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arXiv:2610.01704

Less precise but less noisy: local circuits for momentum-space state preparation and measurement

Etienne Granet, Henrik Dreyer

On Aqora:Etienne GranetEtienne Granet
quant-phSubmitted Oct 1, 2026• Announced Oct 2, 2026• 0 citations
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Abstract

Quantum algorithms are usually optimized for gate count or circuit depth. We find on Quantinuum System Model H2 quantum computer that for a tight-binding chain ground state preparation, there is a system size $N$ beyond which the adiabatic evolution reaches significantly lower energies than the Fermionic Fourier Transform (FFT), with the same number of gates, and with the same circuit depth. We attribute this high noise sensitivity of the FFT to its high precision, being able to distinguish momenta by $1/N$. This high resolution in momentum space requires long-range couplings in real space, which propagates errors faster. In contrast, although local and physical circuits such as the adiabatic evolution have a coarser momentum resolution, they also propagate errors more slowly. For physical applications, high momentum resolution is rarely required and is often worth trading for low noise sensitivity. We also introduce a momentum measurement scheme that although less precise than FFT, is less costly and less noisy. We show that it achieves better performance than FFT for spectral function measurement on Quantinuum System Model H2 quantum computer. Our work emphasizes the importance of reducing the noise sensitivity of quantum algorithms, beyond the number of gates or circuit depth.

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Quantum algorithms are usually optimized for gate count or circuit depth. We find on Quantinuum System Model H2 quantum computer that for a tight-binding chain ground state preparation, there is a system size NNN beyond which the adiabatic evolution reaches significantly lower energies than the Fermionic Fourier Transform (FFT), with the same number of gates, and with the same circuit depth. We attribute this high noise sensitivity of the FFT to its high precision, being able to distinguish momenta by 1/N1/N1/N. This high resolution in momentum space requires long-range couplings in real space, which propagates errors faster. In contrast, although local and physical circuits such as the adiabatic evolution have a coarser momentum resolution, they also propagate errors more slowly. For physical applications, high momentum resolution is rarely required and is often worth trading for low noise sensitivity. We also introduce a momentum measurement scheme that although less precise than FFT, is less costly and less noisy. We show that it achieves better performance than FFT for spectral function measurement on Quantinuum System Model H2 quantum computer. Our work emphasizes the importance of reducing the noise sensitivity of quantum algorithms, beyond the number of gates or circuit depth.
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Despite its simplicity and strong theoretical guarantees, adiabatic state preparation has received considerably less interest than variational approaches for the preparation of low-energy electronic structure states. Two major reasons for this are the large number of gates required for Trotterizing time-dependent electronic structure Hamiltonians, as well as discretization errors heating the state. We show that a recently proposed randomized algorithm [E. Granet and H. Dreyer, npj Quantum Inf. 10, 82 (2024)], which implements exact adiabatic evolution without heating and with far fewer gates than Trotterization, can overcome this problem. We develop three methods for measuring the energy of the prepared state in an efficient and noise-resilient manner, yielding chemically accurate results on a four-qubit molecule in the presence of realistic gate noise, without the need for error mitigation. These findings suggest that adiabatic approaches to state preparation could play a key role in quantum chemistry simulations both in the era of noisy as well as error-corrected quantum computers.
Quantum computing not only holds the potential to solve long-standing problems in quantum physics, but also to offer speed-ups across a broad spectrum of other fields. Access to a computational space that incorporates quantum effects, such as superposition and entanglement, enables the derivation of promising quantum algorithms for important tasks, including preparing the ground state of a quantum system or predicting its evolution over time. Successfully tackling these tasks promises insights into significant theoretical and technological questions, such as superconductivity and the design of new materials. The aim of quantum algorithms is to use a series of quantum operations in a quantum circuit to solve a problem beyond the reach of classical computers. However, the noise and limited scale of current quantum computers restricts these circuits to moderate sizes and depths. As a result, many prominent algorithms are currently infeasible to run for problem sizes of practical interest. In response, recent research focused on variational quantum algorithms, which allow the selection of circuits that act within a quantum device's capabilities. Yet, these algorithms can require the execution of a large number of circuits, leading to prohibitively long computation times. This doctoral thesis develops two main techniques to reduce these quantum computational resource requirements, with the goal of scaling up application sizes on current quantum processors. The first approach is based on stochastic approximations of computationally costly quantities, such as quantum circuit gradients or the quantum geometric tensor (QGT). The second method takes a different perspective on the QGT, leading to a potentially more efficient description of time evolution on current quantum computers. Both techniques rely on maintaining available information and only computing necessary corrections, instead of re-computing possibly redundant data. The main focus of application for our algorithms is the simulation of quantum systems, broadly defined as including the preparation of ground and thermal states, and the real- and imaginary-time propagation of a system. The developed subroutines, however, can further be utilized in the fields of optimization or machine learning. Our algorithms are benchmarked on a range of representative models, such as Ising or Heisenberg spin models, both in numerical simulations and experiments on the hardware. In combination with error mitigation techniques, the latter is scaled up to 27 qubits; into a regime that variational quantum algorithms are challenging to scale to on noisy quantum computers without our algorithms.
Estimating the eigenstate properties of quantum systems is a long-standing, challenging problem for both classical and quantum computing. Existing universal quantum algorithms typically rely on ideal and efficient query models (e.g., time evolution operator or block encoding of the Hamiltonian), which, however, become suboptimal for actual implementation at the quantum circuit level. Here, we present a full-stack design of quantum algorithms for estimating the eigenenergy and eigenstate properties, which can achieve high precision and good scaling with system size. The gate complexity per circuit for estimating generic Hamiltonians' eigenstate properties is [Formula: see text], which has a logarithmic dependence on the inverse precision ε. For lattice Hamiltonians, the circuit depth of our design achieves near-optimal system-size scaling, even with local qubit connectivity. Our full-stack algorithm has low overhead in circuit compilation, which thus results in a small actual gate count (cnot and non-Clifford gates) for lattice and molecular problems compared to advanced eigenstate algorithms. The algorithm is implemented on IBM quantum devices using up to 2000 two-qubit gates and 20,000 single-qubit gates and achieves high-precision eigenenergy estimation for Heisenberg-type Hamiltonians, demonstrating its noise robustness.