Efficient Quantum Trace Estimation with Reconfigurable Real-Time
Circuits
- URL: http://arxiv.org/abs/2401.04176v1
- Date: Mon, 8 Jan 2024 19:00:06 GMT
- Title: Efficient Quantum Trace Estimation with Reconfigurable Real-Time
Circuits
- Authors: Yizhi Shen, Katherine Klymko, Eran Rabani, Daan Camps, Roel Van
Beeumen, Michael Lindsey
- Abstract summary: We introduce an efficient near-term quantum algorithm for computing the trace of a broad class of operators.
Our circuit is reconfigurable and suitable for realization on both digital and platforms.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: Recently, quantum algorithms that leverage real-time evolution under a
many-body Hamiltonian have proven to be exceptionally effective in estimating
individual eigenvalues near the edge of the Hamiltonian spectrum, such as the
ground state energy. By contrast, evaluating the trace of an operator requires
the aggregation of eigenvalues across the entire spectrum. In this work, we
introduce an efficient near-term quantum algorithm for computing the trace of a
broad class of operators, including matrix functions of the target Hamiltonian.
Our trace estimator is similar to the classical Girard-Hutchinson estimator in
that it involves the preparation of many random states. Although the exact
Girard-Hutchinson estimator is not tractably realizable on a quantum computer,
we can construct random states that match the variance of the Girard-Hutchinson
estimator through only real-time evolution. Importantly, our random states are
all generated using the same Hamiltonians for real-time evolution, with
randomness owing only to stochastic variations in the duration of the
evolutions. In this sense, the circuit is reconfigurable and suitable for
realization on both digital and analog platforms. For numerical illustration,
we highlight important applications in the physical, chemical, and materials
sciences, such as calculations of density of states and free energy.
Related papers
- Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
We explore the applicability of quantum-data learning to practical problems in high-energy physics.
We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states.
The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
arXiv Detail & Related papers (2023-06-29T18:00:01Z) - Inferring interpretable dynamical generators of local quantum
observables from projective measurements through machine learning [17.27816885271914]
We utilize a machine-learning approach to infer the dynamical generator governing the evolution of local observables in a many-body system from noisy data.
Our method is not only useful for extracting effective dynamical generators from many-body systems, but may also be applied for inferring decoherence mechanisms of quantum simulation and computing platforms.
arXiv Detail & Related papers (2023-06-06T18:01:18Z) - Calculating the many-body density of states on a digital quantum
computer [58.720142291102135]
We implement a quantum algorithm to perform an estimation of the density of states on a digital quantum computer.
We use our algorithm to estimate the density of states of a non-integrable Hamiltonian on the Quantinuum H1-1 trapped ion chip for a controlled register of 18bits.
arXiv Detail & Related papers (2023-03-23T17:46:28Z) - Variational Quantum Time Evolution without the Quantum Geometric Tensor [0.6562256987706128]
variational quantum time evolution is a promising candidate for near-term devices.
We show that our algorithm accurately reproduces the system dynamics at a fraction of the cost of standard variational quantum time evolution algorithms.
As an application of quantum imaginary-time evolution, we calculate a thermodynamic observable, the energy per site, of the Heisenberg model.
arXiv Detail & Related papers (2023-03-22T18:00:08Z) - Sparse random Hamiltonians are quantumly easy [105.6788971265845]
A candidate application for quantum computers is to simulate the low-temperature properties of quantum systems.
This paper shows that, for most random Hamiltonians, the maximally mixed state is a sufficiently good trial state.
Phase estimation efficiently prepares states with energy arbitrarily close to the ground energy.
arXiv Detail & Related papers (2023-02-07T10:57:36Z) - Designing exceptional-point-based graphs yielding topologically
guaranteed quantum search [0.0]
We show how to construct walks with the property that all the eigenvalues of the non-Hermitian survival operator, coalesce to zero.
The resulting search is guaranteed to succeed in a bounded time for any initial condition.
arXiv Detail & Related papers (2022-02-08T04:30:24Z) - Numerical Simulations of Noisy Quantum Circuits for Computational
Chemistry [51.827942608832025]
Near-term quantum computers can calculate the ground-state properties of small molecules.
We show how the structure of the computational ansatz as well as the errors induced by device noise affect the calculation.
arXiv Detail & Related papers (2021-12-31T16:33:10Z) - Algebraic Compression of Quantum Circuits for Hamiltonian Evolution [52.77024349608834]
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.
arXiv Detail & Related papers (2021-08-06T19:38:01Z) - Computing molecular excited states on a D-Wave quantum annealer [52.5289706853773]
We demonstrate the use of a D-Wave quantum annealer for the calculation of excited electronic states of molecular systems.
These simulations play an important role in a number of areas, such as photovoltaics, semiconductor technology and nanoscience.
arXiv Detail & Related papers (2021-07-01T01:02:17Z) - Preparation of Many-body Ground States by Time Evolution with
Variational Microscopic Magnetic Fields and Incomplete Interactions [1.6554452963165365]
State preparation is of fundamental importance in quantum physics.
We study the latter on quantum many-body systems by the time evolution with fixed couplings and variational magnetic fields.
An optimization method is proposed to optimize the magnetic fields by "fine-graining" the discretization of time.
arXiv Detail & Related papers (2021-06-03T12:04:36Z) - Local Operator Entanglement in Spin Chains [0.0]
Local perturbations can affect the entire quantum system.
quantum computers employ non-equilibrium processes for computations.
In this paper, we investigate the evolution of bi- and tripartite operator mutual information of the time-evolution operator and the Pauli spin operators.
arXiv Detail & Related papers (2020-12-29T05:11:28Z)
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.