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Paper 1
Universal Quantum Random Access Memory: A Data-Independent Unitary with a Commuting-Projector Hamiltonian
Leonardo Bohac
- Year
- 2025
- Journal
- arXiv preprint
- DOI
- arXiv:2512.12999
- arXiv
- 2512.12999
Quantum random access memory (QRAM) is a central primitive for coherent data access in quantum algorithms, yet it remains controversial in practice because the wall-clock cost of "one lookup" can hide routing depth, control overhead, and geometric constraints. We present a universal QRAM construction (U-QRAM) in which the database is a physical memory register that participates in the lookup unitary as quantum control. This yields a single fixed, data-independent lookup unitary on $A \otimes D \otimes M$ that is correct for all basis-encoded databases. Our first contribution is an explicit, exact Hamiltonian realization: U-QRAM equals a single time-independent evolution $U_{QRAM} = \exp(-iH_{tot})$ where $H_{tot}$ is a sum of mutually commuting projector terms, one per memory cell, and the construction avoids control-dependent phase ambiguities. Our second contribution is an architectural sharpening: under unary (one-hot, mode-addressed) encoding of the address, each cell term becomes uniform and 3-local, delineating the most direct path toward constant-latency interpretations. We keep claims conservative by separating latency from work and stating explicit hardware assumptions required for constant wall-clock queries.
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Quantum Simulation of Nonlinear Dynamical Systems Using Repeated Measurement
Joseph Andress, Alexander Engel, Yuan Shi, Scott Parker
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.03838
- arXiv
- 2410.03838
We present a quantum algorithm based on repeated measurement to solve initial-value problems for nonlinear ordinary differential equations (ODEs), which may be generated from partial differential equations in plasma physics. We map a dynamical system to a Hamiltonian form, where the Hamiltonian matrix is a function of dynamical variables. To advance in time, we measure expectation values from the previous time step, and evaluate the Hamiltonian function classically, which introduces stochasticity into the dynamics. We then perform standard quantum Hamiltonian simulation over a short time, using the evaluated constant Hamiltonian matrix. This approach requires evolving an ensemble of quantum states, which are consumed each step to measure required observables. We apply this approach to the classic logistic and Lorenz systems, in both integrable and chaotic regimes. Out analysis shows that solutions' accuracy is influenced by both the stochastic sampling rate and the nature of the dynamical system.
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