Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2204.11042 · IEEE International Conference on Software Architecture Companion (ICSA-C)

Simple Quantum State Encodings for Hybrid Programming of Quantum Simulators

Thomas Gabor, Marian Lingsch-Rosenfeld, Claudia Linnhoff–Popien

Published Mar 1, 2022• 1 citation
arXivHTMLPDF

Abstract

Especially sparse quantum states can be efficiently encoded with simple classical data structures. We show the admissibility of using a classical database to encode quantum states for a few practical examples and argue in favor of further optimizations for quantum simulation targeting simpler, only "semi-quantum" circuits.
DOI
10.1109/icsa-c54293.2022.00040

Related papers

Explicit Quantum Circuits for Block Encodings of Certain Sparse Matrices

Daan Camps, Lin Lin, Roel Van Beeumen +1 more

Abstract. Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding embeds a properly scaled matrix of interest [Formula: see text] in a larger unitary transformation [Formula: see text] that can be decomposed into a product of simpler unitaries and implemented efficiently on a quantum computer. Although quantum algorithms can potentially achieve exponential speedup in solving linear algebra problems compared to the best classical algorithm, such a gain in efficiency ultimately hinges on our ability to construct an efficient quantum circuit for the block encoding of [Formula: see text], which is difficult in general, and not trivial even for well structured sparse matrices. In this paper, we give a few examples on how efficient quantum circuits can be explicitly constructed for some well structured sparse matrices and discuss a few strategies used in these constructions. We also provide implementations of these quantum circuits in MATLAB.

arXiv:2203.10236•SIAM Journal on Matrix Analysis and Applications•Mar 11, 2024•78 citations

Quantum Data Encoding Patterns and their Consequences

Martin Gogeissl, Hila Safi, Wolfgang Mauerer

The use of quantum processing units (QPUs) promises speed-ups for solving computational problems, in particular for discrete optimisation. While a few groundbreaking algorithmic approaches are known that can provably outperform classical computers, we observe a scarcity of programming abstractions for constructing efficient quantum algorithms. A good fraction of the literature that addresses solving concrete problems related to database management concentrates on casting them as quadratic unconstrained binary optimisation problems (QUBOs), which can then, among others, be processed on gate-based machines (using the quantum approximate optimisation algorithm), or quantum annealers. A critical aspect that affects efficiency and scalability of either of these approaches is how classical data are loaded into qubits, respectively how problems are encoded into QUBO representation. The effectiveness of encodings is known to be of crucial importance for quantum computers, especially since the amount of available qubits is strongly limited in the era of noisy, intermediate-size quantum computers.

Workshop on Quantum Computing and Quantum-Inspired Technology for Data-Intensive Systems and Applications (Q-Data)•Jun 9, 2024•11 citations

Trading Classical and Quantum Computational Resources

Sergey Bravyi, Graeme Smith, John A. Smolin

We propose examples of a hybrid quantum-classical simulation where a classical computer assisted by a small quantum processor can efficiently simulate a larger quantum system.First, we consider sparse quantum circuits such that each qubit participates in Oð1Þ two-qubit gates.It is shown that any sparse circuit on n þ k qubits can be simulated by sparse circuits on n qubits and a classical processing that takes time 2 OðkÞ polyðnÞ.Second, we study Pauli-based computation (PBC), where allowed operations are nondestructive eigenvalue measurements of n-qubit Pauli operators.The computation begins by initializing each qubit in the so-called magic state.This model is known to be equivalent to the universal quantum computer.We show that any PBC on n þ k qubits can be simulated by PBCs on n qubits and a classical processing that takes time 2 OðkÞ polyðnÞ.Finally, we propose a purely classical algorithm that can simulate a PBC on n qubits in a time 2 αn polyðnÞ, where α ≈ 0.94.This improves upon the brute-force simulation method, which takes time 2 n polyðnÞ.Our algorithm exploits the fact that n-fold tensor products of magic states admit a low-rank decomposition into n-qubit stabilizer states.

arXiv:1506.01396•Physical Review X•Jun 29, 2016•338 citations

Efficient quantum circuit simulation.

