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Simulating a fermionic system on a quantum computer requires encoding the anti-commuting fermionic variables into the operators acting on the qubit Hilbert space. The most familiar of which, the Jordan-Wigner transformation, encodes…
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…
The variational quantum eigensolver (VQE) is one of the most appealing quantum algorithms to simulate electronic structure properties of molecules on near-term noisy intermediate-scale quantum devices. In this work, we generalize the VQE…
The ability to perform classically intractable electronic structure calculations is often cited as one of the principal applications of quantum computing. A great deal of theoretical algorithmic development has been performed in support of…
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…
Quantum simulations before fault tolerance suffer from the intrinsic noise present in quantum computers. In this regime, extracting meaningful results greatly benefits from stability against that noise. This stability, defined as an error…
Quantum computers potentially have an exponential advantage over classical computers for the quantum simulation of many-fermion quantum systems. Nonetheless, fermions are more expensive to simulate than bosons due to the fermionic encoding…
We present a quantum algorithm for the simulation of molecular systems that is asymptotically more efficient than all previous algorithms in the literature in terms of the main problem parameters. As in previous work [Babbush et al., New…
Number-conserved subspace encoding reduces resources needed for quantum simulations, but scalable complexity trade-off bounds for $M$ modes and $N$ particles with $\mathcal{O}(N\log M)$ qubits have remained unknown. We study…
We present a quantum algorithm for simulating quantum chemistry with gate complexity $\tilde{O}(N^{1/3} \eta^{8/3})$ where $\eta$ is the number of electrons and $N$ is the number of plane wave orbitals. In comparison, the most efficient…
We simulate the excited states of the Lipkin model using the recently proposed Quantum Equation of Motion (qEOM) method. The qEOM generalizes the EOM on classical computers and gives access to collective excitations based on quasi-boson…
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…
We present an exact ansatz for the eigenstate problem of mixed fermion-boson systems that can be implemented on quantum devices. Based on a generalization of the electronic contracted Schr\"odinger equation (CSE), our approach guides a…
We provide a new approach to error mitigation for quantum chemistry simulation that uses a Bravyi-Kitaev Superfast encoding to implement a quantum error detecting code within the fermionic encoding. Our construction has low-weight parity…
Quantum phase estimation (QPE) is a promising quantum algorithm for obtaining molecular ground-state energies with chemical accuracy. However, its computational cost, dominated by the Hamiltonian 1-norm $\lambda$ and the cost of the block…
The simulation of strongly correlated fermionic systems remains one of the most significant challenges in computational physics due to the exponential growth of the Hilbert space and the fermionic sign problem. In this work, we present a…
Reducing the complexity of quantum algorithms to treat quantum chemistry problems is essential to demonstrate an eventual quantum advantage of Noisy-Intermediate Scale Quantum (NISQ) devices over their classical counterpart. Significant…
The simulation of quantum many-body systems, relevant for quantum chemistry and condensed matter physics, is one of the most promising applications of near-term quantum computers before fault-tolerance. However, since the vast majority 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…
Quantum simulation of chemical Hamiltonians enables the efficient calculation of chemical properties. Mapping is one of the essential steps in simulating fermionic systems on quantum computers. In this work, a unified framework of…