Time-optimal control with finite bandwidth

Time-optimal control theory provides recipes to achieve quantum operations with high fidelity and speed, as required in quantum technologies such as quantum sensing and computation. While technical advances have achieved the ultrastrong driving regime in many physical systems, these capabilities have yet to be fully exploited for the precise control of quantum systems, as other limitations, such as the generation of higher harmonics or the finite response time of the control apparatus, prevent the implementation of theoretical time-optimal control. Here we present a method to achieve time-optimal control of qubit systems that can take advantage of fast driving beyond the rotating wave approximation. We exploit results from time-optimal control theory to design driving protocols that can be implemented with realistic, finite-bandwidth control fields, and we find a relationship between bandwidth limitations and achievable control fidelity.     

Using non-ideal gates to implement universal quantum computing between uncoupled qubits

In many physical systems, when implementing quantum gate operations unavoidable global and relative phases occur as by-products due to the internal structure of the governing Hamiltonian. To correct, additional phase rotation gates are used, which increases the computational overhead. Here, we show how these phase by-products can actually be used to our advantage by using them to implement universal quantum computing between qubits not directly coupled to each other. The gate operations, CNOT, Toffoli, and swap gates, require much less computational overhead than present schemes, and are achieved with fidelity greater than 99%. We then present a linear nearest-neighbor architecture that takes full advantage of the phase by-products, and we show how to implement gates from a universal set efficiently in this layout. In this scheme gate operations are realized by only varying a single control parameter per data qubit, and the ability to tune couplings is not required.     

Scheme for implementing multitarget qubit controlled-NOT gate of photons and controlled-phase gate of electron spins via quantum dot-microcavity coupled system

We propose a deterministic scheme to implement the multiqubit controlled-NOT gate of photons and multiqubit controlled-phase gate of electron spins with one control qubit and multiple target qubits using quantum dots in double-sided optical cavities. The scheme is based on spin selective photon reflection from the cavity and can be achieved in a nondestructive way. We assess the feasibility of the scheme and show that the gates can be implemented with high average fidelities by choosing the realistic system parameters appropriately. The scheme is useful in quantum information processing such as entanglement preparation, quantum error correction, and quantum algorithms.     

Efficient quantum computing between remote qubits in linear nearest neighbor architectures

We propose a new scheme for implementing gate operations between remote qubits in linear nearest neighbor (LNN) architectures, one that does not require qubits to be adjacent to each other in order to perform a gate operation between them. The key feature of our scheme is a new two-control, one-target controlled-unitary gate operation, which we refer to as the C²(?I) gate. The gate operation can be implemented easily in a single step, requiring only a single control parameter of the system Hamiltonian. Using the C²(?I) gate, we show how to implement CNOT gate operations between remote qubits that do not have any direct coupling between them, along an LNN array. Since this is achieved without requiring swap operations or additional ancilla qubits in the circuit, the quantum cost of our circuit can be more than 50 % lower than those using conventional swap methods. All CNOT gate operations between remote qubits can be achieved with fidelity greater than 99.5 %.     

Room-temperature spin-photon interface for quantum networks

Although remarkable progress has been achieved recently, to construct an optical cavity where a nitrogen-vacancy (NV) colour centre in diamond is coupled to an optical field in the strong coupling regime is rather difficult. We propose an architecture for a scalable quantum interface capable of interconverting photonic and NV spin qubits, which can work well without the strong coupling requirement. The dynamics of the interface applies an adiabatic passage to sufficiently reduce the decoherence from an excited state of a NV colour centre in diamond. This quantum interface can accomplish many quantum network operations like state transfer and entanglement distribution between qubits at distant nodes. Exact numerical simulations show that high-fidelity quantum interface operations can be achieved under room-temperature and realistic experimental conditions.     

Controlling quantum information processing in hybrid systems on chips

We investigate quantum information processing, transfer and storage in hybrid systems comprised of diverse blocks integrated on chips. Strong coupling between superconducting (SC) qubits and ensembles of ultracold atoms or NV-center spins is mediated by a microwave transmission-line resonator that interacts near-resonantly with the atoms or spins. Such hybrid devices allow us to benefit from the advantages of each block and compensate for their disadvantages. Specifically, the SC qubits can rapidly implement quantum logic gates, but are “noisy” (prone to decoherence), while collective states of the atomic or spin ensemble are “quiet”(protected from decoherence) and thus can be employed for storage of quantum information. To improve the overall performance (fidelity) of such devices we discuss dynamical control to optimize quantum state-transfer from a “noisy” qubit to the “quiet” storage ensemble. We propose to maximize the fidelity of transfer and storage in a spectrally inhomogeneous spin ensemble, by pre-selecting the optimal spectral portion of the ensemble. Significant improvements of the overall fidelity of hybrid devices are expected under realistic conditions. Experimental progress towards the realization of these schemes is discussed.     