John P. Hayes, Igor L. Markov, George F. Viamontes

Quantum-mechanical phenomena are playing an increasing role in information processing as transistor sizes approach the nanometer level, while the securest forms of communication rely on quantum data encoding. When they involve a finite number of basis states, these phenomena can be modeled as quantum circuits, the quantum analogue of conventional or classical logic circuits. Simulation of quantum circuits can therefore be used as a tool to evaluate issues in the design of quantum information processors. Unfortunately, simulating such phenomena efficiently is exceedingly difficult. The matrices representing quantum operators (gates) and vectors modeling quantum states grow exponentially with the number of quantum bits. The information represented by quantum states and operators often exhibits structure that can be exploited when simulating certain classes of quantum circuits. We study the development of simulation methods that run on classical computers and take advantage of such repetitions and redundancies. In particular, we define a new data structure for simulating quantum circuits called the quantum information decision diagram (QuIDD). A QuIDD is a compressed graph representation of a vector or matrix and permits computations to be performed directly on the compressed data. We develop a comprehensive set of algorithms for operating on QuIDDs in both the state-vector and density-matrix formats, and evaluate their complexity. These algorithms have been implemented in a general-purpose simulator program for quantum-mechanical applications called QuIDDPro. Through extensive experiments conducted on representative quantum simulation applications, including Grover's search algorithm, error characterization, and reversible circuits, we demonstrate that QuIDDPro is faster than other existing quantum-mechanical simulators such as the National Institute of Standards and Technology's QCSim program, and is far more memory-efficient. Using QuIDDPro, we explore the advantages of quantum computation over classical computation, simulate quantum errors and error correction, and study the impact of numerical precision on the fidelity of simulations. We also develop several novel algorithms for testing quantum circuit equivalence and compare them empirically. The QuIDDPro software is equipped with a user-friendly interface and is distributed with numerous example scripts. It has been used as a laboratory supplement for quantum computing courses at several universities.

•Jan 1, 2007•15 citations

Hybrid Quantum State Preparation via Data Compression

Emad Rezaei Fard Boosari, Maryam Afsary

Quantum state preparation (QSP) for a general $n$-qubit state requires $O(2^n)$ CNOT gates and circuit depth, making exact amplitude encoding (EAE) impractical for near-term quantum hardware. We introduce an ancilla-free hybrid classical-quantum strategy that reduces this cost to $O(poly(n))$ for a broad class of compressible data. The method first applies a classical compression step to obtain a $d$-sparse representation of the input, loads this sparse vector using a sparse-state preparation routine, and then reconstructs the target state through a polynomial-depth quantum inverse transform. We evaluate the framework on synthetic benchmark signals and real biomedical time series using Fourier and Haar transforms, demonstrating substantial reductions in CNOT counts and circuit depth compared to EAE, together with competitive performance relative to the Fourier Series Loader (FSL). The quantum simulation results show that combining classical data compression with quantum decompression provides a scalable framework for efficient QSP, reducing quantum overhead without requiring variational training or ancillary registers.

quant-pharXiv:2512.01798•Dec 2, 2025•0 citations

Quantum autoencoders for efficient compression of quantum data

Jonathan Romero, Jonathan P Olson, Alán Aspuru‐Guzik

Abstract Classical autoencoders are neural networks that can learn efficient low-dimensional representations of data in higher-dimensional space. The task of an autoencoder is, given an input x , to map x to a lower dimensional point y such that x can likely be recovered from y . The structure of the underlying autoencoder network can be chosen to represent the data on a smaller dimension, effectively compressing the input. Inspired by this idea, we introduce the model of a quantum autoencoder to perform similar tasks on quantum data. The quantum autoencoder is trained to compress a particular data set of quantum states, where a classical compression algorithm cannot be employed. The parameters of the quantum autoencoder are trained using classical optimization algorithms. We show an example of a simple programmable circuit that can be trained as an efficient autoencoder. We apply our model in the context of quantum simulation to compress ground states of the Hubbard model and molecular Hamiltonians.

