Automatic quantum circuit encoding of a given arbitrary quantum state

Abstract

We propose a quantum-classical hybrid algorithm to encode a given arbitrarily quantum state $|\Psi ⟩$ onto an optimal quantum circuit $\hat{\mathcal{C}}$ with a finite number of single- and two-qubit quantum gates. The proposed algorithm employs as an objective function the absolute value of fidelity $F=⟨0|{\hat{\mathcal{C}}}^{†}|\Psi ⟩$, which is maximized iteratively to construct an optimal quantum circuit $\hat{\mathcal{C}}$ with controlled accuracy. The key ingredient of the algorithm is the sequential determination of a set of optimal two-qubit unitary operators one by one via the singular value decomposition of the fidelity tensor. Once the optimal unitary operators are determined, including the location of qubits on which each unitary operator acts, elementary quantum gates are assigned algebraically. With noiseless numerical simulations, we demonstrate the algorithm to encode a ground state of quantum many-body systems, including the spin-1/2 antiferromagnetic Heisenberg model and the spin-1/2 XY model. The results are also compared with the quantum circuit encoding of the same quantum state onto a quantum circuit in a given circuit structure. Moreover, we demonstrate that the algorithm can also be applied to construct an optimal quantum circuit for classical data such as a classical image that is represented as a quantum state by the amplitude encoding. Finally, we also experimentally demonstrate that a quantum circuit generated by the AQCE algorithm can indeed represent the original quantum state reasonably on a noisy real quantum device.

arXiv comment25 pages, 14 figures

References in corpus (57)

• Quantum Machine Learning
• A variational eigenvalue solver on a quantum processor
• Variational Quantum Algorithms
• Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
• Supervised learning with quantum enhanced feature spaces
• Barren plateaus in quantum neural network training landscapes
• Quantum support vector machine for big data classification
• Quantum machine learning in feature Hilbert spaces
• Quantum computational chemistry
• Quantum Circuit Learning
• Quantum Convolutional Neural Networks
• An introduction to quantum machine learning
• Entanglement renormalization
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• An adaptive variational algorithm for exact molecular simulations on a quantum computer
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• A class of quantum many-body states that can be efficiently simulated
• Scalable Quantum Simulation of Molecular Energies
• Noise-Induced Barren Plateaus in Variational Quantum Algorithms
• Synthesis of Quantum Logic Circuits
• Exact and Approximate Unitary 2-Designs: Constructions and Applications
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Digitized adiabatic quantum computing with a superconducting circuit
• Quantum Natural Gradient
• Optimal Quantum Circuits for General Two-Qubit Gates
• Optimal Creation of Entanglement Using a Two--Qubit Gate
• qubit-ADAPT-VQE: An adaptive algorithm for constructing hardware-efficient ansatze on a quantum processor
• Absence of Barren Plateaus in Quantum Convolutional Neural Networks
• Digital quantum simulation of fermionic models with a superconducting circuit
• Quantum-state preparation with universal gate decompositions
• Algorithms for entanglement renormalization
• Random Quantum Circuits are Approximate 2-designs
• Quantum Implementation of Unitary Coupled Cluster for Simulating Molecular Electronic Structure
• A universal quantum circuit for two-qubit transformations with three CNOT gates
• Prediction by linear regression on a quantum computer
• Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
• Tensor network states and geometry
• From transistor to trapped-ion computers for quantum chemistry
• Exact Parameterization of Fermionic Wave Functions via Unitary Coupled Cluster Theory
• Sequential minimal optimization for quantum-classical hybrid algorithms
• Ground state fidelity from tensor network representations
• Quantum circuits with uniformly controlled one-qubit gates
• Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
• Variational Quantum State Eigensolver
• Capacity and quantum geometry of parametrized quantum circuits
• Adaptive Variational Quantum Dynamics Simulations
• Black-box quantum state preparation without arithmetic
• Approximate amplitude encoding in shallow parameterized quantum circuits and its application to financial market indicator
• The Variational Power of Quantum Circuit Tensor Networks
• Symmetry-adapted variational quantum eigensolver
• Adaptive variational quantum eigensolvers for highly excited states
• An efficient adaptive variational quantum solver of the Schrodinger equation based on reduced density matrices
• Comment on the paper "Random Quantum Circuits are Approximate 2-designs"
• Absence of barren plateaus in finite local-depth circuits with long-range entanglement
• Holographic quantum simulation of entanglement renormalization circuits
• Automatically Differentiable Quantum Circuit for Many-qubit State Preparation
• Discretized quantum adiabatic process for free fermions and comparison with the imaginary-time evolution

Cited by in corpus (9)

• Quantum algorithm for partial differential equations of non-conservative systems with spatially varying parameters
• Tensor-based quantum phase difference estimation for large-scale demonstration
• Anderson impurity solver integrating tensor network methods with quantum computing
• Deep Circuit Compression for Quantum Dynamics via Tensor Networks
• Classical variational optimization of PREPARE circuit for quantum phase estimation of quantum chemistry Hamiltonians
• A coherent approach to quantum-classical optimization
• Quantum circuit synthesis with SQiSW
• Preparing the Gutzwiller wave function for attractive SU(3) fermions on a quantum computer
• Tensor-based phase difference estimation on time series analysis