Related papers: Exact Factorization of Unitary Transformations wit…
Recent work has deployed linear combinations of unitaries techniques to reduce the cost of fault-tolerant quantum simulations of correlated electron models. Here, we show that one can sometimes improve upon those results with optimized…
The Quantum Fourier transform (QFT) is a key ingredient in most quantum algorithms. We have compared various spin-based quantum computing schemes to implement the QFT from the point of view of their actual time-costs and the accuracy of the…
Recently double-bracket quantum algorithms have been proposed as a way to compile circuits for approximating eigenstates. Physically, they consist of appropriately composing evolutions under an input Hamiltonian together with diagonal…
We introduce the problem of unitarization. Unitarization is the problem of taking $k$ input quantum circuits that produce orthogonal states from the all $0$ state, and create an output circuit implementing a unitary with its first $k$…
By expressing the electronic wavefunction in an explicitly-correlated (Jastrow-factorised) form, a similarity-transformed effective Hamiltonian can be derived. The effective Hamiltonian is non-Hermitian and contains three-body interactions.…
A formal analysis is conducted on the exactness of various forms of unitary coupled cluster (UCC) theory based on particle-hole excitation and de-excitation operators. Both the conventional single exponential UCC parameterization and a…
Many applications of practical interest rely on time evolution of Hamiltonians that are given by a sum of Pauli operators. Quantum circuits for exact time evolution of single Pauli operators are well known, and can be extended trivially to…
Achieving an accurate description of fermionic systems typically requires considerably many more orbitals than fermions. Previous resource analyses of quantum chemistry simulation often failed to exploit this low fermionic number…
We demonstrate how structured decompositions of unitary operators can be employed to derive control schemes for finite-level quantum systems that require only sequences of simple control pulses such as square wave pulses with finite rise…
Quantum operations on pure states can be fully represented by unitary matrices. Variational quantum circuits, also known as quantum neural networks, embed data and trainable parameters into gate-based operations and optimize the parameters…
The Variational Quantum Eigensolver approach to the electronic structure problem on a quantum computer involves measurement of the Hamiltonian expectation value. Formally, quantum mechanics allows one to measure all mutually commuting or…
In the fermion loop formulation the contributions to the partition function naturally separate into topological equivalence classes with a definite sign. This separation forms the basis for an efficient fermion simulation algorithm using a…
Developing optimal strategies to calibrate quantum processors for high-fidelity operation is one of the outstanding challenges in quantum computing today. Here, we demonstrate multiple examples of high-fidelity operations achieved using a…
Estimating the expectation value of an operator corresponding to an observable is a fundamental task in quantum computation. It is often impossible to obtain such estimates directly, as the computer is restricted to measuring in a fixed…
We propose a method for the realization of the two-qubit quantum Fourier transform (QFT) using a Hamiltonian which possesses the circulant symmetry. Importantly, the eigenvectors of the circulant matrices are the Fourier modes and do not…
Shor's algorithm for the prime factorization of numbers provides an exponential speedup over the best known classical algorithms. However, nontrivial practical applications have remained out of reach due to experimental limitations. The…
Transformations which convert between Fermionic modes and qubit operations have become a ubiquitous tool in quantum algorithms for simulating systems. Similarly, collections of Pauli operators might be obtained from solutions of non-local…
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…
We introduce a novel parameterization of complex unitary matrices, which allows for the efficient photonic implementation of arbitrary linear discrete unitary operators. The proposed architecture is built on factorizing an $N \times N$…
We establish a toolbox for studying and applying spin-adapted generalized Pauli constraints (GPCs) in few-electron quantum systems. By exploiting the spin symmetry of realistic $N$-electron wave functions, the underlying one-body pure…