Enhanced quantum state detection efficiency through quantum information processing

We investigate theoretically and experimentally how quantum state-detection efficiency is improved by the use of quantum information processing (QIP). Experimentally, we encode the state of one 9Be(+) ion qubit with one additional ancilla qubit. By measuring both qubits, we reduce the state-detection error in the presence of noise. The deviation from the theoretically allowed reduction is due to infidelities of the QIP operations. Applying this general scheme to more ancilla qubits suggests that error in the individual qubit measurements need not be a limit to scalable quantum computation.     

Nonadiabatic geometric quantum computation protected by dynamical decoupling via the XXZ Hamiltonian

Nonadiabatic geometric quantum computation protected by dynamical decoupling combines the robustness of nonadiabatic geometric gates and the decoherence-resilience feature of dynamical decoupling. Solid-state systems provide an appealing candidate for the realization of nonadiabatic geometric quantum computation protected dynamical decoupling since the solid-state qubits are easily embedded in electronic circuits and scaled up to large registers. In this paper, we put forward a scheme of nonadiabatic geometric quantum computation protected by dynamical decoupling via the XXZ Hamiltonian, which not only combines the merits of nonadiabatic geometric gates and dynamical decoupling but also can be realized in a number of solid-state systems, such as superconducting circuits and quantum dots.     

Quantum wave processing

In recent years, the concept of quantum computing has arisen as a methodology by which very rapid computations can be achieved. In general, the ‘speed’ of these computations is compared to that of (classical) digital computers, which use sequential algorithms. However, in most quantum computing approaches, the qubits themselves are treated as analog objects. One then needs to ask whether this computational speed-up of the computation is a result of the quantum mechanics, or whether it is due to the nature of the analog structures that are being ‘generated’ for quantum computation? In this paper, we will make two points: (1) quantum computation utilizes analog, parallel computation which often offers no speed advantage over classical computers which are implemented using analog, parallel computation; (2) once this is realized, then there is little advantage in projecting the quantum computation onto the pseudo-binary construct of a qubit. Rather, it becomes more effective to seek the equivalent wave processing that is inherent in the analog, parallel processing. We will examine some wave processing systems which may be useful for quantum computation.     

Quantum computing with an always-on Heisenberg interaction

Many promising schemes for quantum computing (QC) involve switching "on" and "off" a physical coupling between qubits. This may prove extremely difficult to achieve experimentally. Here we show that systems with a constant Heisenberg coupling can be employed for QC if we actively "tune" the transition energies of individual qubits. Moreover, we can collectively tune the qubits to obtain an exceptionally simple scheme: computations are controlled via a single "switch" of only six settings. Our schemes are applicable to a wide range of physical implementations, from excitons and spins in quantum dots through to bulk magnets.     

Experimental test of the quantum no-hiding theorem

The no-hiding theorem says that if any physical process leads to bleaching of quantum information from the original system, then it must reside in the rest of the Universe with no information being hidden in the correlation between these two subsystems. Here, we report an experimental test of the no-hiding theorem with the technique of nuclear magnetic resonance. We use the quantum state randomization of a qubit as one example of the bleaching process and show that the missing information can be fully recovered up to local unitary transformations in the ancilla qubits.     

Sequential implementation of global quantum operations

We study the possibility for a global unitary applied on an arbitrary number of qubits to be decomposed in a sequential unitary procedure, where an ancillary system is allowed to interact only once with each qubit. We prove that sequential unitary decompositions are in general impossible for genuine entangling operations, even with an infinite-dimensional ancilla, being the controlled-NOT gate a paradigmatic example. Nevertheless, we find particular nontrivial operations in quantum information that can be performed in a sequential unitary manner, as is the case of quantum error correction and quantum cloning.     

Efficient classical simulation of slightly entangled quantum computations

We present a classical protocol to efficiently simulate any pure-state quantum computation that involves only a restricted amount of entanglement. More generally, we show how to classically simulate pure-state quantum computations on n qubits by using computational resources that grow linearly in n and exponentially in the amount of entanglement in the quantum computer. Our results imply that a necessary condition for an exponential computational speedup (with respect to classical computations) is that the amount of entanglement increases with the size n of the computation, and provide an explicit lower bound on the required growth.     

Quantum teleportation with a quantum dot single photon source

We report the experimental demonstration of a quantum teleportation protocol with a semiconductor single photon source. Two qubits, a target and an ancilla, each defined by a single photon occupying two optical modes (dual-rail qubit), were generated independently by the single photon source. Upon measurement of two modes from different qubits and postselection, the state of the two remaining modes was found to reproduce the state of the target qubit. In particular, the coherence between the target qubit modes was transferred to the output modes to a large extent. The observed fidelity is 80%, in agreement with the residual distinguishability between consecutive photons from the source. An improved version of this teleportation scheme using more ancillas is the building block of the recent Knill, Laflamme, and Milburn proposal for efficient linear optics quantum computation.     

Quantum superposition of localized and delocalized phases of photons

Based on a variant of 2-site Jaynes–Cummings–Hubbard model constructed using superconducting circuits, we propose a method to coherently superpose the localized and delocalized phases of microwave photons, which makes it possible to engineer the collective features of multiple photons in the quantum way using an individual two-level system. Our proposed architecture is also a promising candidate for implementing distributed quantum computation since it is capable of coupling remote qubits in separate resonators in a controllable way.     

