On connectivity-dependent resource requirements for digital quantum
simulation of $d$-level particles
- URL: http://arxiv.org/abs/2005.13070v3
- Date: Fri, 2 Oct 2020 03:38:59 GMT
- Title: On connectivity-dependent resource requirements for digital quantum
simulation of $d$-level particles
- Authors: Nicolas P. D. Sawaya, Gian Giacomo Guerreschi, Adam Holmes
- Abstract summary: We study the number of SWAP gates required to Trotterize commonly used quantum operators.
Results are applicable in hardware co-design and in choosing efficient qudit encodings for a given set of near-term quantum hardware.
- Score: 0.703901004178046
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A primary objective of quantum computation is to efficiently simulate quantum
physics. Scientifically and technologically important quantum Hamiltonians
include those with spin-$s$, vibrational, photonic, and other bosonic degrees
of freedom, i.e. problems composed of or approximated by $d$-level particles
(qudits). Recently, several methods for encoding these systems into a set of
qubits have been introduced, where each encoding's efficiency was studied in
terms of qubit and gate counts. Here, we build on previous results by including
effects of hardware connectivity. To study the number of SWAP gates required to
Trotterize commonly used quantum operators, we use both analytical arguments
and automatic tools that optimize the schedule in multiple stages. We study the
unary (or one-hot), Gray, standard binary, and block unary encodings, with
three connectivities: linear array, ladder array, and square grid. Among other
trends, we find that while the ladder array leads to substantial efficiencies
over the linear array, the advantage of the square over the ladder array is
less pronounced. These results are applicable in hardware co-design and in
choosing efficient qudit encodings for a given set of near-term quantum
hardware. Additionally, this work may be relevant to the scheduling of other
quantum algorithms for which matrix exponentiation is a subroutine.
Related papers
- Automated Synthesis of Quantum Algorithms via Classical Numerical Techniques [2.7536859673878857]
We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers.
Our methods are evaluated on single-qubit systems as well as on larger systems.
arXiv Detail & Related papers (2024-08-27T17:43:58Z) - Tensor Quantum Programming [0.0]
We develop an algorithm that encodes Matrix Product Operators into quantum circuits with a depth that depends linearly on the number of qubits.
It demonstrates effectiveness on up to 50 qubits for several frequently encountered in differential equations, optimization problems, and quantum chemistry.
arXiv Detail & Related papers (2024-03-20T10:44:00Z) - QuantumSEA: In-Time Sparse Exploration for Noise Adaptive Quantum
Circuits [82.50620782471485]
QuantumSEA is an in-time sparse exploration for noise-adaptive quantum circuits.
It aims to achieve two key objectives: (1) implicit circuits capacity during training and (2) noise robustness.
Our method establishes state-of-the-art results with only half the number of quantum gates and 2x time saving of circuit executions.
arXiv Detail & Related papers (2024-01-10T22:33:00Z) - Iterative Qubits Management for Quantum Index Searching in a Hybrid
System [56.39703478198019]
IQuCS aims at index searching and counting in a quantum-classical hybrid system.
We implement IQuCS with Qiskit and conduct intensive experiments.
Results demonstrate that it reduces qubits consumption by up to 66.2%.
arXiv Detail & Related papers (2022-09-22T21:54:28Z) - Quantum State Preparation with Optimal Circuit Depth: Implementations
and Applications [10.436969366019015]
We show that any $Theta(n)$-depth circuit can be prepared with a $Theta(log(nd)) with $O(ndlog d)$ ancillary qubits.
We discuss applications of the results in different quantum computing tasks, such as Hamiltonian simulation, solving linear systems of equations, and realizing quantum random access memories.
arXiv Detail & Related papers (2022-01-27T13:16:30Z) - Efficient realization of quantum algorithms with qudits [0.70224924046445]
We propose a technique for an efficient implementation of quantum algorithms with multilevel quantum systems (qudits)
Our method uses a transpilation of a circuit in the standard qubit form, which depends on the parameters of a qudit-based processor.
We provide an explicit scheme of transpiling qubit circuits into sequences of single-qudit and two-qudit gates taken from a particular universal set.
arXiv Detail & Related papers (2021-11-08T11:09:37Z) - Adiabatic Quantum Graph Matching with Permutation Matrix Constraints [75.88678895180189]
Matching problems on 3D shapes and images are frequently formulated as quadratic assignment problems (QAPs) with permutation matrix constraints, which are NP-hard.
We propose several reformulations of QAPs as unconstrained problems suitable for efficient execution on quantum hardware.
The proposed algorithm has the potential to scale to higher dimensions on future quantum computing architectures.
arXiv Detail & Related papers (2021-07-08T17:59:55Z) - Variational Quantum Optimization with Multi-Basis Encodings [62.72309460291971]
We introduce a new variational quantum algorithm that benefits from two innovations: multi-basis graph complexity and nonlinear activation functions.
Our results in increased optimization performance, two increase in effective landscapes and a reduction in measurement progress.
arXiv Detail & Related papers (2021-06-24T20:16:02Z) - QUANTIFY: A framework for resource analysis and design verification of
quantum circuits [69.43216268165402]
QUANTIFY is an open-source framework for the quantitative analysis of quantum circuits.
It is based on Google Cirq and is developed with Clifford+T circuits in mind.
For benchmarking purposes QUANTIFY includes quantum memory and quantum arithmetic circuits.
arXiv Detail & Related papers (2020-07-21T15:36:25Z) - Supervised Learning Using a Dressed Quantum Network with "Super
Compressed Encoding": Algorithm and Quantum-Hardware-Based Implementation [7.599675376503671]
Implementation of variational Quantum Machine Learning (QML) algorithms on Noisy Intermediate-Scale Quantum (NISQ) devices has issues related to the high number of qubits needed and the noise associated with multi-qubit gates.
We propose a variational QML algorithm using a dressed quantum network to address these issues.
Unlike in most other existing QML algorithms, our quantum circuit consists only of single-qubit gates, making it robust against noise.
arXiv Detail & Related papers (2020-07-20T16:29:32Z) - Quantum Gram-Schmidt Processes and Their Application to Efficient State
Read-out for Quantum Algorithms [87.04438831673063]
We present an efficient read-out protocol that yields the classical vector form of the generated state.
Our protocol suits the case that the output state lies in the row space of the input matrix.
One of our technical tools is an efficient quantum algorithm for performing the Gram-Schmidt orthonormal procedure.
arXiv Detail & Related papers (2020-04-14T11:05:26Z)
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.