Abstract
We propose VQE circuit fabrics with advantageous properties for the simulation of strongly correlated ground and excited states of molecules and materials under the Jordan–Wigner mapping that can be implemented linearly locally and preserve all relevant quantum numbers: the number of spin up (α) and down (β) electrons and the total spin squared. We demonstrate that our entangler circuits are expressive already at low depth and parameter count, appear to become universal, and may be trainable without having to cross regions of vanishing gradient, when the number of parameters becomes sufficiently large and when these parameters are suitably initialized. One particularly appealing construction achieves this with just orbital rotations and pair exchange gates. We derive optimal four-term parameter shift rules for and provide explicit decompositions of our quantum number preserving gates and perform numerical demonstrations on highly correlated molecules on up to 20 qubits.
Highlights
Hybrid quantum classical variational algorithms, including those of the variational quantum eigensolver (VQE) type [1, 2], are among the leading candidates for quantum algorithms that may yield quantum advantage in areas such as computational chemistry or machine learning already in the era of noisy intermediate scale quantum (NISQ) computing [3]
Within the context of VQE for spin-1/2 fermions governed by real, spin-free Hamiltonian operators, a variety of compelling VQE entangler circuit recipes have been discussed in the litera
The tail of amplitudes exactly zero in full configuration interaction (FCI) is exactly extinguished in the VQE state only when numerical universality is achieved at a 180-parameter VQE gate fabric
Summary
Hybrid quantum classical variational algorithms, including those of the variational quantum eigensolver (VQE) type [1, 2], are among the leading candidates for quantum algorithms that may yield quantum advantage in areas such as computational chemistry or machine learning already in the era of noisy intermediate scale quantum (NISQ) computing [3]. Perhaps the most notable property of our fabrics is the exact preservation of all relevant quantum numbers the individual gate elements of the fabric, which is why we refer to them as quantum number preserving (QNP) This property may be critical for employment of VQE in larger systems, where contaminations from or even variational collapse onto states with different particle or spin quantum numbers can severely degrade the quality of the VQE wavefunction. This paper refactors k-UpCCGSD to use nearest-neighbor connectivity, yielding a circuit fabric that could be written in terms of four-qubit gates containing diagonal pair exchange and orbital rotation elements in a very similar manner as our Q-type QNP gate fabric discussed below. We encourage any readers interested in the present manuscript to explore [17]
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