Scalable quantum circuits for exponential of Pauli strings and Hamiltonian simulations
- URL: http://arxiv.org/abs/2405.13605v2
- Date: Mon, 04 Nov 2024 17:22:36 GMT
- Title: Scalable quantum circuits for exponential of Pauli strings and Hamiltonian simulations
- Authors: Rohit Sarma Sarkar, Sabyasachi Chakraborty, Bibhas Adhikari,
- Abstract summary: We design quantum circuits for the exponential of scaled $n$-qubit Pauli strings using single-qubit rotation gates, Hadamard gate, and CNOT gates.
A key result we derive is that any two Pauli-string operators composed of identity and $X$ gates are permutation similar.
We apply these circuit models to approximate unitary evolution for several classes of Hamiltonians using the Suzuki-Trotter approximation.
- Score: 0.0
- License:
- Abstract: In this paper, we design quantum circuits for the exponential of scaled $n$-qubit Pauli strings using single-qubit rotation gates, Hadamard gate, and CNOT gates. A key result we derive is that any two Pauli-string operators composed of identity and $X$ gates are permutation similar, and the corresponding permutation matrices are product of CNOT gates, with the $n$-th qubit serving as the control qubit. Consequently, we demonstrate that the proposed circuit model for exponential of any Pauli-string is implementable on low-connected quantum hardware and scalable i.e. quantum circuits for $(n+1)$-qubit systems can be constructed from $n$-qubit circuits by adding additional quantum gates and the extra qubit. We then apply these circuit models to approximate unitary evolution for several classes of Hamiltonians using the Suzuki-Trotter approximation. These Hamiltonians include $2$-sparse block-diagonal Hamiltonians, Ising Hamiltonians, and both time-independent and time-dependent Random Field Heisenberg Hamiltonians and Transverse Magnetic Random Quantum Ising Hamiltonians. Simulations for systems of up to 18 qubits show that the circuit approximation closely matches the exact evolution, with errors comparable to the numerical Trotterization error. Finally, we consider noise models in quantum circuit simulations to account for gate implementation errors in NISQ computers and observe that the noisy simulation closely resembles the noiseless one when gate and idle errors are on the order of $O(10^{-3})$ or smaller.
Related papers
- Linear Circuit Synthesis using Weighted Steiner Trees [45.11082946405984]
CNOT circuits are a common building block of general quantum circuits.
This article presents state-of-the-art algorithms for optimizing the number of CNOT gates.
A simulated evaluation shows that the suggested is almost always beneficial and reduces the number of CNOT gates by up to 10%.
arXiv Detail & Related papers (2024-08-07T19:51:22Z) - Local Hamiltonian decomposition and classical simulation of parametrized
quantum circuits [0.0]
We develop a classical algorithm of complexity $O(K, 2n)$ to simulate parametrized quantum circuits (PQCs) of $n$ qubits.
arXiv Detail & Related papers (2024-01-24T00:30:31Z) - Quantum circuit model for discrete-time three-state quantum walks on
Cayley graphs [0.0]
We develop qutrit circuit models for discrete-time three-state quantum walks on Cayley graphs.
We numerically simulate these circuits to mimic its performance on noisy quantum computers.
arXiv Detail & Related papers (2024-01-19T20:45:26Z) - Classical variational optimization of PREPARE circuit for quantum phase
estimation of quantum chemistry Hamiltonians [0.8009842832476994]
We propose a method for constructing $textttPREPARE$ circuits for quantum phase estimation of a molecular Hamiltonian in quantum chemistry.
The $textttPREPARE$ circuit generates a quantum state which encodes the coefficients of the terms in the Hamiltonian as probability amplitudes.
arXiv Detail & Related papers (2023-08-26T05:32:38Z) - Unimon qubit [42.83899285555746]
Superconducting qubits are one of the most promising candidates to implement quantum computers.
Here, we introduce and demonstrate a superconducting-qubit type, the unimon, which combines the desired properties of high non-linearity, full insensitivity to dc charge noise, insensitivity to flux noise, and a simple structure consisting only of a single Josephson junction in a resonator.
arXiv Detail & Related papers (2022-03-11T12:57:43Z) - Quantum simulation of $\phi^4$ theories in qudit systems [53.122045119395594]
We discuss the implementation of quantum algorithms for lattice $Phi4$ theory on circuit quantum electrodynamics (cQED) system.
The main advantage of qudit systems is that its multi-level characteristic allows the field interaction to be implemented only with diagonal single-qudit gates.
arXiv Detail & Related papers (2021-08-30T16:30:33Z) - 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) - 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) - Parallel Quantum Algorithm for Hamiltonian Simulation [9.680246554758343]
A parallel quantum algorithm is proposed for simulating the dynamics of a large class of Hamiltonians.
The running time of our parallel quantum simulation algorithm measured by the quantum circuit depth has a doubly (poly-)logarithmic dependence.
We show that the total gate depth of our algorithm has a $operatornamepolyloglog (1/epsilon)$ dependence in the parallel setting.
arXiv Detail & Related papers (2021-05-25T12:46:33Z) - Simulating nonnative cubic interactions on noisy quantum machines [65.38483184536494]
We show that quantum processors can be programmed to efficiently simulate dynamics that are not native to the hardware.
On noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates.
arXiv Detail & Related papers (2020-04-15T05:16:24Z) - Universal topological quantum computation with strongly correlated
Majorana edge modes [7.930410828384357]
Majorana-based quantum gates are not complete for performing universal topological quantum computation.
We show the application to Shor's integer factorization algorithm.
arXiv Detail & Related papers (2020-04-07T12:03:14Z)
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.