Observing a Quantum Measurement

Lawrence, Jay

doi:10.1007/s10701-021-00522-0

Cited by 4 publications

(6 citation statements)

References 37 publications

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“…where ⊗ denote a tensor product, A † is the adjoin of A, and P is the qubit pointer [28,29]. If we simulate the Hamiltonian H in ( 27) with the initial state |z⟩ |z⟩ |0⟩ P in a quantum computer, the quantum system will evolve in accordance with H for a time step 𝜖 following (19) to reach the following steady-state |Ψ⟩ [21] (see Appendix A.2):…”

Section: Simulating State Function In a Quantum Computermentioning

confidence: 99%

Solving differential‐algebraic equations in power system dynamic analysis with quantum computing

Tran,

Nguyen,

et al. 2024

Energy Conversion and Econom

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Power system dynamics are generally modeled by high dimensional nonlinear differential‐algebraic equations (DAEs) given a large number of components forming the network. These DAEs' complexity can grow exponentially due to the increasing penetration of distributed energy resources, whereas their computation time becomes sensitive due to the increasing interconnection of the power grid with other energy systems. This paper demonstrates the use of quantum computing algorithms to solve DAEs for power system dynamic analysis. We leverage a symbolic programming framework to equivalently convert the power system's DAEs into ordinary differential equations (ODEs) using index reduction methods and then encode their data into qubits using amplitude encoding. The system nonlinearity is captured by Hamiltonian simulation with truncated Taylor expansion so that state variables can be updated by a quantum linear equation solver. Our results show that quantum computing can solve the power system's DAEs accurately with a computational complexity polynomial in the logarithm of the system dimension. We also illustrate the use of recent advanced tools in scientific machine learning for implementing complex computing concepts, that is, Taylor expansion, DAEs/ODEs transformation, and quantum computing solver with abstract representation for power engineering applications.

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Section: Simulating State Function In a Quantum Computermentioning

confidence: 99%

Solving differential‐algebraic equations in power system dynamic analysis with quantum computing

Tran,

Nguyen,

et al. 2024

Energy Conversion and Econom

View full text Add to dashboard Cite

show abstract

“…We follow the steps of Ref. [17], which treated the d = 2 case. We choose the initial spin state to maximize the entanglement which will develop with the ancilla qubit system.…”

Section: The Quantum Pointermentioning

confidence: 99%

“…This section comprises a generalization of the Ref. [17] treatment to arbitrary nonbinary spins. It is remarkable that the spin-ancilla system is again described completely by three commuting observables -two for collapse properties and one for the superposition property.…”

Section: A Nondestructive Measurementsmentioning

confidence: 99%

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Pointers for Quantum Measurement Theory

Lawrence¹

2022

Preprint

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In the iconic measurements of atomic spin-1/2 or photon polarization, one employs two spatially separated and noninteracting detectors. Each detector is binary, registering the presence or absence of the atom or the photon. For measurements on a d-state particle, we recast the standard von Neumann measurement formalism by replacing the familiar pointer variable with an array of such detectors, one for each of the d possible outcomes. We show that the unitary dynamics of the pre-measurement process restricts the detector outputs to the subspace of single outcomes, so that the pointer emerges from the apparatus. We propose a physical extension of this apparatus which replaces each detector with an ancilla qubit coupled to a readout device. This explicitly separates the pointer into distinct quantum and (effectively) classical parts, and delays the quantum to classical transition. As a result, one not only recovers the collapse scenario of an ordinary apparatus, but one can also observe a superposition of the quantum pointer states.

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“…There are, of course, many other suggested solutions to the measurement problem [10,11] with some of these distinct from those mentioned above and some novel modifications [12,13,14,15,16]. Here, we resolve the measurement problem by postulating the existence of unique phase-sets that are tied to the eigenvectors of a Hamiltonian.…”

Section: Introductionmentioning

confidence: 99%

Collapse of the Wavefunction Following Destructive Interference with a Macroscopic Measuring Device

Camparo

2023

Preprint

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Measurement in quantum mechanics is a long-standing issue, and the measurement problem consists of essentially two parts: 1) no matter what the initial wavefunction of an object, the result of a measurement always results in the observation of a single eigenstate (i.e., “wavefunction collapse”), and 2) once the wavefunction collapses it remains collapsed. Though there have been a number of proposed solutions to the measurement problem, none to date is without debate. Here we discuss a solution to the measurement problem that avoids some others’ difficulties. We assume that for every eigenvector of an operator there is a set of unique discrete phases, and that the phase sets among eigenvectors are disjoint. With this hypothesis it is possible to show that wavefunction collapse is a consequence of destructive interference when a quantum object interacts with the large set of “quantum-measurement mapping operators” that must comprise a classical measuring device.

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Observing a Quantum Measurement

Cited by 4 publications

References 37 publications

Solving differential‐algebraic equations in power system dynamic analysis with quantum computing

Solving differential‐algebraic equations in power system dynamic analysis with quantum computing

Pointers for Quantum Measurement Theory

Collapse of the Wavefunction Following Destructive Interference with a Macroscopic Measuring Device

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