Algebraic Compression of Quantum Circuits for Hamiltonian Evolution
- URL: http://arxiv.org/abs/2108.03282v2
- Date: Fri, 20 Aug 2021 17:51:20 GMT
- Title: Algebraic Compression of Quantum Circuits for Hamiltonian Evolution
- Authors: Efekan K\"okc\"u, Daan Camps, Lindsay Bassman, James K. Freericks,
Wibe A. de Jong, Roel Van Beeumen, Alexander F. Kemper
- Abstract summary: Unitary evolution under a time dependent Hamiltonian is a key component of simulation on quantum hardware.
We present an algorithm that compresses the Trotter steps into a single block of quantum gates.
This results in a fixed depth time evolution for certain classes of Hamiltonians.
- Score: 52.77024349608834
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Unitary evolution under a time dependent Hamiltonian is a key component of
simulation on quantum hardware. Synthesizing the corresponding quantum circuit
is typically done by breaking the evolution into small time steps, also known
as Trotterization, which leads to circuits whose depth scales with the number
of steps. When the circuit elements are limited to a subset of SU(4) -- or
equivalently, when the Hamiltonian may be mapped onto free fermionic models --
several identities exist that combine and simplify the circuit. Based on this,
we present an algorithm that compresses the Trotter steps into a single block
of quantum gates. This results in a fixed depth time evolution for certain
classes of Hamiltonians. We explicitly show how this algorithm works for
several spin models, and demonstrate its use for adiabatic state preparation of
the transverse field Ising model.
Related papers
- Gate Efficient Composition of Hamiltonian Simulation and Block-Encoding with its Application on HUBO, Fermion Second-Quantization Operators and Finite Difference Method [0.0]
This article proposes a simple formalism which unifies Hamiltonian simulation techniques from different fields.
It leads to a gate decomposition and a scaling different from the usual strategy.
It can significantly reduce the quantum circuit number of rotational gates, multi-qubit gates, and the circuit depth.
arXiv Detail & Related papers (2024-10-24T12:26:50Z) - Quantum emulation of the transient dynamics in the multistate
Landau-Zener model [50.591267188664666]
We study the transient dynamics in the multistate Landau-Zener model as a function of the Landau-Zener velocity.
Our experiments pave the way for more complex simulations with qubits coupled to an engineered bosonic mode spectrum.
arXiv Detail & Related papers (2022-11-26T15:04:11Z) - Characterization and Verification of Trotterized Digital Quantum
Simulation via Hamiltonian and Liouvillian Learning [0.0]
We propose Floquet Hamiltonian learning to reconstruct the experimentally realized Floquet Hamiltonian order-by-order.
We show that our protocol provides the basis for feedback-loop design and calibration of new types of quantum gates.
arXiv Detail & Related papers (2022-03-29T18:29:01Z) - Simulating the Mott transition on a noisy digital quantum computer via
Cartan-based fast-forwarding circuits [62.73367618671969]
Dynamical mean-field theory (DMFT) maps the local Green's function of the Hubbard model to that of the Anderson impurity model.
Quantum and hybrid quantum-classical algorithms have been proposed to efficiently solve impurity models.
This work presents the first computation of the Mott phase transition using noisy digital quantum hardware.
arXiv Detail & Related papers (2021-12-10T17:32:15Z) - An Algebraic Quantum Circuit Compression Algorithm for Hamiltonian
Simulation [55.41644538483948]
Current generation noisy intermediate-scale quantum (NISQ) computers are severely limited in chip size and error rates.
We derive localized circuit transformations to efficiently compress quantum circuits for simulation of certain spin Hamiltonians known as free fermions.
The proposed numerical circuit compression algorithm behaves backward stable and scales cubically in the number of spins enabling circuit synthesis beyond $mathcalO(103)$ spins.
arXiv Detail & Related papers (2021-08-06T19:38:03Z) - Synthesis of Quantum Circuits with an Island Genetic Algorithm [44.99833362998488]
Given a unitary matrix that performs certain operation, obtaining the equivalent quantum circuit is a non-trivial task.
Three problems are explored: the coin for the quantum walker, the Toffoli gate and the Fredkin gate.
The algorithm proposed proved to be efficient in decomposition of quantum circuits, and as a generic approach, it is limited only by the available computational power.
arXiv Detail & Related papers (2021-06-06T13:15:25Z) - Fast-forwarding quantum evolution [0.2621730497733946]
We show that certain quantum systems can be simulated with gate complexity that is sublinear in the evolution time.
We provide a definition of fast-forwarding that considers the model of quantum computation, the Hamiltonians that induce the evolution, and the properties of the initial states.
arXiv Detail & Related papers (2021-05-15T22:41:28Z) - 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) - Low-depth Hamiltonian Simulation by Adaptive Product Formula [3.050399782773013]
Various Hamiltonian simulation algorithms have been proposed to efficiently study the dynamics of quantum systems on a quantum computer.
Here, we propose an adaptive approach to construct a low-depth time evolution circuit.
Our work sheds light on practical Hamiltonian simulation with noisy-intermediate-scale-quantum devices.
arXiv Detail & Related papers (2020-11-10T18:00:42Z) - Inverse iteration quantum eigensolvers assisted with a continuous
variable [0.0]
We propose inverse iteration quantum eigensolvers, which exploit the power of quantum computing for the classical inverse power iteration method.
A key ingredient is constructing an inverse Hamiltonian as a linear combination of coherent Hamiltonian evolution.
We demonstrate the quantum algorithm with numerical simulations under finite squeezing for various physical systems.
arXiv Detail & Related papers (2020-10-07T07:31:11Z)
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.