By: Dmitry Budker, Valerie Domcke, Joachim Kopp, Oleg Tretiak
Gravitational waves affect the propagation of electromagnetic waves in laser cavities, modulating the frequency of emitted photons. We use this effect to search for high-frequency gravitational waves between 100 kHz and 100 MHz using optical precision spectroscopy. Our limits constrain much of this frequency range for the first time. We discuss future improvements of the technique, which we expect to enhance the sensitivity by eight orders of... more
Gravitational waves affect the propagation of electromagnetic waves in laser cavities, modulating the frequency of emitted photons. We use this effect to search for high-frequency gravitational waves between 100 kHz and 100 MHz using optical precision spectroscopy. Our limits constrain much of this frequency range for the first time. We discuss future improvements of the technique, which we expect to enhance the sensitivity by eight orders of magnitude, and to extend the frequency coverage up to at least 1 GHz. less
By: Dmitry Budker, Valerie Domcke, Joachim Kopp, Oleg Tretiak
Gravitational waves affect the propagation of electromagnetic waves in laser cavities, modulating the frequency of emitted photons. We use this effect to search for high-frequency gravitational waves between 100 kHz and 100 MHz using optical precision spectroscopy. Our limits constrain much of this frequency range for the first time. We discuss future improvements of the technique, which we expect to enhance the sensitivity by eight orders of... more
Gravitational waves affect the propagation of electromagnetic waves in laser cavities, modulating the frequency of emitted photons. We use this effect to search for high-frequency gravitational waves between 100 kHz and 100 MHz using optical precision spectroscopy. Our limits constrain much of this frequency range for the first time. We discuss future improvements of the technique, which we expect to enhance the sensitivity by eight orders of magnitude, and to extend the frequency coverage up to at least 1 GHz. less
By: Abhijit Chakraborty, Bharath Sambasivam, Karunya Shirali, Hunter Nelson, Mafalda Ramôa, Sophia E. Economou, Edwin Barnes
We propose an efficient algorithm based on shadow Hamiltonian simulation to approximately simulate the real-time dynamics of observables under time-independent Hamiltonians. Shadow Hamiltonian simulation works at the level of the operator algebra generated by the observables through commutators with the Hamiltonian. Exactly encoding the quantum state in this picture is generally inefficient for interacting systems due to the exponential growt... more
We propose an efficient algorithm based on shadow Hamiltonian simulation to approximately simulate the real-time dynamics of observables under time-independent Hamiltonians. Shadow Hamiltonian simulation works at the level of the operator algebra generated by the observables through commutators with the Hamiltonian. Exactly encoding the quantum state in this picture is generally inefficient for interacting systems due to the exponential growth of the operator algebra. Our algorithm overcomes this bottleneck by systematically identifying the elements of the algebra most relevant to the target observables. This targeted approach is a controlled approximation that yields a highly efficient quantum state encoding that substantially reduces the size of the qubit register required to perform the time evolution using the shadow Hamiltonian. We propose two main pruning schemes, one based on a predefined operator basis and another on a constructed Krylov basis. We also present a hybrid scheme that builds a Krylov basis within a pruned algebra in the predefined basis. We benchmark our algorithm using lattice spin systems in one and two dimensions, for both one- and higher-point correlators as observables. less
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Coherent Quantum Schrodinger Bridge: Two-Boundary Optimal Control for Quantum Algorithm Design
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By: Masayuki Ohzeki
Quantum algorithms are intrinsically two-boundary processes: an input state is prepared, and an output state or subspace is selected as the computational answer. We formulate this observation as a coherent Quantum Schrödinger Bridge (QSB), a pure-state Hamiltonian counterpart of Schrödinger bridge theory in which the endpoint constraint is imposed on state vectors and the transport cost is the quadratic control action. In this setting Aharono... more
Quantum algorithms are intrinsically two-boundary processes: an input state is prepared, and an output state or subspace is selected as the computational answer. We formulate this observation as a coherent Quantum Schrödinger Bridge (QSB), a pure-state Hamiltonian counterpart of Schrödinger bridge theory in which the endpoint constraint is imposed on state vectors and the transport cost is the quadratic control action. In this setting Aharonov's two-state vector becomes the natural optimal-control pair: a forward state from the input and a backward state from the target. Pontryagin's principle then yields a universal optimal Hamiltonian whose weak value is purely imaginary in the geodesic gauge. Thus weak values are not an auxiliary interpretation; they are the local response functions that quantify the drift of the pre-selected state toward the post-selected boundary. Applying this framework to unstructured search, periodicity finding, and matrix arithmetic, we reconstruct Grover's algorithm, the quantum Fourier transform underlying Shor's algorithm, and quantum singular value transformation (QSVT). The usual circuit components -- oracles, diffusion reflections, controlled phases, and signal-processing rotations -- emerge as Lie-algebraic syntheses of the optimal weak-value drift. This perspective unifies distinct algorithmic paradigms into a single geometric principle: algorithm design is the problem of choosing computational boundary conditions and realizing the corresponding optimal flow. less