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First-quantized, real-space formulations of quantum chemistry on quantum computers are appealing: qubit count scales logarithmically with spatial resolution, and Coulomb operators achieve quadratic instead of quartic computational scaling…
We discuss encodings of fermionic many-body systems by qubits in the presence of symmetries. Such encodings eliminate redundant degrees of freedom in a way that preserves a simple structure of the system Hamiltonian enabling quantum…
Quantum simulation of fermionic systems is a leading application of quantum computers. One promising approach is to represent fermions with qubits via fermion-to-qubit mappings. In this work, we present high-distance fermion-to-qubit…
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…
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…
We introduce a protocol for the fast simulation of $n$-dimensional quantum systems on $n$-qubit quantum computers with tunable couplings. A mapping is given between the control parameters of the quantum computer and the matrix elements of…
Solving atomic nuclei from first principles places enormous demands on computational resources, which grow exponentially with increasing number of particles and the size of the space they occupy. We present first quantum simulations based…
Quantum simulation of fermionic Hamiltonians is a leading application of quantum computing, but accurate execution on present-day hardware is limited by error accumulation in deep Trotter circuits. We present a device-matched…
The ability to simulate a fermionic system on a quantum computer is expected to revolutionize chemical engineering, materials design, nuclear physics, to name a few. Thus, optimizing the simulation circuits is of significance in harnessing…
The transformation of a molecular Hamiltonian from the fermionic space to the qubit space results in a series of Pauli strings. Calculating the energy then involves evaluating the expectation values of each of these strings, which presents…
Quantum processors may enhance machine learning by mapping high-dimensional data onto quantum systems for processing. Conventional feature maps, for encoding data onto a quantum circuit are currently impractical, as the number of entangling…
Current quantum devices execute specific tasks that are hard for classical computers and have the potential to solve problems such as quantum simulation of material science and chemistry, even without error correction. For practical…
Quantum computers hold great promise for efficiently simulating Fermionic systems, benefiting fields like quantum chemistry and materials science. To achieve this, algorithms typically begin by choosing a Fermion-to-qubit mapping to encode…
The simulation of entangled ground-states of quantum materials remains challenging for classical computational methods in more than one spatial dimension, and is a prime target for quantum computational advantage. To this end, an important…
Simulating quantum systems is one of the most important potential applications of quantum computers. The high-level circuit defining the simulation needs to be compiled into one that complies with hardware limitations such as qubit…
Many promising quantum applications depend on the efficient quantum simulation of an exponentially large sparse Hamiltonian, a task known as sparse Hamiltonian simulation, which is fundamentally important in quantum computation. Although…
Light-matter coupled Hamiltonians are central to cavity materials engineering and polaritonic chemistry, but are challenging to simulate with classical hardware due to the scaling of the Hilbert space with the number of quantum photon modes…
Simulating the dynamics of electrons and other fermionic particles in quantum chemistry, materials science, and high-energy physics is one of the most promising applications of fault-tolerant quantum computers. However, the overhead in…
Simulating strongly correlated fermionic systems is notoriously hard on classical computers. An alternative approach, as proposed by Feynman, is to use a quantum computer. Here, we discuss quantum simulation of strongly correlated fermionic…
Non-Markovian $1/f$ noise consists a dominant source of decoherence in superconducting qubits, yet its slow nature poses a significant challenge for accurate simulation. Here we develop a hierarchical equations of motion (HEOM) framework…