Quantum State Energy Estimation via Time-Evolution Sampling
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Solution Overview
Problem
Current quantum computers, particularly noisy intermediate-scale quantum (NISQ) devices, face significant noise issues that limit the accuracy of determining the energy of quantum states, especially for complex systems, leading to decoherence and discretization errors, making it difficult to achieve chemical accuracy in energy measurements.
Innovation Solution
A computer-implemented method using adiabatic evolution and random sampling of quantum circuits to determine the energy of quantum states, employing a time-evolution operator with randomly generated quantum gates to avoid discretization errors and enhance noise resilience, allowing for chemical accuracy on NISQ devices.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If standard quantum phase estimation or variational methods are used on NISQ devices, then energy measurements can be performed, but noise and decoherence cause discretization errors and reduce measurement accuracy below chemical accuracy
Solution Approach 1:
The patent transforms the energy measurement problem into a parameter estimation problem by using the relationship between evolution time and phase accumulation. By measuring the imaginary part of ⟨ψ|e^(-iHt)|ψ⟩ at different times and fitting to extract energy, the method changes the measurement parameter from direct energy eigenvalue to time-dependent phase information, which is more robust to noise on NISQ devices
Solution Approach 2:
The patent introduces an intermediary measurement approach using the imaginary part of the time-evolved state as a mediator to indirectly determine energy. Instead of directly measuring the energy eigenvalue through standard phase estimation, the method uses the time-dependent expectation value ⟨ψ|e^(-iHt)|ψ⟩_im as an intermediary quantity that encodes energy information and can be measured more reliably on noisy hardware
2Measurement precision
If circuit depth is increased to improve energy measurement precision, then more accurate results are obtained, but noise accumulation and decoherence increase, reducing reliability on NISQ devices
Solution Approach 1:
The patent uses partial action by measuring only the imaginary part of the time-evolved state expectation value, rather than performing complete quantum phase estimation. This partial measurement approach extracts sufficient energy information through time-dependent fitting while avoiding the full circuit depth and noise accumulation required by standard QPE methods
Solution Approach 2:
The method employs periodic action by evaluating the time-evolved state at multiple discrete time points and using the periodic oscillation of the imaginary part to extract energy information. By sampling at different times and fitting the oscillation pattern, the method achieves accurate energy measurement without requiring deep circuits that would accumulate excessive noise
3Ease of manufacture
If Trotterization is used to simulate time evolution, then the evolution can be implemented on quantum computers, but discretization errors arise that reduce measurement precision
Solution Approach 1:
The patent applies dynamics by using the continuous time evolution relationship e^(-iHt) and its dependence on evolution time t to extract energy information. By measuring at multiple time points and fitting the time-dependent behavior, the method captures the dynamic evolution pattern without requiring discrete Trotter steps, thereby avoiding discretization errors while maintaining implementability on quantum computers
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The method achieves chemical accuracy in energy measurements on NISQ devices without error mitigation, reducing circuit depth and sensitivity to noise, and is applicable to small molecules with high-fidelity qubits.
Implementation Method 1
quantum computers utilise qubits or qudits which may exist in a superposition of different computational states
Implementation Method 2
A(t) = e^(-i∫₀ᵗ H(τ)dτ) is an adiabatic evolution operator that transforms an initial quantum state |ψ(0)〉 to a final quantum state |ψ(t)〉
Data Source
AI summary
Provided are computer-implemented methods and quantum computing systems for preparing computational states representing quantum states of a physical system, including performing a computational evolution of the state and then determining physical properties of the system using the time-evolved computational state. Hamiltonian dynamics of observables are computed on a quantum computer to provide information about the physical system represented by the Hamiltonian. Low energy electronic structure states of a physical system are prepared using adiabatic evolution. The energy of an equilibrium quantum state of a physical system is determined using a time-evolution operator. The energy of an eigenstate of a physical system is indirectly determined by evaluating expectation values of a time-evolution operator averaged across multiple shots for randomly-generated quantum circuits. Example methods enable calculation of the energy of an evolved computational state with chemical accuracy, due to avoiding discretization errors, with a smaller circuit depth than known alternatives.