Related papers: Better bounds for low-energy product formulas
Establishing the precise computational boundary between classically tractable fermionic systems and those capable of genuine quantum advantage is a central challenge in quantum simulation. While injecting non-Gaussian ``magic" inputs into…
We present a new approach to simulating Hamiltonian dynamics based on implementing linear combinations of unitary operations rather than products of unitary operations. The resulting algorithm has superior performance to existing simulation…
Despite significant progress in quantum computing in recent years, executing quantum circuits for practical problems remains challenging due to error-prone quantum hardware. Hence, quantum error correction becomes essential but induces…
Analog quantum simulation is emerging as a powerful tool for uncovering classically unreachable physics such as many-body real-time dynamics. A complete quantification of uncertainties is necessary in order to make precise predictions using…
The well-conditioned multi-product formula (MPF), proposed by [Low, Kliuchnikov, and Wiebe, 2019], is a simple high-order time-independent Hamiltonian simulation algorithm that implements a linear combination of standard product formulas of…
Quantum computing holds promise for revolutionizing computational chemistry simulations, particularly in drug discovery. However, current quantum hardware is limited by noise and scale, necessitating bridging technologies. This study…
Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized…
We propose a novel technique for optimizing a modular fault-tolerant quantum computing architecture, taking into account any desired space-time trade-offs between the number of physical qubits and the fault-tolerant execution time of a…
The Lie-Trotter formula, together with its higher-order generalizations, provides a direct approach to decomposing the exponential of a sum of operators. Despite significant effort, the error scaling of such product formulas remains poorly…
The power system of the future will be governed by complex interactions and non-linear phenomena at small time-scales, that should be studied more and more through computationally expensive software simulations. To solve the abovementioned…
Suppressing the Trotter error in dynamical quantum simulation typically requires running deeper circuits, posing a great challenge for noisy near-term quantum devices. Studies have shown that the empirical error is usually much smaller than…
Complicated boundary conditions are essential to accurately describe phenomena arising in nature and engineering. Recently, the investigation of a potential speedup through quantum algorithms in simulating the governing ordinary and partial…
Trotter product formulas are a natural and powerful approach to perform quantum simulation. However, the error analysis of product formulas is challenging, and their cost is often overestimated. It is established that Trotter error can be…
In this paper, we address the problem of state communication in finite-level quantum systems through noise-affected channels. Our approach is based on a self-consistent theory of decoding inner products associated with the code and error…
We investigate the effect of analog control errors which deterministically occurs on isolated quantum dynamics. Quantum information technologies require careful control for preparing a desired quantum state used as an information resource.…
We analyze the long time behavior of a quantum computer running a quantum error correction (QEC) code in the presence of a correlated environment. Starting from a Hamiltonian formulation of realistic noise models, and assuming that QEC is…
A multi-product formula (MPF) is a promising approach for Hamiltonian simulation efficiently both in the system size $N$ and the inverse allowable error $1/\varepsilon$ by combining Trotterization and the linear combination of unitaries…
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
The ground state energy and the free energy of Quantum Local Hamiltonians are fundamental quantities in quantum many-body physics, however, it is QMA-Hard to estimate them in general. In this paper, we develop new techniques to find…
Compared with time independent Hamiltonians, the dynamics of generic quantum Hamiltonians $H(t)$ are complicated by the presence of time ordering in the evolution operator. In the context of digital quantum simulation, this difficulty…