Quantum Computation with Untunable Couplings

Abstract

Most quantum computer realizations require the ability to apply local fields and tune the couplings between qubits, in order to realize single bit and two bit gates which are necessary for universal quantum computation. We present a scheme to remove the necessity of switching the couplings between qubits for two bit gates, which are more costly in many cases. Our strategy is to compute in and out of carefully designed interaction free subspaces analogous to decoherence free subspaces, which allows us to effectively turn off and turn on the interactions between the encoded qubits. We give two examples to show how universal quantum computation is realized in our scheme with local manipulations to physical qubits only, for both diagonal and off diagonal interactions. Quantum computation is generally formulated in terms of a collection of qubits subject to a sequence of single and two bit operations [1]. This implies that the effective local fields applied to individual qubits, and the couplings between the qubits, are variable functions subject to external control. In many cases, two bit operations, whose implementation depends on certain interactions between qubits, are more difficult than single bit gates. They can require more sophisticated manipulations, therefore may take a longer time and cause stronger decoherence. This usually results from the requirement to vary (in the simplest case just switch on and off) the couplings between qubits, which is not always possible, or easy to realize. One such example is quantum computing with Josephson junction devices, both charge and flux type [2,3,4,5,6]. In this case, the coupling between qubits is most naturally realized with a hard wired capacitor or inductor, whose value is fixed by the fabrication and cannot be tuned during the computation. The superconducting quantum computing community has been working hard to devise variable coupling schemes [5,7,8,9], but it is generally agreed that none of these proposed switches is completely satisfactory [9]. Most of them [5,7] require external controls, thus are likely to be major decoherence sources. Others were designed to avoid such external controls, but may suffer other problems, for instance the number of qubits that can be incorporated into the system can be limited [8,9], which is at odd with the supposed scalability of a solid state quantum computer.An always on and un-tunable coupling causes certain problems for quantum computation, depending on the particular form of the interaction. If the interaction Hamiltonian is diagonal in the computational basis, each qubit state will gain additional phases depending on the states of the qubits to which it is coupled, even in the idle mode. It is then necessary to keep track of these phases, or suppress them by repeated refocusing pulses like those used in NMR, which requires high precisions and complicates the operation [8,9]. The situation is more serious in the case of off diagonal interactions, because these interactions will cause the states of the qubits to propaga...

Unified approach for universal quantum gates in a coupled superconducting two-qubit system with fixed always-on coupling

“…The second one is additional decoherence introduced by the supplementary circuits. 22,23 This is one of the biggest obstacles for quantum computing with solid-state qubits, particularly in coupled multiqubit systems. 2 In addition, the use of supplementary circuits also significantly increases the complexity of fabrication and manipulation of the coupled qubits.…”

“…This approach can be used to construct scalable quantum information processing with simpler and fewer hardware resources when it is combined with other schemes. [18][19][20][21][22]24 In this approach, each single-qubit gate is realized via two controlled two-qubit gates which we call ͉0͘-controlled and ͉1͘-controlled twoqubit gates, respectively. The ͉0͘ ͉͑1͒͘-controlled gate implements a desired gate in one of the two coupled qubits when the other is in ͉0͘ ͉͑1͒͘.…”

“…However, the scalable quantum information processing for a system with a large number of qubits can be achieved by a hybrid architecture ͑HA͒ 25 in which adjacent basic units are linked by adjustable couplers. [18][19][20][21][22]24 The HA can significantly reduce the complexity of the circuit compared to the conventional scheme ͑CS͒ which uses a qubit as a basic unit. For the sake of concreteness let us consider a generic 1D array of an even number of N qubits with the nearest neighbor coupling.…”

“…For the sake of concreteness let us consider a generic 1D array of an even number of N qubits with the nearest neighbor coupling. 22,24 In this architecture the CS needs N − 1 adjustable couplers, while the HA only needs N /2−1 adjustable couplers if each basic unit contains, for example, two qubits with fixed always-on coupling. Compared to the CS the HA saves about 50% in the couplers for large N. Further let us consider an rf-driven N-qubit gate which comprises a Hadamard gate on each single qubit followed by a CNOT gate on the nearest neighbors from left to right.…”

“…This approach is demonstrated by using a unit of two SQUID flux qubits with realistic device parameters and constant always-on coupling. Compared to other methods [18][19][20][21][22]24,25 our approach for a unit with two coupled qubits has the following characteristics and advantages: ͑1͒ The approach is universal as long as each qubit can be locally addressed; ͑2͒ no extra hardware resources required; ͑3͒ no additional decoherence from the hardware added to control interqubit coupling; ͑4͒ gate errors induced by the population propagation from one qubit to another is completely eliminated; and ͑5͒ the architecture for both hardware ͑circuits͒ and software ͑pulse sequence͒ is much simplified. For a system with N coupled qubits the scalable quantum information processing can be achieved by the hybrid architecture.…”