We implement a linear Heisenberg spin-1/2 chain with XXZ couplings, which in it self can be used as an analog quantum simulator, using superconducting circuits. Depending on the circuit
the spin chain can have arbitrary length. For a specific length of four qubits we show that the circuit can be used to implement a quantum spin transistor following the protocol proposed in Nature Communication 5 13070 (2016). We do this by finding experimentally realistic parameters for the circuit and proposing a chip design. The quantum transistor works similarly to its classical analogue allowing transfer or blockage depending on the state of the two gate qubits, but opens up a variety of possibilities when quantum mechanical superpositions are considered. The transistor is simulated under realistic decoherence and it is shown that it allows high-fidelity transfer when open, while it allows no transfer when closed. The main effect of the decoherence is faster leakage from the transistor. The transistor is also considered when it is in an superposition of open and closed. We obtain transition times less than 200ns, and rule out leakage to higher excited states in the superconducting circuit design. Finally, we discuss further spin models which can be obtained be altering the circuit in different ways.
As classical computers struggle to keep up with Moore’s law, quantum computing may represent a big step in technology and yield significant improvement over classical computing
for many important tasks. Building a quantum computer, however, is a daunting challenge since it requires good control but also good isolation from the environment to minimize decoherence. It is therefore important to realize quantum gates efficiently, using as few operations as possible, to reduce the amount of required control and operation time and thus improve the quantum state coherence. Here we propose a superconducting circuit for implementing a tunable spin chain consisting of a qutrit (three-level system analogous to spin-1) coupled to two qubits (spin-1/2). Our system can efficiently accomplish various quantum information tasks, including generation of entanglement of the two qubits and conditional three-qubit quantum gates, such as the Toffoli and Fredkin gates, which are universal for reversible classical computations. Furthermore, our system realizes a conditional geometric gate which may be used for holonomic (non-adiabatic) quantum computing. The efficiency, robustness and universality of our circuit makes it a promising candidate to serve as a building block for larger spin networks capable of performing involved quantum computational tasks.
Transistors play a vital role in classical computers, and their quantum mechanical counterparts could potentially be as important in quantum computers. Where a classical transistor
is operated as a switch that either blocks or allows an electric current, the quantum transistor should operate on quantum information. In terms of a spin model the in-going quantum information is an arbitrary qubit state (spin-1/2 state). In this paper, we derive a model of four qubits with Heisenberg interactions that works as a quantum spin transistor, i.e. a system with perfect state transfer or perfect blockade depending on the state of two gate qubits. We propose a realistic implementation of the model using state-of-the-art superconducting circuits. Finally, we demonstrate that our proposal operates with high-fidelity under realistic decoherence, and without fine-tuning of any of the parameters.