Parallel-in-time quantum simulation via Page and Wootters quantum time
- URL: http://arxiv.org/abs/2308.12944v1
- Date: Thu, 24 Aug 2023 17:32:41 GMT
- Title: Parallel-in-time quantum simulation via Page and Wootters quantum time
- Authors: N. L. Diaz, Paolo Braccia, Martin Larocca, J.M. Matera, R. Rossignoli,
M. Cerezo
- Abstract summary: We present quantum algorithms for parallel-in-time simulations inspired by the Page and Wooters formalism.
We show that our algorithms can compute temporal properties over $N$ different times of many-body systems.
We rigorously prove that the entanglement created between the system qubits and the clock qubits has operational meaning.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In the past few decades, researchers have created a veritable zoo of quantum
algorithm by drawing inspiration from classical computing, information theory,
and even from physical phenomena. Here we present quantum algorithms for
parallel-in-time simulations that are inspired by the Page and Wooters
formalism. In this framework, and thus in our algorithms, the classical
time-variable of quantum mechanics is promoted to the quantum realm by
introducing a Hilbert space of "clock" qubits which are then entangled with the
"system" qubits. We show that our algorithms can compute temporal properties
over $N$ different times of many-body systems by only using $\log(N)$ clock
qubits. As such, we achieve an exponential trade-off between time and spatial
complexities. In addition, we rigorously prove that the entanglement created
between the system qubits and the clock qubits has operational meaning, as it
encodes valuable information about the system's dynamics. We also provide a
circuit depth estimation of all the protocols, showing an exponential advantage
in computation times over traditional sequential in time algorithms. In
particular, for the case when the dynamics are determined by the Aubry-Andre
model, we present a hybrid method for which our algorithms have a depth that
only scales as $\mathcal{O}(\log(N)n)$. As a by product we can relate the
previous schemes to the problem of equilibration of an isolated quantum system,
thus indicating that our framework enable a new dimension for studying
dynamical properties of many-body systems.
Related papers
- Combining Matrix Product States and Noisy Quantum Computers for Quantum
Simulation [0.0]
Matrix Product States (MPS) and Operators (MPO) have been proven to be a powerful tool to study quantum many-body systems.
We show that using classical knowledge in the form of tensor networks provides a way to better use limited quantum resources.
arXiv Detail & Related papers (2023-05-30T17:21:52Z) - Classical Algorithm for the Mean Value problem over Short-Time
Hamiltonian Evolutions [0.0]
This article presents an efficient classical algorithm for simulating time-dependent quantum mechanical Hamiltonians over constant periods of time.
We use Lieb-Robinson type bounds to limit the evolution of local operators within a lightcone.
This allows us to divide the task of simulating a large quantum system into smaller systems that can be handled on normal classical computers.
arXiv Detail & Related papers (2023-01-26T21:19:19Z) - Algorithmic Shadow Spectroscopy [0.0]
We present a simulator-agnostic quantum algorithm for estimating energy gaps using very few circuit repetitions (shots) and no extra resources (ancilla qubits)
We demonstrate that our method is intuitively easy to use in practice, robust against gate noise, to a new type of algorithmic error mitigation technique, and uses orders of magnitude fewer number of shots than typical near-term quantum algorithms -- as low as 10 shots per timestep is sufficient.
arXiv Detail & Related papers (2022-12-21T14:23:48Z) - Quantum Clustering with k-Means: a Hybrid Approach [117.4705494502186]
We design, implement, and evaluate three hybrid quantum k-Means algorithms.
We exploit quantum phenomena to speed up the computation of distances.
We show that our hybrid quantum k-Means algorithms can be more efficient than the classical version.
arXiv Detail & Related papers (2022-12-13T16:04:16Z) - Entanglement and coherence in Bernstein-Vazirani algorithm [58.720142291102135]
Bernstein-Vazirani algorithm allows one to determine a bit string encoded into an oracle.
We analyze in detail the quantum resources in the Bernstein-Vazirani algorithm.
We show that in the absence of entanglement, the performance of the algorithm is directly related to the amount of quantum coherence in the initial state.
arXiv Detail & Related papers (2022-05-26T20:32:36Z) - A quantum generative model for multi-dimensional time series using
Hamiltonian learning [0.0]
We propose using the inherent nature of quantum computers to simulate quantum dynamics as a technique to encode such features.
We use the learned model to generate out-of-sample time series and show that it captures unique and complex features of the learned time series.
We experimentally demonstrate the proposed algorithm on an 11-qubit trapped-ion quantum machine.
arXiv Detail & Related papers (2022-04-13T03:06:36Z) - Efficient Fully-Coherent Quantum Signal Processing Algorithms for
Real-Time Dynamics Simulation [3.3917542048743865]
We develop fully-coherent simulation algorithms based on quantum signal processing (QSP)
We numerically analyze these algorithms by applying them to the simulation of spin dynamics of the Heisenberg model.
arXiv Detail & Related papers (2021-10-21T17:56:33Z) - Quantum algorithms for quantum dynamics: A performance study on the
spin-boson model [68.8204255655161]
Quantum algorithms for quantum dynamics simulations are traditionally based on implementing a Trotter-approximation of the time-evolution operator.
variational quantum algorithms have become an indispensable alternative, enabling small-scale simulations on present-day hardware.
We show that, despite providing a clear reduction of quantum gate cost, the variational method in its current implementation is unlikely to lead to a quantum advantage.
arXiv Detail & Related papers (2021-08-09T18:00:05Z) - Fixed Depth Hamiltonian Simulation via Cartan Decomposition [59.20417091220753]
We present a constructive algorithm for generating quantum circuits with time-independent depth.
We highlight our algorithm for special classes of models, including Anderson localization in one dimensional transverse field XY model.
In addition to providing exact circuits for a broad set of spin and fermionic models, our algorithm provides broad analytic and numerical insight into optimal Hamiltonian simulations.
arXiv Detail & Related papers (2021-04-01T19:06:00Z) - Imaginary Time Propagation on a Quantum Chip [50.591267188664666]
Evolution in imaginary time is a prominent technique for finding the ground state of quantum many-body systems.
We propose an algorithm to implement imaginary time propagation on a quantum computer.
arXiv Detail & Related papers (2021-02-24T12:48:00Z) - Information Scrambling in Computationally Complex Quantum Circuits [56.22772134614514]
We experimentally investigate the dynamics of quantum scrambling on a 53-qubit quantum processor.
We show that while operator spreading is captured by an efficient classical model, operator entanglement requires exponentially scaled computational resources to simulate.
arXiv Detail & Related papers (2021-01-21T22:18:49Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.