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Simulation of interacting fermionic Hamiltonians is one of the most promising applications of quantum computers. However, the feasibility of analysing fermionic systems with a quantum computer hinges on the efficiency of fermion-to-qubit…

Simulating fermionic systems on a quantum computer requires a high-performing mapping of fermionic states to qubits. A characteristic of an efficient mapping is its ability to translate local fermionic interactions into local qubit…

We present a general strategy for mapping fermionic systems to quantum hardware with square qubit connectivity which yields low-depth quantum circuits, counted in the number of native two-qubit fSIM gates. We achieve this by leveraging…

The utility of solving the Fermi-Hubbard model has been estimated in the billions of dollars. Digital quantum computers can in principle address this task, but have so far been limited to quasi one-dimensional models. This is because of…

Simulating molecular systems on quantum computers requires efficient mappings from Fermionic operators to qubit operators. Traditional mappings such as Jordan-Wigner or Bravyi-Kitaev often produce high-weight Pauli terms, increasing circuit…

Simulation of fermionic systems is one of the most promising applications of quantum computers. It spans problems in quantum chemistry, high-energy physics and condensed matter. Underpinning the core steps of any quantum simulation…

Fermion-to-qubit mappings are used to represent fermionic modes on quantum computers, an essential first step in many quantum algorithms for electronic structure calculations. In this work, we present a formalism to design flexible…

This paper introduces the Hamiltonian-Adaptive Ternary Tree (HATT) framework to compile optimized Fermion-to-qubit mapping for specific Fermionic Hamiltonians. In the simulation of Fermionic quantum systems, efficient Fermion-to-qubit…

Simulation of fermionic Hamiltonians with gate-based quantum computers requires the selection of an encoding from fermionic operators to quantum gates, the most widely used being the Jordan-Wigner transform. Many alternative encodings…

Variational quantum algorithms rely on the optimization of parameterized quantum circuits in noisy settings. The commonly used back-propagation procedure in classical machine learning is not directly applicable in this setting due to the…

This paper introduces Fermihedral, a compiler framework focusing on discovering the optimal Fermion-to-qubit encoding for targeted Fermionic Hamiltonians. Fermion-to-qubit encoding is a crucial step in harnessing quantum computing for…

This paper introduces an abstract framework for randomized subspace correction methods for convex optimization, which unifies and generalizes a broad class of existing algorithms, including domain decomposition, multigrid, and block…

Learning quantum Hamiltonians with high precision is important for quantum physics and quantum information science. We propose a multi-stage neural network framework that significantly enhances Hamiltonian learning precision through…

In ab-initio electronic structure simulations, fermion-to-qubit mappings represent the initial encoding step of the fermionic problem into qubits. This work introduces a physically-inspired method for constructing mappings that…

In recent work [arXiv:2003.06939v2] a novel fermion to qubit mapping -- called the compact encoding -- was introduced which outperforms all previous local mappings in both the qubit to mode ratio, and the locality of mapped operators. There…

We introduce a fermion-to-qubit mapping defined on ternary trees, where any single Majorana operator on an $n$-mode fermionic system is mapped to a multi-qubit Pauli operator acting nontrivially on $\lceil \log_3(2n+1)\rceil$ qubits. The…

We present a framework for computing the solution to Hamiltonian eigenproblems in a subspace defined by bit-strings sampled from a quantum computer. Hamiltonians are represented using an extended alphabet that includes projection and ladder…

This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of…

Numerous applications require algorithms that can align partially overlapping point sets while maintaining invariance to geometric transformations (e.g., similarity, affine, rigid). This paper introduces a novel global optimization method…

In this paper, we present a new set of local fermion-to-qudit mappings for simulating fermionic lattice systems. We focus on the use of multi-level qudits, specifically ququarts. Traditional mappings, such as the Jordan-Wigner…