Related papers: Efficient Product Formulas for Commutators and App…
This paper builds and extends on the authors' previous work related to the algorithmic tool, Cylindrical Algebraic Decomposition (CAD), and one of its core applications, Real Quantifier Elimination (QE). These topics are at the heart of…
We prove classical simulation hardness, under the generalized $\mathsf{P}\neq\mathsf{NP}$ conjecture, for quantum circuit families with applications in near-term chemical ground state estimation. The proof exploits a connection to particle…
Embedding layers are commonly used to map discrete symbols into continuous embedding vectors that reflect their semantic meanings. Despite their effectiveness, the number of parameters in an embedding layer increases linearly with the…
We present an approach to simulating quantum computation based on a classical model that directly imitates discrete quantum systems. Qubits are represented as harmonic functions in a 2D vector space. Multiplication of qubit representations…
We investigate the quantum algorithm of Babbush et al. (arXiv:2303.13012v3) for simulating coupled harmonic oscillators, which promises exponential speedups over classical methods. Focusing on linearly connected oscillator chains, we bridge…
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 Fermi-Hubbard model, a fundamental framework for studying strongly correlated phenomena could significantly benefit from quantum simulations when exploring non-trivial settings. However, simulating this problem requires twice as many…
With the increasing size of quantum processors, sub-modules that constitute the processor hardware will become too large to accurately simulate on a classical computer. Therefore, one would soon have to fabricate and test each new design…
In this paper, we establish a determinantal formula for 2 x 2 matrix commutators [X,Y] = XY - YX over a commutative ring, using (among other invariants) the quantum traces of X and Y. Special forms of this determinantal formula include a…
An efficient parallelization approach to simulate optical properties of ensembles of quantum emitters in realistic electromagnetic environments is considered. It relies on balancing computing load of utilized processors and is built into…
Efficient quantum circuit optimization schemes are central to quantum simulation of strongly interacting quantum many body systems. Here, we present an optimization algorithm which combines machine learning techniques and tensor network…
A central task in the field of quantum computing is to find applications where quantum computer could provide exponential speedup over any classical computer. Machine learning represents an important field with broad applications where…
Multi-product formulas (MPF) are linear combinations of Trotter circuits offering high-quality simulation of Hamiltonian time evolution with fewer Trotter steps. Here we report two contributions aimed at making multi-product formulas more…
We develop a hybrid oscillator-qubit processor framework for quantum simulation of strongly correlated fermions and bosons that avoids the boson-to-qubit mapping overhead encountered in qubit hardware. This framework gives exact…
The effort to generate matrix exponentials and associated differentials, required to determine the time evolution of quantum systems, frequently constrains the evaluation of problems in quantum control theory, variational circuit…
Quantum simulation has shown great potential in many fields due to its powerful computational capabilities. However, the limited fidelity can lead to a severe limitation on the number of gate operations, which requires us to find optimized…
Recent advances in the field of adiabatic quantum computing and the closely related field of quantum annealers has centered around using more advanced and novel Hamiltonian representations to solve optimization problems. One of these…
A strong direct product theorem says that if we want to compute k independent instances of a function, using less than k times the resources needed for one instance, then our overall success probability will be exponentially small in k. We…
A compression algorithm is introduced for multi-determinant wave functions which can greatly reduce the number of determinants that need to be evaluated in quantum Monte Carlo calculations. We have devised an algorithm with three levels of…
A universal quantum simulator would enable efficient simulation of quantum dynamics by implementing quantum-simulation algorithms on a quantum computer. Specifically the quantum simulator would efficiently generate qubit-string states that…