Spin-path truncation plus symmetric-group rules yields sparse local qubit Hamiltonians for the Heisenberg model, with shallow adiabatic circuits reaching about 99 percent fidelity for N=16.
Approximating many-body quantum states with quantum circuits and measurements
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We introduce protocols to prepare many-body quantum states with quantum circuits assisted by local operations and classical communication. We show that by lifting the requirement of exact preparation, one can substantially save resources. In particular, the so-called $W$ and, more generally, Dicke states require a circuit depth and number of ancillas per site that are independent of the system size. As a byproduct of our work, we introduce an efficient scheme to implement certain non-local, non-Clifford unitary operators. We also discuss how similar ideas may be applied in the preparation of eigenstates of well-known spin models, both free and interacting.
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Quantum computing in spin-adapted representations for efficient simulations of spin systems
Spin-path truncation plus symmetric-group rules yields sparse local qubit Hamiltonians for the Heisenberg model, with shallow adiabatic circuits reaching about 99 percent fidelity for N=16.