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arXiv:0808.2306 · Physical Review A

Quantum state transfer with untunable couplings

P. K. Gagnebin, S.R. Skinner, Elizabeth Behrman, James E. Steck

Published Feb 12, 2007• 11 citations
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Abstract

We present a general scheme for implementing bidirectional quantum state transfer in a quantum swapping channel. Unlike many other schemes for quantum computation and communication, our method does not require qubit couplings to be switched on and off. The only control variable is the bias acting on individual qubits. We show how to derive the parameters of the system (fixed and variable) such that perfect state transfer can be achieved. Since these parameters vary linearly with the pulse width, our scheme allows flexibility in the time scales under which qubits evolve. Unlike quantum spin networks, our scheme allows the transmission of several quantum states at a time, requiring only a two qubit separation between quantum states. By pulsing the biases of several qubits at the same time, we show that only eight bias control lines are required to achieve state transfer along a channel of arbitrary length. Furthermore, when the information to be transferred is purely classical in nature, only three bias control lines are required, greatly simplifying the circuit complexity.

DOI
10.1103/physreva.75.022310

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We present a general scheme for implementing bidirectional quantum state transfer in a quantum swapping channel. Unlike many other schemes for quantum computation and communication, our method does not require qubit couplings to be switched on and off. The only control variable is the bias acting on individual qubits. We show how to derive the parameters of the system (fixed and variable) such that perfect state transfer can be achieved. Since these parameters vary linearly with the pulse width, our scheme allows flexibility in the time scales under which qubits evolve. Unlike quantum spin networks, our scheme allows the transmission of several quantum states at a time, requiring only a two qubit separation between quantum states. By pulsing the biases of several qubits at the same time, we show that only eight bias control lines are required to achieve state transfer along a channel of arbitrary length. Furthermore, when the information to be transferred is purely classical in nature, only three bias control lines are required, greatly simplifying the circuit complexity.
We propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary entangled states between two distant parties, and can, by using such systems in parallel, transmit the higher-dimensional systems states across the network. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to NNN-qubit spin networks of identical qubit couplings, we show that 2log3N2\phantom{\rule{0.2em}{0ex}}{\mathrm{log}}_{3}N2log3​N is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits then perfect state transfer can be achieved over arbitrarily long distances in a linear chain. This paper expands and extends the work done by Christandl et al., Phys. Rev. Lett. 92, 187902 (2004).
We propose a class of qubit networks that admit the perfect state transfer of any quantum state in a fixed period of time. Unlike many other schemes for quantum computation and communication, these networks do not require qubit couplings to be switched on and off. When restricted to N-qubit spin networks of identical qubit couplings, we show that 2log3N is the maximal perfect communication distance for hypercube geometries. Moreover, if one allows fixed but different couplings between the qubits, then perfect state transfer can be achieved over arbitrarily long distances in a linear chain.
Spin chains have been proposed as wires to transport information between distributed registers in a quantum information processor. Unfortunately, the challenges in manufacturing linear chains with engineered couplings has hindered experimental implementations. Here we present strategies to achieve perfect quantum information transport in arbitrary spin networks. Our proposal is based on the weak coupling limit for pure state transport, where information is transferred between two end spins that are only weakly coupled to the rest of the network. This regime allows ignoring the complex, internal dynamics of the bulk network and relying on virtual transitions or on the coupling to a single bulk eigenmode. We further introduce control methods capable of tuning the transport process and achieve perfect fidelity with limited resources, involving only manipulation of the end qubits. These strategies could be thus applied not only to engineered systems with relaxed fabrication precision, but also to naturally occurring networks; specifically, we discuss the practical implementation of quantum state transfer between two separated nitrogen vacancy (NV) centers through a network of nitrogen substitutional impurities.
Perfect quantum state transfer is achievable in different settings, including linear qubit chains, bi-dimensional arrays, ladders, etc. The most studied case contemplates transferring arbitrary one-qubit pure states in systems with homogeneous interactions. These restrictions allow finding numerous examples of systems that show perfect transfer but in geometries that are not implementable or are very difficult to implement in actual experimental settings. Relaxing the homogeneity of the interactions and inspired by the XXXXXX qubit chains that show perfect transmission, we present a simple scheme based on the Givens Transformations to analyse and obtain a class of qubit graphs that possess perfect quantum state transmission. We present some simple examples and show how it is possible to generalize them for longer transmission lengths.
Quantum information processing requires faithful on-chip transfer of quantum states, but the couplings in solid-state systems are usually preset and not tunable, and thus in general cannot meet the special configurations needed for perfect quantum state transfer. The authors demonstrate such a perfect transfer in a chain of four superconducting qubits with nearest-neighbor coupling through $i\phantom{\rule{0}{0ex}}n$ $s\phantom{\rule{0}{0ex}}i\phantom{\rule{0}{0ex}}t\phantom{\rule{0}{0ex}}u$ parametric modulation, in a single step, with high fidelity (99.2%) in a short time (84 ns), thus overcoming the fixed-coupling problem. Their scheme for flexible tunability of multiqubit coupling can be easily extended to larger systems.
We introduce a scheme for realizing arbitrary controlled-unitary operations in a two-qubit system. If the $2\ifmmode\times\else\texttimes\fi{}2$ unitary matrix is special unitary (has unit determinant), the controlled-unitary gate operation can be realized in a single pulse operation. The pulse in our scheme will constitute varying one of the parameters of the system between an arbitrarily maximum and a ``calculated'' minimum value. This parameter will constitute the variable parameter of the system while the other parameters, which include the coupling between the two qubits, will be treated as fixed parameters. The values of the parameters are what we solve for using our approach in order to realize an arbitrary controlled-unitary operation. We further show that the computational complexity of the operation is no greater than that required for a controlled-NOT (CNOT) gate. Since conventional schemes realize a controlled-unitary operation by breaking it into a sequence of single-qubit and CNOT gate operations, our method is an improvement because we not only require less time duration, but also fewer control lines to implement the same operation. To demonstrate improvement over other schemes, we show, as examples, how two controlled-unitary operations, one being the controlled-Hadamard gate, can be realized in a single pulse operation using our scheme. Furthermore, our method can be applied to a wide range of coupling schemes and can be used to realize gate operations between two qubits coupled via Ising, Heisenberg, and anisotropic interactions.