Abstract
We propose a superconducting qubit that fully emulates a quantum spin-1/2, with an effective vector dipole moment whose three components obey the commutation relations of an angular momentum in the computational subspace. Each of these components of the dipole moment also couples approximately linearly to an independently-controllable external bias, emulating the linear Zeeman effect due to a fictitious, vector magnetic field over a broad range of effective total fields around zero. This capability, combined with established techniques for qubit coupling, should enable for the first time the direct, controllable hardware emulation of nearly arbitrary, interacting quantum spin-1/2 systems, including the canonical Heisenberg model. Furthermore, it constitutes a crucial step both towards realizing the full potential of quantum annealing, as well as exploring important quantum information processing capabilities that have so far been inaccessible to available hardware, such as quantum error suppression, Hamiltonian and holonomic quantum computing, and adiabatic quantum chemistry.
Highlights
We propose a superconducting qubit circuit that can fully emulate a quantum vector spin-1/2, with an effective dipole moment having three independent components whose operators obey the commutation relations of a vector angular momentum in the computational subspace
Quantum spin-1/2 models serve as basic paradigms for a wide variety of physical systems in quantum statistical mechanics and many-body physics, and are among the most highly studied in the context of quantum phase transitions and topological order [1]
Quantum spin-1/2 language is used to describe most of the constructions underlying quantum errorcorrection [2] and error-suppression [3, 4] methods
Summary
Superconducting circuits are already among the most engineerable high-coherence quantum systems available, allowing a range of behavior and interactions to be constructed by design [29, 30]. The difference in potential energy between these two minima is controlled by δΦz (panel (d)), and approximately corresponds to the interaction energy between an applied field and the two equal and opposite persistent currents (panel (e)) These two states naturally play the role of | ± z , the eigenstates of σz for the emulated spin. Since the effective x magnetic moment of each qubit [c.f., eq 5] is the derivative with respect to Φx of this energy, it can only be large when the energy is itself large In spin language, this constraint on transverse coupling between flux qubits corresponds to the x magnetic moments of the emulated spins going exponentially to zero as their local x fields go to zero, as shown in fig. Panel (f) shows the effect of charge displacements away from half a Cooper pair, which act as transverse fields in the y direction
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