Related papers: Optimisation of Quantum Hamiltonian Evolution: Fro…
A potential approach for demonstrating quantum advantage is using quantum computers to simulate fermionic systems. Quantum algorithms for fermionic system simulation usually involve the Hamiltonian evolution and measurements. However, in…
Quantum computing promises transformative impacts in simulating Hamiltonian dynamics, essential for studying physical systems inaccessible by classical computing. However, existing compilation techniques for Hamiltonian simulation, in…
Variational compression can significantly lower implementation overheads for encoding the time evolution of Hamiltonians into quantum circuits. However, they usually lack global convergence guarantees and well-established scaling behavior.…
The physics of quantum mechanics is the inspiration for, and underlies, quantum computation. As such, one expects physical intuition to be highly influential in the understanding and design of many quantum algorithms, particularly…
The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly…
This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…
The real- and imaginary-time evolution of quantum states are powerful tools in physics, chemistry, and beyond, to investigate quantum dynamics, prepare ground states or calculate thermodynamic observables. On near-term devices, variational…
This work demonstrates that the Deutsch algorithm can be effectively modelled using a two-level harmonic oscillator within the second quantization formalism. By adopting this framework, evolution operators are derived. We present a…
Hamiltonian simulation is a central task in quantum computing, with wide-ranging applications in quantum chemistry, condensed matter physics, and combinatorial optimization. A fundamental challenge lies in approximating the unitary…
Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…
We develop a protocol for continuous operation of a quantum error correcting code for protection of coherent evolution due to an encoded Hamiltonian against environmental errors, using the three qubit bit flip code and bit flip errors as a…
We consider the task of simulating time evolution under a Hamiltonian $H$ within its low-energy subspace. Assuming access to a block-encoding of $H'=(H-E)/\lambda$ for some $E \in \mathbb R$, the goal is to implement an…
Recently double-bracket quantum algorithms have been proposed as a way to compile circuits for approximating eigenstates. Physically, they consist of appropriately composing evolutions under an input Hamiltonian together with diagonal…
An explicit algorithm for calculating the optimized Euler angles for both qubit state transfer and gate engineering given two arbitary fixed Hamiltonians is presented. It is shown how the algorithm enables us to efficiently implement single…
This work provides a rigorous and self-contained introduction to numerical methods for Hamiltonian simulation in quantum computing, with a focus on high-order product formulas for efficiently approximating the time evolution of quantum…
Grover's algorithm is one of the most important quantum algorithms, which performs the task of searching an unsorted database without a priori probability. Recently the adiabatic evolution has been used to design and reproduce quantum…
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical tradeoff between improved accuracy for finer…
We introduce a method to perform imaginary time evolution in a controllable quantum system using measurements and conditional unitary operations. By performing a sequence of weak measurements based on the desired Hamiltonian constructed by…
Quantum simulation promises to address many challenges in fields ranging from quantum chemistry to material science, and high-energy physics, and could be implemented in noisy intermediate-scale quantum devices. A challenge in building good…
Hamiltonian simulation, i.e., simulating the real time evolution of a target quantum system, is a natural application of quantum computing. Trotter-Suzuki splitting methods can generate corresponding quantum circuits; however, a faithful…