48 research outputs found
Clock Quantum Monte Carlo: an imaginary-time method for real-time quantum dynamics
In quantum information theory, there is an explicit mapping between general
unitary dynamics and Hermitian ground state eigenvalue problems known as the
Feynman-Kitaev Clock. A prominent family of methods for the study of quantum
ground states are quantum Monte Carlo methods, and recently the full
configuration interaction quantum Monte Carlo (FCIQMC) method has demonstrated
great promise for practical systems. We combine the Feynman-Kitaev Clock with
FCIQMC to formulate a new technique for the study of quantum dynamics problems.
Numerical examples using quantum circuits are provided as well as a technique
to further mitigate the sign problem through time-dependent basis rotations.
Moreover, this method allows one to combine the parallelism of Monte Carlo
techniques with the locality of time to yield an effective parallel-in-time
simulation technique
Increasing the representation accuracy of quantum simulations of chemistry without extra quantum resources
Proposals for near-term experiments in quantum chemistry on quantum computers
leverage the ability to target a subset of degrees of freedom containing the
essential quantum behavior, sometimes called the active space. This
approximation allows one to treat more difficult problems using fewer qubits
and lower gate depths than would otherwise be possible. However, while this
approximation captures many important qualitative features, it may leave the
results wanting in terms of absolute accuracy (basis error) of the
representation. In traditional approaches, increasing this accuracy requires
increasing the number of qubits and an appropriate increase in circuit depth as
well. Here we introduce a technique requiring no additional qubits or circuit
depth that is able to remove much of this approximation in favor of additional
measurements. The technique is constructed and analyzed theoretically, and some
numerical proof of concept calculations are shown. As an example, we show how
to achieve the accuracy of a 20 qubit representation using only 4 qubits and a
modest number of additional measurements for a simple hydrogen molecule. We
close with an outlook on the impact this technique may have on both near-term
and fault-tolerant quantum simulations
Qubitization of Arbitrary Basis Quantum Chemistry Leveraging Sparsity and Low Rank Factorization
Recent work has dramatically reduced the gate complexity required to quantum simulate chemistry by using linear combinations of unitaries based methods to exploit structure in the plane wave basis Coulomb operator. Here, we show that one can achieve similar scaling even for arbitrary basis sets (which can be hundreds of times more compact than plane waves) by using qubitized quantum walks in a fashion that takes advantage of structure in the Coulomb operator, either by directly exploiting sparseness, or via a low rank tensor factorization. We provide circuits for several variants of our algorithm (which all improve over the scaling of prior methods) including one with Õ(N^(3/2)λ) T complexity, where N is number of orbitals and λ is the 1-norm of the chemistry Hamiltonian. We deploy our algorithms to simulate the FeMoco molecule (relevant to Nitrogen fixation) and obtain circuits requiring about seven hundred times less surface code spacetime volume than prior quantum algorithms for this system, despite us using a larger and more accurate active space