Scalable quantum computing model in the circuit-QED lattice with circulator function

We propose a model for a scalable quantum computing in the circuit quantum electrodynamics architecture. In the Kagome lattice of qubits, three qubits are connected to each other through a superconducting three-junction flux qubit at the vertices of the lattice. By controlling one of the three-Josephson-junction energies of the intervening flux qubit, we can achieve the circulator function that couples arbitrary pair of two qubits among three. This selective coupling enables the interaction between two nearest neighbor qubits in the Kagome lattice, and further the two-qubit gate operation between any pair of qubits in the whole lattice by performing consecutive nearest neighbor two-qubit gates.     

求解量子系统时间最优控制问题的同伦算法研究

针对数值求解量子系统时间最优控制问题中反复调用梯度算法导致计算量大的问题,本文提出一类同伦算法用以快速求解量子系统的时间最优控制问题.与已有算法不同,这一算法通过引入同伦变量在减小终端时间的方向上搜索最优解.在这一算法中,可通过自由函数构造保真度函数对控制变量的梯度方向,也可通过方向函数引导算法的搜索方向,以加快算法的搜索速度.本文将这一算法用于求解量子系统态转移和门变换的时间最优控制问题.仿真结果表明这一算法的有效性.     

Quantum information processing in a decoherence-free subspace for the $$\hat{\sigma }_{x}$$-type collective noise

Based on a cavity-assisted single-photon input–output process, we first construct the hybrid controlled-phase-flip gate between photon and the single-logic qubit in decoherence-free subspaces. And we also achieve the universal single-qubit logic operations. We realize the distributed quantum information processing with the hybrid controlled-phase-flip gate and single-qubit logic operations. Finally, we discuss the experimental feasibility of our scheme, which is satisfied with currently available technology.     

Signatures of Incoherence in a Quantum Information Processor

Incoherent noise is manifest in measurements of expectation values when the underlying ensemble evolves under a classical distribution of unitary processes. While many incoherent processes appear decoherent, there are important differences. The distribution functions underlying incoherent processes are either static or slowly varying with respect to control operations and so the errors introduced by these distributions are refocusable. The observation and control of incoherence in small Hilbert spaces is well known. Here we explore incoherence during an entangling operation, such as is relevant in quantum information processing. As expected, it is more difficult to separate incoherence and decoherence over such processes. However, by studying the fidelity decay under a cyclic entangling map we are able to identify distinctive experimental signatures of incoherence. This is demonstrated both through numerical simulations and experimentally in a three qubit nuclear magnetic resonance implementation.      

Construction of quantum gates for concatenated Greenberger–Horne–Zeilinger-type logic qubit

Concatenated Greenberger–Horne–Zeilinger (C-GHZ) state is a kind of logic qubit which is robust in noisy environment. In this paper, we encode the C-GHZ state as the logic qubit and design two kinds of quantum gates for such logic qubit. The first kind is the single logic-qubit gate which contains the logic-qubit bit-flip gate and phase-flip gate. The second kind is the logic-qubit controlled-not (CNOT) gate. We exploit the single quantum gate for physical qubit, such as bit-flip gate and phase-flip gate, and two-qubit CNOT gate to realize the logic-qubit gate. We also calculated the success probability of such logic-qubit gate based on the imperfect physical quantum gate. This protocol may be useful for future quantum computation.     

Information Gain versus State Disturbance for a Single Qubit

The trade-off between the information gain and the state disturbance is derived for quantum operations on a single qubit prepared in a uniformly distributed pure state. The derivation is valid for a class of measures quantifying the state disturbance and the information gain which satisfy certain invariance conditions. This class includes in particular the Shannon entropy versus the operation fidelity. The central role in the derivation is played by efficient quantum operations, which leave the system in a pure output state for any measurement outcome. It is pointed out that the optimality of efficient quantum operations among those inducing a given operator-valued measure is related to Davies' characterization of convex invariant functions on hermitian operators.     

Quantum state transfer between an optomechanical cavity and a diamond nuclear spin ensemble

We explore an efficient scheme for transferring quantum state between an optomechanical cavity and nuclear spins of nitrogen-vacancy centers in diamond, where quantum information can be efficiently stored (retrieved) into (from) the nuclear spin ensemble assisted by a mechanical resonator in a dispersive regime. Our scheme works for a broad range of cavity frequencies and might have potential applications in employing the nuclear spin ensemble as a memory in quantum information processing. The feasibility of our protocol is analyzed using currently available parameters.     

An atom�Cmolecule platform for quantum computing

We propose a combined atom–molecule system for quantum information processing in individual traps, such as provided by optical lattices. In this platform, different species of atoms—one atom carrying a qubit and the other enabling the interaction—are used to store and process quantum information via intermediate molecular states. We show how gates, initialization, and readout operations could be implemented using this approach. In particular, we describe in some detail the implementation of a two-qubit phase gate in which a pair of atoms is transferred into the ground rovibrational state of a polar molecule with a large dipole moment, thus allowing atoms transferred into molecules to interact via their dipole-dipole interaction. We also discuss how the reverse process could be used as a non-destructive readout tool of molecular qubit states. Finally, we generalize these ideas to use a decoherence-free subspace for qubit encoding to minimize the decoherence due to magnetic field fluctuations. In this case, qubits will be encoded into field-insensitive states of two identical atoms, while a third atom of a different species will be used to realize a phase gate.     

