Demonstrating Bayesian Quantum Phase Estimation with Quantum Error Detection

Abstract

Quantum phase estimation (QPE) serves as a building block of many different quantum algorithms and finds important applications in computational chemistry problems. Despite the rapid development of quantum hardware, experimental demonstration of QPE for chemistry problems remains challenging due to its large circuit depth and the lack of quantum resources to protect the hardware from noise with fully fault-tolerant protocols. In the present work, we take a step towards fault-tolerant quantum computing by demonstrating a QPE algorithm on a Quantinuum trapped-ion computer. We employ a Bayesian approach to QPE and introduce a routine for optimal parameter selection, which we combine with a $[[n+2,n,2]]$ quantum error detection code carefully tailored to the hardware capabilities. As a simple quantum chemistry example, we take a hydrogen molecule represented by a two-qubit Hamiltonian and estimate its ground state energy using our QPE protocol. In the experiment, we use the quantum circuits containing as many as 920 physical two-qubit gates to estimate the ground state energy within $6\times 10^{-3}$ hartree of the exact value.

arXiv comment16 pages, 9 figures

References in corpus (36)

• Quantum computational chemistry
• Quantum Chemistry in the Age of Quantum Computing
• Simulated Quantum Computation of Molecular Energies
• Error mitigation for short-depth quantum circuits
• Quantum Algorithms Revisited
• Multi-particle entanglement of hot trapped ions
• A Theory of Fault-Tolerant Quantum Computation
• A quantum algorithm providing exponential speed increase for finding eigenvalues and eigenvectors
• Scalable Quantum Simulation of Molecular Energies
• Efficient variational quantum simulator incorporating active error minimisation
• Entanglement-free Heisenberg-limited phase estimation
• Demonstration of the trapped-ion quantum-CCD computer architecture
• Noise tailoring for scalable quantum computation via randomized compiling
• Simple Quantum Error Correcting Codes
• t$|$ket$⟩$ : A Retargetable Compiler for NISQ Devices
• Complete methods set for scalable ion trap quantum information processing
• Experimental demonstration of fault-tolerant state preparation with superconducting qubits
• Quantum error correction with only two extra qubits
• Robust Online Hamiltonian Learning
• Arbitrary accuracy iterative phase estimation algorithm as a two qubit benchmark
• Optimal Quantum Measurements of Expectation Values of Observables
• Efficient Bayesian Phase Estimation
• Heisenberg-limited ground state energy estimation for early fault-tolerant quantum computers
• Experimental Bayesian Quantum Phase Estimation on a Silicon Photonic Chip
• Review of Decoherence Free Subspaces, Noiseless Subsystems, and Dynamical Decoupling
• Quantum phase estimation of multiple eigenvalues for small-scale (noisy) experiments
• Fault-tolerant quantum error detection
• Fault-Tolerant Logical Gates in the IBM Quantum Experience
• Fault-tolerant quantum computation with few qubits
• A randomized quantum algorithm for statistical phase estimation
• Error detection on quantum computers improves accuracy of chemical calculations
• Protecting quantum memories using coherent parity check codes
• Testing quantum fault tolerance on small systems
• Noise-resilient phase estimation with randomized compiling
• Statistical phase estimation and error mitigation on a superconducting quantum processor
• Efficient Bayesian phase estimation using mixed priors

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• A Perspective on Quantum Computing Applications in Quantum Chemistry using 25--100 Logical Qubits
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• Encoded probabilistic imaginary-time evolution on a trapped-ion quantum computer for ground and excited states of spin qubits
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• Does the full configuration interaction method based on quantum phase estimation with Trotter decomposition satisfy the size consistency condition?
• Towards Practical Quantum Phase Estimation: A Modular, Scalable, and Adaptive Approach
• General Approach to Error Detection of Bosonic Codes via Phase Estimation
• Towards Compact Wavefunctions from Quantum-Selected Configuration Interaction
• Error detection without post-selection in adaptive quantum circuits
• Weakly Fault-Tolerant Computation in a Quantum Error-Detecting Code
• Double-bracket quantum algorithms for high-fidelity ground state preparation
• Fault Tolerant Quantum Simulation via Symplectic Transvections