Quantum algorithm for preparing the ground state of a system via resonance transition

Wang, Hefeng

doi:10.1038/s41598-017-16396-0

Cited by 9 publications

(3 citation statements)

References 27 publications

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“…We also point out quantum imaginary time evolution [6] which involves a classical minimization routine based on state tomography to construct unitary circuits to implement non-unitary operators. This is also in contrast to a strictly "gate-based" method to calculate the ground state of a quantum Hamiltonian with some finite probability [7][8][9][10][11]. Nor is what we propose a quantum Metropolis algorithm, where a thermal quantum state is sampled [12,13], or a state is adiabatically annealed [14][15][16][17] to its ground state.…”

Section: Introductionmentioning

confidence: 91%

Metropolis-style random sampling of quantum gates for the estimation of low-energy observables

Unmuth-Yockey

2021

Preprint

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Section: Introductionmentioning

confidence: 91%

Metropolis-style random sampling of quantum gates for the estimation of low-energy observables

Unmuth-Yockey

2021

Preprint

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“…Simulating an entire bath would require an impractically large quantum register; however it has long been suggested that this may be mimicked by coupling to a single qubit which may be reset to its ground state with sufficient frequency [3]. This idea has been since studied in digital quantum computing for the initialization of * polla@lorentz.leidenuniv.nl quantum devices [17,18] and as an inspiration of an algorithm based on resonant transitions and postselection [19]. This idea was also explored in analog simulation settings, for the preparation of physical [20] and artificial [21,22] ground states.…”

Section: Introductionmentioning

confidence: 99%

Quantum digital cooling

2021

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We introduce a method for digital preparation of ground states of simulated Hamiltonians, inspired by cooling in nature and adapted to leverage the capabilities of digital quantum hardware. The cold bath is simulated by a single ancillary qubit, which is reset periodically and coupled to the system nonperturbatively. Studying this cooling method on a 1-qubit system toy model, we optimize two cooling protocols based on weak-coupling and strong-coupling approaches. Extending the insight from the 1-qubit system model, we develop two scalable protocols for larger systems. The LogSweep protocol extends the weak-coupling approach by sweeping energies to resonantly match any targeted transition. We test LogSweep on the 1D transverse-field Ising model, demonstrating approximate ground-state preparation with an error that can be made polynomially small in the computation time for all three phases of the system. The BangBang protocol extends the strong-coupling approach, and exploits a heuristics for local Hamiltonians to maximize the probability of deexciting system transitions in the shortest possible time. Although this protocol does not promise long-time convergence, it allows for a rapid cooling to an approximation of the ground state, making this protocol appealing for near-term demonstrations.

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“…Recently, algorithms that mimic cooling by coupling to a simulated low-entropy bath [18][19][20][21][22][23][24] have been proposed as alternative routes that may overcome some of these challenges.…”

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confidence: 99%

Programmable adiabatic demagnetization for systems with trivial and topological excitations

Matthies¹,

Rudner²,

Rosch³

et al. 2022

Preprint

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We propose a simple, robust protocol to prepare a low-energy state of an arbitrary Hamiltonian on a quantum computer or programmable quantum simulator. The protocol is inspired by the adiabatic demagnetization technique, used to cool solid-state systems to extremely low temperatures. A fraction of the qubits (or spins) is used to model a spin bath that is coupled to the system. By an adiabatic ramp down of a simulated Zeeman field acting on the bath spins, energy and entropy are extracted from the system. The bath spins are then measured and reset to the polarized state, and the process is repeated until convergence to a low-energy steady state is achieved. We demonstrate the protocol via application to the quantum Ising model. We study the protocol's performance in the presence of noise and show how the information from the measurement of the bath spins can be used to monitor the cooling process. The performance of the algorithm depends on the nature of the excitations of the system; systems with non-local (topological) excitations are more difficult to cool than those with local excitations. We explore the possible mitigation of this problem by trapping topological excitations.

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Quantum algorithm for preparing the ground state of a system via resonance transition

Cited by 9 publications

References 27 publications

Metropolis-style random sampling of quantum gates for the estimation of low-energy observables

Metropolis-style random sampling of quantum gates for the estimation of low-energy observables

Quantum digital cooling

Programmable adiabatic demagnetization for systems with trivial and topological excitations

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