Search for: All records

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 

Mu2e and COMET will search for electrons produced via the neutrinoless conversion of stopped muons bound in 1s atomic orbits of ${}^{27}\mathrm{Al}$, improving existing limits on charged lepton flavor violation (CLFV) by roughly four orders of magnitude. Conventionally, $\mu \to e$conversion experiments are optimized to detect electrons originating from transitions where the nucleus remains in the ground state, thereby maximizing the energy of the outgoing electron. Clearly, detection of a positive signal in forthcoming experiments would stimulate additional work—including subsequent conversion experiments using complementary nuclear targets—to further constrain the new physics responsible for CLFV. Here we argue that additional information can be extracted without the need for additional experiments, by considering inelastic conversion in ${}^{27}\mathrm{Al}$. Transitions to low-lying nuclear excited states can modify the near-endpoint spectrum of conversion electrons, with the ratio of the elastic and inelastic responses being sensitive to the underlying CLFV operator. We extend the nuclear effective theory of $\mu \to e$conversion to the inelastic case, which adds five new response functions to the six that arise for the elastic process. We evaluate these nuclear response functions in ${}^{27}\mathrm{Al}$and calculate the resulting conversion-electron signal, taking into account the resolution anticipated in Mu2e/COMET. We find that ${}^{27}\mathrm{Al}$is an excellent target choice from the perspective of the new information that can be obtained from inelastic $\mu \to e$conversion. Published by the American Physical Society2025 

The Mu2e and COMET experiments are expected to improve existing limits on charged lepton flavor violation (CLFV) by roughly 4 orders of magnitude. $\mu \to e$conversion experiments are typically optimized for electrons produced without nuclear excitation, as this maximizes the electron energy and minimizes backgrounds from the free decay of the muon. Here we argue that Mu2e and COMET will be able to extract additional constraints on CLFV from inelastic $\mu \to e$conversion, given the ${}^{27}\mathrm{Al}$target they have chosen and backgrounds they anticipate. We describe CLFV scenarios in which inelastic CLFV can induce measurable distortions in the near-endpoint spectrum of conversion electrons, including cases where certain contributing operators cannot be probed in elastic $\mu \to e$conversion. We extend the nonrelativistic EFT treatment of elastic $\mu \to e$conversion to include the new nuclear operators needed for the inelastic process, evaluate the associated nuclear response functions, and describe several new-physics scenarios where the inelastic process can provide additional information on CLFV. Published by the American Physical Society2024 

A<sc>bstract</sc> We present theoretical predictions forμ→econversion rates using a tower of effective field theories connecting the UV to nuclear physics scales. The interactions in nuclei are described using a recently developed nonrelativistic effective theory (NRET) that organizes contributions according to bound nucleon and muon velocities,$$ {\overrightarrow{v}}_N $$ ${\overrightarrow{v}}_N$and$$ {\overrightarrow{v}}_{\mu } $$ ${\overrightarrow{v}}_{\mu }$, with$$ \left|{\overrightarrow{v}}_N\right| $$ $\left({\overrightarrow{v}}_N\right)$>$$ \left|{\overrightarrow{v}}_{\mu}\right| $$ $\left({\overrightarrow{v}}_{\mu }\right)$. To facilitate the top-down matching, we enlarge the set of Lorentz covariant nucleon-level interactions mapped onto the NRET operators to include those mediated by tensor interactions, in addition to the scalar and vector interactions already considered previously, and then match NRET nonperturbatively onto the Weak Effective Theory (WET). At the scaleμ≈ 2 GeV WET is formulated in terms ofu,d,squarks, gluons and photons as the light degrees of freedom, along with the flavor-violating leptonic current. We retain contributions from WET operators up to dimension 7, which requires the full set of 26 NRET operators. The results are encoded in the open-source Python- and Mathematica-based software suite MuonBridge, which we make available to the theoretical and experimental communities interested inμ→econversion. 

The Mu2E and COMET μ→e collaborations plan to advance branching ratio sensitivities by four orders of magnitude, further constraining new sources of charged lepton flavor violation (CLFV). We formulate a non-relativistic nucleon-level effective theory for this process, in order to clarify what can and cannot be learned about CLFV operator coefficients from elastic μ→e conversion. Utilizing state-of-the-art shell model wave functions, we derive bounds on operator coefficients from existing μ→e conversion results, and estimate the improvement in these bounds that will be possible if Mu2E and COMET reach their design goals. In the conversion process, we employ a treatment of the lepton Coulomb physics that is very accurate, yet yields transparent results and preserves connections to standard-model processes like β decay and μ capture. The formulation provides a bridge between the nuclear physics needed in form factor evaluations and the particle physics needed to relate low-energy constraints from μ→e conversion to UV sources of CLFV.