Related papers: Optimised Fermion-Qubit Encodings for Quantum Simu…
We consider a hybrid digital-analog quantum computing approach, which allows implementing any quantum algorithm without standard two-qubit gates. This approach is based on the always-on interaction between qubits, which can provide an…
Simulating the real-time dynamics of lattice gauge theories, underlying the Standard Model of particle physics, is a notoriously difficult problem where quantum simulators can provide a practical advantage over classical approaches. In this…
When designing quantum circuits for a given unitary, it can be much cheaper to achieve a good approximation on most inputs than on all inputs. In this work we formalize this idea, and propose that such "optimistic quantum circuits" are…
Quantum chemistry simulations on a quantum computer suffer from the overhead needed for encoding the fermionic problem in a bosonic system of qubits. By exploiting the block diagonality of a fermionic Hamiltonian, we show that the number of…
Quantum noise in real-world devices poses a significant challenge in achieving practical quantum advantage, since accurately compiled and executed circuits are typically deep and highly susceptible to decoherence. To facilitate the…
Recent work [M. J. Gullans et al., Physical Review X, 11(3):031066 (2021)] has shown that quantum error correcting codes defined by random Clifford encoding circuits can achieve a non-zero encoding rate in correcting errors even if the…
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…
We investigate the simulation of fermionic systems on a quantum computer. We show in detail how quantum computers avoid the dynamical sign problem present in classical simulations of these systems, therefore reducing a problem believed to…
We develop a hardware-efficient ansatz for variational optimization, derived from existing ansatze in the literature, that parametrizes subsets of all interactions in the Cost Hamiltonian in each layer. We treat gate orderings as a…
Fault tolerant quantum simulation via the phase estimation algorithm and qubitization has a T-gate count that scales proportionally to the 1-norm of the Hamiltonian, the cost of block encoding the Hamiltonian, and inversely proportionally…
We develop new algorithms for Quantum Singular Value Transformation (QSVT), a unifying framework that encapsulates most known quantum algorithms and serves as the foundation for new ones. Existing implementations of QSVT rely on block…
Performing large-scale, accurate quantum simulations of many-fermion systems is a central challenge in quantum science, with applications in chemistry, materials, and high-energy physics. Despite significant progress, realizing generic…
Quantum computing applications in the noisy intermediate-scale quantum (NISQ) era require algorithms that can generate shallower circuits feasible for today's quantum systems. This is particularly challenging for quantum chemistry…
The time evolution operator plays a crucial role in the precise computation of chemical experiments on quantum computers and holds immense promise for advancing the fields of physical and computer sciences, with applications spanning…
Quantum simulation of the electronic structure problem is one of the most researched applications of quantum computing. The majority of quantum algorithms for this problem encode the wavefunction using $N$ Gaussian orbitals, leading to…
We develop and analyze a method for simulating quantum circuits on classical computers by representing quantum states as rooted tree tensor networks. Our algorithm first determines a suitable, fixed tree structure adapted to the expected…
Simulating quantum dynamics on classical computers is challenging for large systems due to the significant memory requirements. Simulation on quantum computers is a promising alternative, but fully optimizing quantum circuits to minimize…
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…
Quantum simulations of fermionic many-body systems crucially rely on mappings from indistinguishable fermions to distinguishable qubits. The non-local structure of fermionic Fock space necessitates encodings that either map local fermionic…
In this paper, we design quantum circuits for the exponential of scaled $n$-qubit Pauli strings using single-qubit rotation gates, Hadamard gate, and CNOT gates. A key result we derive is that any two Pauli-string operators composed of…