Tensor-based quantum phase difference estimation for large-scale demonstration

Abstract

We develop an energy calculation algorithm leveraging quantum phase difference estimation (QPDE) scheme and a tensor-network-based unitary compression method in the preparation of superposition states and time-evolution gates. Alongside its efficient implementation, this algorithm reduces depolarization noise affections exponentially. We demonstrated energy gap calculations for one-dimensional Hubbard models on IBM superconducting devices using circuits up to 32-system (plus one-ancilla) qubits, a five-fold increase over previous QPE demonstrations, at the 7242 controlled-Z gate level of standard transpilation, utilizing a Q-CTRL error suppression module. Additionally, we propose a technique towards molecular executions using spatial orbital localization and index sorting, verified linear polyene simulations up to 21 qubits. Since QPDE can handle the same objectives as QPE, our algorithm represents a leap forward in quantum computing on real devices.

31 pages, Code repository

References in corpus (17)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• The density-matrix renormalization group in the age of matrix product states
• Quantum algorithm for solving linear systems of equations
• Quantum computing with Qiskit
• Efficient Tree Tensor Network States (TTNS) for Quantum Chemistry: Generalizations of the Density Matrix Renormalization Group Algorithm
• Classically optimized Hamiltonian simulation
• Towards adiabatic quantum computing using compressed quantum circuits
• Demonstrating Bayesian Quantum Phase Estimation with Quantum Error Detection
• Experimental benchmarking of an automated deterministic error suppression workflow for quantum algorithms
• Statistical phase estimation and error mitigation on a superconducting quantum processor
• Quantum computing quantum Monte Carlo with hybrid tensor network for electronic structure calculations
• Combining Matrix Product States and Noisy Quantum Computers for Quantum Simulation
• Integrated error-suppressed pipeline for quantum optimization of nontrivial binary combinatorial optimization problems on gate-model hardware at the 156-qubit scale
• The generative quantum eigensolver (GQE) and its application for ground state search
• Scalable simulation of non-equilibrium quantum dynamics via classically optimised unitary circuits
• Classical variational optimization of PREPARE circuit for quantum phase estimation of quantum chemistry Hamiltonians
• Exponentially Reduced Circuit Depths Using Trotter Error Mitigation

Cited by in corpus (4)

• Hamiltonian simulation-based quantum-selected configuration interaction for large-scale electronic structure calculations with a quantum computer
• Phase Estimation with Compressed Controlled Time Evolution
• Tensor-based phase difference estimation on time series analysis
• Towards Compact Wavefunctions from Quantum-Selected Configuration Interaction