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Molecular simulations generally require fermionic encoding in which fermion statistics are encoded into the qubit representation of the wave function. Recent calculations suggest that fermionic encoding of the wave function can be bypassed, leading to more efficient quantum computations. Here we show that the energy can be expressed as a functional of the two-electron reduced density matrix (2-RDM) where the 2-RDM is a unique functional of the unencoded $N$-qubit-particle wave function. Contrasts are made with current hardware-efficient methods. An application to computing the ground-state energy and 2-RDM of H$_{4}$ is presented.
Simulating quantum many-body systems is a highly demanding task since the required resources grow exponentially with the dimension of the system. In the case of fermionic systems, this is even harder since nonlocal interactions emerge due to the anti
We investigate the encoding of higher-dimensional logic into quantum states. To that end we introduce finite-function-encoding (FFE) states which encode arbitrary $d$-valued logic functions and investigate their structure as an algebra over the ring
In quantum communications, quantum states are employed for the transmission of information between remote parties. This usually requires sharing knowledge of the measurement bases through a classical public channel in the sifting phase of the protoco
Simulation of fermionic many-body systems on a quantum computer requires a suitable encoding of fermionic degrees of freedom into qubits. Here we revisit the Superfast Encoding introduced by Kitaev and one of the authors. This encoding maps a target
Simulating a fermionic system on a quantum computer requires encoding the anti-commuting fermionic variables into the operators acting on the qubit Hilbert space. The most familiar of which, the Jordan-Wigner transformation, encodes fermionic operato