arXiv:1612.02806•Quantum Science and Technology•Aug 17, 2017•559 citations
Abstract. Many standard linear algebra problems can be solved on a quantum computer by using recently developed quantum linear algebra algorithms that make use of block encodings and quantum eigenvalue/singular value transformations. A block encoding embeds a properly scaled matrix of interest [Formula: see text] in a larger unitary transformation [Formula: see text] that can be decomposed into a product of simpler unitaries and implemented efficiently on a quantum computer. Although quantum algorithms can potentially achieve exponential speedup in solving linear algebra problems compared to the best classical algorithm, such a gain in efficiency ultimately hinges on our ability to construct an efficient quantum circuit for the block encoding of [Formula: see text], which is difficult in general, and not trivial even for well structured sparse matrices. In this paper, we give a few examples on how efficient quantum circuits can be explicitly constructed for some well structured sparse matrices and discuss a few strategies used in these constructions. We also provide implementations of these quantum circuits in MATLAB.
The use of quantum processing units (QPUs) promises speed-ups for solving computational problems, in particular for discrete optimisation. While a few groundbreaking algorithmic approaches are known that can provably outperform classical computers, we observe a scarcity of programming abstractions for constructing efficient quantum algorithms. A good fraction of the literature that addresses solving concrete problems related to database management concentrates on casting them as quadratic unconstrained binary optimisation problems (QUBOs), which can then, among others, be processed on gate-based machines (using the quantum approximate optimisation algorithm), or quantum annealers. A critical aspect that affects efficiency and scalability of either of these approaches is how classical data are loaded into qubits, respectively how problems are encoded into QUBO representation. The effectiveness of encodings is known to be of crucial importance for quantum computers, especially since the amount of available qubits is strongly limited in the era of noisy, intermediate-size quantum computers.
We propose examples of a hybrid quantum-classical simulation where a classical computer assisted by a small quantum processor can efficiently simulate a larger quantum system.First, we consider sparse quantum circuits such that each qubit participates in Oð1Þ two-qubit gates.It is shown that any sparse circuit on n þ k qubits can be simulated by sparse circuits on n qubits and a classical processing that takes time 2 OðkÞ polyðnÞ.Second, we study Pauli-based computation (PBC), where allowed operations are nondestructive eigenvalue measurements of n-qubit Pauli operators.The computation begins by initializing each qubit in the so-called magic state.This model is known to be equivalent to the universal quantum computer.We show that any PBC on n þ k qubits can be simulated by PBCs on n qubits and a classical processing that takes time 2 OðkÞ polyðnÞ.Finally, we propose a purely classical algorithm that can simulate a PBC on n qubits in a time 2 αn polyðnÞ, where α ≈ 0.94.This improves upon the brute-force simulation method, which takes time 2 n polyðnÞ.Our algorithm exploits the fact that n-fold tensor products of magic states admit a low-rank decomposition into n-qubit stabilizer states.
Quantum-mechanical phenomena are playing an increasing role in information processing as transistor sizes approach the nanometer level, while the securest forms of communication rely on quantum data encoding. When they involve a finite number of basis states, these phenomena can be modeled as quantum circuits, the quantum analogue of conventional or classical logic circuits. Simulation of quantum circuits can therefore be used as a tool to evaluate issues in the design of quantum information processors. Unfortunately, simulating such phenomena efficiently is exceedingly difficult. The matrices representing quantum operators (gates) and vectors modeling quantum states grow exponentially with the number of quantum bits. The information represented by quantum states and operators often exhibits structure that can be exploited when simulating certain classes of quantum circuits. We study the development of simulation methods that run on classical computers and take advantage of such repetitions and redundancies. In particular, we define a new data structure for simulating quantum circuits called the quantum information decision diagram (QuIDD). A QuIDD is a compressed graph representation of a vector or matrix and permits computations to be performed directly on the compressed data. We develop a comprehensive set of algorithms for operating on QuIDDs in both the state-vector and density-matrix formats, and evaluate their complexity. These algorithms have been implemented in a general-purpose simulator program for quantum-mechanical applications called QuIDDPro. Through extensive experiments conducted on representative quantum simulation applications, including Grover's search algorithm, error characterization, and reversible circuits, we demonstrate that QuIDDPro is faster than other existing quantum-mechanical simulators such as the National Institute of Standards and Technology's QCSim program, and is far more memory-efficient. Using QuIDDPro, we explore the advantages of quantum computation over classical computation, simulate quantum errors and error correction, and study the impact of numerical precision on the fidelity of simulations. We also develop several novel algorithms for testing quantum circuit equivalence and compare them empirically. The QuIDDPro software is equipped with a user-friendly interface and is distributed with numerous example scripts. It has been used as a laboratory supplement for quantum computing courses at several universities.
Quantum state preparation (QSP) for a general nnn-qubit state requires O(2n)O(2^n)O(2n) CNOT gates and circuit depth, making exact amplitude encoding (EAE) impractical for near-term quantum hardware. We introduce an ancilla-free hybrid classical-quantum strategy that reduces this cost to O(poly(n))O(poly(n))O(poly(n)) for a broad class of compressible data. The method first applies a classical compression step to obtain a ddd-sparse representation of the input, loads this sparse vector using a sparse-state preparation routine, and then reconstructs the target state through a polynomial-depth quantum inverse transform. We evaluate the framework on synthetic benchmark signals and real biomedical time series using Fourier and Haar transforms, demonstrating substantial reductions in CNOT counts and circuit depth compared to EAE, together with competitive performance relative to the Fourier Series Loader (FSL). The quantum simulation results show that combining classical data compression with quantum decompression provides a scalable framework for efficient QSP, reducing quantum overhead without requiring variational training or ancillary registers.
Abstract Classical autoencoders are neural networks that can learn efficient low-dimensional representations of data in higher-dimensional space. The task of an autoencoder is, given an input x , to map x to a lower dimensional point y such that x can likely be recovered from y . The structure of the underlying autoencoder network can be chosen to represent the data on a smaller dimension, effectively compressing the input. Inspired by this idea, we introduce the model of a quantum autoencoder to perform similar tasks on quantum data. The quantum autoencoder is trained to compress a particular data set of quantum states, where a classical compression algorithm cannot be employed. The parameters of the quantum autoencoder are trained using classical optimization algorithms. We show an example of a simple programmable circuit that can be trained as an efficient autoencoder. We apply our model in the context of quantum simulation to compress ground states of the Hubbard model and molecular Hamiltonians.