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An efficient explicit implementation of a near-optimal quantum algorithm for simulating linear dissipative differential equations
We propose an efficient block-encoding technique for the implementation of the Linear Combination of Hamiltonian Simulations (LCHS) for simulating dissipative initial-value problems. This algorithm approximates a target nonunitary operator as a weighted sum of Hamiltonian evolutions, thereby emulating a dissipative problem by mixing various time scales. We introduce an efficient encoding of the LCHS into a quantum circuit based on a simple coordinate transformation that turns the dependence on the summation index into a trigonometric function. Classically, this method is equivalent to the use of a highly accurate Fejér-Clenshaw-Curtis quadrature formula. Quantumly, this significantly simplifies block-encoding of a dissipative problem and allows one to perform an exponential number of Hamiltonian simulations by a single Quantum Signal Processing (QSP) circuit. The resulting LCHS circuit has high success probability and the selector scales logarithmically with the number of terms in the LCHS sum and linearly with time. Careful analysis of error convergence proves that this method is more efficient than other LCHS circuits that have recently appeared in the literature. We verify the quantum circuit and its scaling by simulating it on a digital emulator of fault-tolerant quantum computers and, as a test problem, solve the advection-diffusion equation. The proposed algorithm can be used for simulating a wide class of nonunitary initial-value problems including the Liouville equation with added dissipation and linear embeddings of nonlinear systems, such as the Koopman-von Neumann and Carleman embeddings.
Optimized Quantum Phase Estimation for Simulating Electronic States in Various Energy Regimes
While quantum algorithms for simulation exhibit better asymptotic scaling than their classical counterparts, they currently cannot be implemented on real-world devices. Instead, chemists and computer scientists rely on costly classical simulations of these quantum algorithms. In particular, the quantum phase estimation (QPE) algorithm is among several approaches that have attracted much attention in recent years for its genuine quantum character. However, it is memory-intensive to simulate and intractable for moderate system sizes. Herein, this paper discusses the performance and applicability of QPESIM, a new simulation of the QPE algorithm designed to take advantage of modest computational resources. In particular, we demonstrate the versatility of QPESIM in simulating various electronic states by examining the ground and core-level states of H 2 O. For these states, we also discuss the effect of the active-space size on the quality of the calculated energies. For the high-energy core-level states, we demonstrate that new QPE simulations for active spaces defined by 15 active orbitals significantly reduce the errors in core-level excitation energies compared to earlier QPE simulations using smaller active spaces.
Characterization of control noise effects in optimal quantum unitary dynamics
Not Available
Nearly Optimal Quantum Algorithm for Estimating Multiple Expectation Values
Not Available
Threshold-Based Quantum Optimization
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Using Reinforcement Learning to Optimize Quantum Circuits in the Presence of Noise
As we move towards devices which utilize more qubits, it becomes increasing more important to map quantum circuits in a way that uses resources efficiently as well as maximizes the reliability of the results of that circuit. To this end, we will need to rely on heuristic algorithms, specifically reinforcement learning (RL) as a method of building quantum circuits based on observations of the noise characteristics in its environment.
Optimizing Quantum Circuit Layout Using Reinforcement Learning
Presentation slides for Summer Internships in Science and Technology (SIST) End of Term Activities 2020.
Lyapunov control-inspired protocol for quantum optimization.
Abstract not provided.
Optimal Quantum Transfer from Input Flying Qubit to Lossy Memory.
Abstract not provided.