Related papers: Second-quantized fermionic operators with polyloga…
Qutrits, three-level quantum systems, have the advantage of potentially requiring fewer components than the typically used two-level qubits to construct equivalent quantum circuits. This work investigates the potential of qutrit parametric…
In recent years simulations of chemistry and condensed materials has emerged as one of the preeminent applications of quantum computing, offering an exponential speedup for the solution of the electronic structure for certain strongly…
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…
Simulation of quantum systems is expected to be one of the most important applications of quantum computing, with much of the theoretical work so far having focused on fermionic and spin-$\frac{1}{2}$ systems. Here, we instead consider…
We found that the actual computational time-cost of the QFT is O(n 2^n) for large n in a quantum computer using nuclear spins. The computational cost of a quantum algorithm has usually been estimated as the sum of the universal gates…
A new approach to efficient quantum computation with probabilistic gates is proposed and analyzed in both a local and non-local setting. It combines heralded gates previously studied for atom or atom-like qubits with logical encoding from…
Current and near-term quantum hardware is constrained by limited qubit counts, circuit depth, and the high cost of repeated measurements. We address these challenges for solid state Hamiltonians by introducing a logarithmic-qubit encoding…
An important approach to the fault-tolerant quantum computation is protecting the logical information using the quantum error correction. Usually, the logical information is in the form of logical qubits, which are encoded in physical…
We analyze fermionic modes as fundamental entities for quantum information processing. To this end we construct a density operator formalism on the underlying Fock space and demonstrate how it can be naturally and unambiguously equipped…
Many-body fermionic systems can be simulated in a hardware-efficient manner using a fermionic quantum processor. Neutral atoms trapped in optical potentials can realize such processors, where non-local fermionic statistics are guaranteed at…
We provide fast algorithms for simulating many body Fermi systems on a universal quantum computer. Both first and second quantized descriptions are considered, and the relative computational complexities are determined in each case. In…
Since simulating quantum computers requires exponentially more classical resources, efficient algorithms are extremely helpful. We analyze algorithms that create single qubit and specific controlled qubit matrix representations of gates.…
We improve the number of $T$ gates needed for a $b$-bit approximation of a multiplexed quantum gate with $c$ controls applying $n$ single-qubit arbitrary phase rotations from $4n b+\mathcal{O}(\sqrt{cn b})$ to $2n b+\mathcal{O}(\sqrt{cn…
Compiling shallow and accurate quantum circuits for Hamiltonian simulation remains challenging due to hardware constraints and the combinatorial complexity of minimizing gate count and circuit depth. Existing optimization method pipelines…
A major challenge in practical quantum computation is the ineludible errors caused by the interaction of quantum systems with their environment. Fault-tolerant schemes, in which logical qubits are encoded by several physical qubits, enable…
We develop theoretical methods for the implementation of creation and destruction operators in separate registers of a quantum computer, allowing for a transparent and dynamical creation and destruction of particle modes in second…
Parallel computation enables multiple processors to execute different parts of a task simultaneously, improving processing speed and efficiency. In quantum computing, parallel gate implementation involves executing gates independently in…
The cost of data input can dominate the run-time of quantum algorithms. Here, we consider data input of arithmetically structured matrices via block encoding circuits, the input model for the quantum singular value transform and related…
We present a quantum algorithm to compute the logarithm of the determinant of the fermion matrix, assuming access to a classical lattice gauge field configuration. The algorithm uses the quantum eigenvalue transform, and quantum mean…
A fermionic operator circuit is a product of fermionic operators of usually different and partially overlapping support. Further elements of fermionic operator circuits (FOCs) are partial traces and partial projections. The presented…