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We develop a constructive approach to generate quantum neural networks capable of representing the exact thermal states of all many-body qubit Hamiltonians. The Trotter expansion of the imaginary time propagator is implemented through an exact block encoding by means of a unitary, restricted Boltzmann machine architecture. Marginalization over the hidden-layer neurons (auxiliary qubits) creates the nonunitary action on the visible layer. Then, we introduce a unitary deep Boltzmann machine architecture in which the hidden-layer qubits are allowed to couple laterally to other hidden qubits. We prove that this wave-function is closed under the action of the imaginary time propagator and, more generally, can represent the action of a universal set of quantum gate operations. We provide analytic expressions for the coefficients for both architectures, thus enabling exact network representations of thermal states without stochastic optimization of the network parameters. In the limit of large imaginary time, the yields the ground state of the system. The number of qubits grows linearly with the number of interactions and total imaginary time for a fixed interaction order. Both networks can be readily implemented on quantum hardware via midcircuit measurements of auxiliary qubits. If only one auxiliary qubit is measured and reset, the circuit depth scales linearly with imaginary time and number of interactions, while the width is constant. Alternatively, one can employ a number of auxiliary qubits linearly proportional to the number of interactions, and circuit depth grows linearly with imaginary time only. Every midcircuit measurement has a postselection success probability, and the overall success probability is equal to the product of the probabilities of the midcircuit measurements. Published by the American Physical Society2025
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This content will become publicly available on April 22, 2026
Quantum Circuit and Mapping Algorithms for Wavepacket Dynamics: Case Study of Anharmonic Hydrogen Bonds in Protonated and Hydroxide Water Clusters
The accurate computational study of wavepacketnuclear dynamics is considered to be a classically intractableproblem, particularly with increasing dimensions. Here, we presenttwo algorithms that, in conjunction with other methods developedby us, may result in one set of contributions for performingquantum nuclear dynamics in arbitrary dimensions. For one of thetwo algorithms discussed here, we present a direct map betweenthe Born−Oppenheimer Hamiltonian describing the nuclearwavepacket time evolution and the control parameters of a spin−lattice Hamiltonian that describes the dynamics of qubit states in anion-trap quantum computer. This map is exact for three qubits, andwhen implemented, the dynamics of the spin states emulates thoseof the nuclear wavepacket in a continuous representation. However, this map becomes approximate as the number of qubits grows.In a second algorithm, we present a general quantum circuit decomposition formalism for such problems using a method called theQuantum Shannon Decomposition. This algorithm is more robust and is exact for any number of qubits at the cost of increasedcircuit complexity. The resultant circuit is implemented on IBM’s quantum simulator (QASM) for 3−7 qubits, without using a noisemodel so as to test the intrinsic accuracy of the method. In both cases, the wavepacket dynamics is found to be in good agreementwith the classical propagation result and the corresponding vibrational frequencies obtained from the wavepacket density timeevolution are in agreement to within a few tenths of a wavenumber.
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- PAR ID:
- 10608146
- Publisher / Repository:
- ACS Publications
- Date Published:
- Journal Name:
- Journal of Chemical Theory and Computation
- Volume:
- 21
- Issue:
- 8
- ISSN:
- 1549-9618
- Page Range / eLocation ID:
- 3814 to 3831
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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