spectral gap and the initial ground-subspace overlap. Because the LCU success event is flagged by a known ancilla outcome, we integrate fixed-point amplitude amplification with an explicit query-complexity bound. Statevector simulations verify the identity on a five-vertex MaxCut (QUBO) and an eight-qubit cubic HUBO instance, and shot-based simulations on the MaxCut instance illustrate the predicted finite-beta threshold and amplification procedure. |
| title | Finite Imaginary-Time Evolution for Polynomial Unconstrained Binary Optimization |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2604.27482 |