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1. Toward extracting the scattering phase shift from integrated correlation functions. II. A relativistic lattice field theory model

   https://doi.org/10.1103/PhysRevD.110.014504  

   Guo, Peng (July 2024, Physical Review D)

   In the present work, a relativistic relation that connects the difference of interacting and noninteracting integrated two-particle correlation functions in finite volume to infinite volume scattering phase shift through an integral is derived. We show that the difference of integrated finite volume correlation functions converges rapidly to its infinite volume limit as the size of the periodic box is increased. The fast convergence of our proposed formalism is illustrated by analytic solutions of a contact interaction model, the perturbation theory calculation, and also the Monte Carlo simulation of a complex ${\varphi }^4$lattice field theory model. Published by the American Physical Society2024 

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2. Toward extracting scattering phase shift from integrated correlation functions. III. Coupled channels

   https://doi.org/10.1103/PhysRevD.111.054506  

   Guo, Peng; Lee, Frank X (March 2025, Physical Review D)

   The formalism developed in the preceding papers that connects integrated correlation function of a trapped two-particle system to infinite volume scattering phase shift is further extended to coupled-channel systems in the present work. Using a trapped nonrelativistic two-channel system as an example, a new relation is derived that retains the same structure as in the single channel, and has explicit dependence on the phase shifts in both channels but not on the inelasticity. The relation is illustrated by a exactly solvable coupled-channel quantum mechanical model with contact interactions. It is further validated by path integral Monte Carlo simulation of a quasi-one-dimensional model that can admit general interaction potentials. In all cases, we found rapid convergence to the infinite volume limit as the trap size is increased, even at short times, making it potentially a good candidate to overcome signal-to-noise issues in Monte Carlo applications. Published by the American Physical Society2025 

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3. Single-ancilla ground state preparation via Lindbladians

   https://doi.org/10.1103/PhysRevResearch.6.033147  

   Ding, Zhiyan; Chen, Chi-Fang; Lin, Lin (August 2024, Physical Review Research)

   We design a quantum algorithm for ground state preparation in the early fault tolerant regime. As a Monte Carlo style quantum algorithm, our method features a Lindbladian where the target state is stationary. The construction of this Lindbladian is algorithmic and should not be seen as a specific approximation to some weakly coupled system-bath dynamics in nature. Our algorithm can be implemented using just one ancilla qubit and efficiently simulated on a quantum computer. It can prepare the ground state even when the initial state has zero overlap with the ground state, bypassing the most significant limitation of methods like quantum phase estimation. As a variant, we also propose a discrete-time algorithm, demonstrating even better efficiency and providing a near-optimal simulation cost depending on the desired evolution time and precision. Numerical simulations using Ising and Hubbard models demonstrate the efficacy and applicability of our method. Published by the American Physical Society2024 

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4. Generalized Cycle Benchmarking Algorithm for Characterizing Midcircuit Measurements

   https://doi.org/10.1103/PRXQuantum.6.010310  

   Zhang, Zhihan; Chen, Senrui; Liu, Yunchao; Jiang, Liang (January 2025, PRX Quantum)

   Midcircuit measurements (MCMs) are crucial ingredients in the development of fault-tolerant quantum computation. While there have been rapid experimental progresses in realizing MCMs, a systematic method for characterizing noisy MCMs is still under exploration. In this work, we develop a cycle benchmarking (CB)-type algorithm to characterize noisy MCMs. The key idea is to use a joint Fourier transform on the classical and quantum registers and then estimate parameters in the Fourier space, analogous to Pauli fidelities used in CB-type algorithms for characterizing the Pauli-noise channel of Clifford gates. Furthermore, we develop a theory of the noise learnability of MCMs, which determines what information can be learned about the noise model (in the presence of state preparation and terminating measurement noise) and what cannot, which shows that all learnable information can be learned using our algorithm. As an application, we show how to use the learned information to test the independence between measurement noise and state-preparation noise in an MCM. Finally, we conduct numerical simulations to illustrate the practical applicability of the algorithm. Similar to other CB-type algorithms, we expect the algorithm to provide a useful toolkit that is of experimental interest. Published by the American Physical Society2025 

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5. Exact block encoding of imaginary time evolution with universal quantum neural networks

   https://doi.org/10.1103/PhysRevResearch.7.013306  

   Rrapaj, Ermal; Rule, Evan (March 2025, Physical Review Research)

   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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