On the Role of Hadamard Gates in Quantum Circuits

We study a reduced quantum circuit computation paradigm in which the only allowable gates either permute the computational basis states or else apply a “global Hadamard operation”, i.e. apply a Hadamard operation to every qubit simultaneously. In this model, we discuss complexity bounds (lower-bounding the number of global Hadamard operations) for common quantum algorithms: we illustrate upper bounds for Shor’s Algorithm, and prove lower bounds for Grover’s Algorithm. We also use our formalism to display a gate that is neither quantum-universal nor classically simulable, on the assumption that Integer Factoring is not in BPP.     

Dephasing of Quantum Bits by a Quasi-Static Mesoscopic Environment

We examine coherent processes in a two-state quantum system that is strongly coupled to a mesoscopic spin bath and weakly coupled to other environmental degrees of freedom. Our analysis is specifically aimed at understanding the quantum dynamics of solid-state quantum bits such as electron spins in semiconductor structures and superconducting islands. The role of mesoscopic degrees of freedom with long correlation times (local degrees of freedom such as nuclear spins and charge traps) in qubit-related dephasing is discussed in terms of a quasi-static bath. A mathematical framework simultaneously describing coupling to the slow mesoscopic bath and a Markovian environment is developed and the dephasing and decoherence properties of the total system are investigated. The model is applied to several specific examples with direct relevance to current experiments. Comparisons to experiments suggests that such quasi-static degrees of freedom play an important role in current qubit implementations. Several methods of mitigating the bath-induced error are considered.Dedicated to Anton Zeilinger, whose work has inspired exploration of quantum phenomenon in many avenues of physics and beyond.     

One-step implementation of a multi-target-qubit controlled phase gate in a multi-resonator circuit QED system

Circuit quantum electrodynamics system composed of many qubits and resonators may provide an excellent way to realize large-scale quantum information processing (QIP). Because of key role for large-scale QIP and quantum computation, multi-qubit gates have drawn intensive attention recently. Here, we present a one-step method to achieve a multi-target-qubit controlled phase gate in a multi-resonator system, which possesses a common control qubit and multiple different target qubits distributed in their respective resonators. Noteworthily, the implementation of this multi-qubit phase gate does not require classical pulses, and the gate operation time is independent of the number of qubits. Besides, the proposed scheme can in principle be adapted to a general type of qubits like natural atoms, quantum dots, and solid-state qubits (e.g., superconducting qubits and NV centers).     

Multi-qubit non-adiabatic holonomic controlled quantum gates in decoherence-free subspaces

Non-adiabatic holonomic quantum gate in decoherence-free subspaces is of greatly practical importance due to its built-in fault tolerance, coherence stabilization virtues, and short run-time. Here, we propose some compact schemes to implement two- and three-qubit controlled unitary quantum gates and Fredkin gate. For the controlled unitary quantum gates, the unitary operator acting on the target qubit is an arbitrary single-qubit gate operation. The controlled quantum gates can be directly implemented by utilizing non-adiabatic holonomy in decoherence-free subspaces and the required resource for the decoherence-free subspace encoding is minimal by using only two neighboring physical qubits undergoing collective dephasing to encode a logical qubit.     

Multifractality in fidelity sequences of optimized Toffoli gates

We analyze the multifractality in the fidelity sequences of several engineered Toffoli gates. Using quantum control methods, we consider several optimization problems whose global solutions realize the gate in a chain of three qubits with XY Heisenberg interaction. Applying a minimum number of control pulses assuring a fidelity above 99 % in the ideal case, we design stable gates that are less sensitive to variations in the interqubits couplings. The most stable gate has the fidelity above 91 % with variations about 0.1 %, for up to 10 % variation in the nominal couplings. We perturb the system by introducing a single source of 1 / f noise that affects all the couplings. In order to quantify the performance of the proposed optimized gates, we calculate the fidelity of a large set of optimized gates under prescribed levels of coupling perturbation. Then, we run multifractal analysis on the sequence of attained fidelities. This way, gate performance can be assessed beyond mere average results, since the chosen multifractality measure (the width of the multifractal spectrum) encapsulates into a single performance indicator the spread of fidelity values around the mean and the presence of outliers. The higher the value of the performance indicator the more concentrated around the mean the fidelity values are and rarer is the occurrence of outliers. The results of the multifractal analysis on the fidelity sequences demonstrate the effectiveness of the proposed optimized gate implementations, in the sense they are rendered less sensitive to variations in the interqubits coupling strengths.