Remote interactions on two distributed quantum systems： nonlocal unambiguous quantum-state discrimination

Remote quantum-state discrimination is a critical step for the implementation of quantum communication network and distributed quantum computation. We present a protocol for remotely implementing the unambiguous discrimination between nonorthogonal states using quantum entanglements, local operations, and classical communications. This protocol consists of a remote generalized measurement described by a positive operator valued measurement （POVM）. We explicitly construct the required remote POVM. The remote POVM can be realized by performing a nonlocal controlled-rotation operation on two spatially separated qubits, one is an ancillary qubit and the other is the qubit which is encoded by two nonorthogonal states to be distinguished, and a conventional local Von Neumann orthogonal measurement on the ancilla. The particular pair of states that can be remotely and unambiguously distinguished is specified by the state of the ancilla. The probability of successful discrimination is not optimal for all admissible pairs. However, for some subset it can be very close to an optimal value in an ordinary local POVM.     

Superconducting quantum bits

Superconducting quantum bits(qubits) and circuits are the leading candidate for the implementation of solid-state quantum computation. They have also been widely used in a variety of studies of quantum physics, atomic physics, quantum optics, and quantum simulation. In this article, we will present an overview of the basic principles of the superconducting qubits, including the phase, flux, charge, and transmon(Xmon) qubits, and the progress achieved so far concerning the improvements of the device design and quantum coherence property. Experimental studies in various research fields using the superconducting qubits and circuits will be briefly reviewed.     

Experimental nonlinear sign shift for linear optics quantum computation

We have realized the nonlinear sign shift operation for photonic qubits. This operation shifts the phase of two photons reflected by a beam splitter using an extra single photon and measurement. We show that the conditional phase shift is (1.05+/-0.06)pi in clear agreement with theory. Our results show that, by using an ancilla photon and conditional detection, nonlinear optical effects can be implemented using only linear optical elements. This experiment represents an essential step for linear optical implementations of scalable quantum computation.     

Continuous-variable quantum information processing with squeezed states of light

We investigate experiments of continuous-variable quantum information processing based on the teleportation scheme. Quantum teleportation, which is realized by a two-mode squeezed vacuum state and measurement-and-feedforward, is considered as an elementary quantum circuit as well as quantum communication. By modifying ancilla states or measurement-and-feedforwards, we can realize various quantum circuits which suffice for universal quantum computation. In order to realize the teleportation-based computation we improve the level of squeezing, and fidelity of teleportation. With a high-fidelity teleporter we demonstrate some advanced teleportation experiments, i.e., teleportation of a squeezed state and sequential teleportation of a coherent state. Moreover, as an example of the teleportation-based computation, we build a QND interaction gate which is a continuous-variable analog of a CNOT gate. A QND interaction gate is constructed only with ancillary squeezed vacuum states and measurement-and-feedforwards. We also create continuous-variable four mode cluster type entanglement for further application, namely, one-way quantum computation.     

Nanoscale superconducting quantum bits

Various physical systems were proposed for quantum information processing. Among those nanoscale devices appear most promising for integration in electronic circuits and large-scale applications. We discuss Josephson junction circuits in two regimes where they can be used for quantum computing. These systems combine intrinsic coherence of the superconducting state with control possibilities of single-charge circuits. In the regime where the typical charging energy dominates over the Josephson coupling, the low-temperature dynamics is limited to two states differing by a Cooper-pair charge on a superconducting island. In the opposite regime of prevailing Josephson energy, the phase (or flux) degree of freedom can be used to store and process quantum information. Under suitable conditions the system reduces to two states with different flux configurations. Several qubits can be joined together into a register. The quantum state of a qubit register can be manipulated by voltage and magnetic field pulses. The qubits are inevitably coupled to the environment. However, estimates of the phase coherence time show that many elementary quantum logic operations can be performed before the phase coherence is lost. In addition to manipulations, the final state of the qubits has to be read out. This quantum measurement process can be accomplished using a single-electron transistor for charge Josephson qubits, and a d.c.-SQUID for flux qubits. Recent successful experiments with superconducting qubits demonstrate for the first time quantum coherence in macroscopic systems.     

Quantum chaos and random matrix theory for fidelity decay in quantum computations with static imperfections

We determine the universal law for fidelity decay in quantum computations of complex dynamics in presence of internal static imperfections in a quantum computer. Our approach is based on random matrix theory applied to quantum computations in presence of imperfections. The theoretical predictions are tested and confirmed in extensive numerical simulations of a quantum algorithm for quantum chaos in the dynamical tent map with up to 18 qubits. The theory developed determines the time scales for reliable quantum computations in absence of the quantum error correction codes. These time scales are related to the Heisenberg time, the Thouless time, and the decay time given by Fermis golden rule which are well-known in the context of mesoscopic systems. The comparison is presented for static imperfection effects and random errors in quantum gates. A new convenient method for the quantum computation of the coarse-grained Wigner function is also proposed.Received: 13 December 2003, Published online: 18 March 2004PACS: 03.67.Lx Quantum computation - 05.45.Pq Numerical simulations of chaotic systems - 05.45.Mt Quantum chaos; semiclassical methods     

Benchmarking a quantum teleportation protocol in superconducting circuits using tomography and an entanglement witness

Teleportation of a quantum state may be used for distributing entanglement between distant qubits in quantum communication and for quantum computation. Here we demonstrate the implementation of a teleportation protocol, up to the single-shot measurement step, with superconducting qubits coupled to a microwave resonator. Using full quantum state tomography and evaluating an entanglement witness, we show that the protocol generates a genuine tripartite entangled state of all three qubits. Calculating the projection of the measured density matrix onto the basis states of two qubits allows us to reconstruct the teleported state. Repeating this procedure for a complete set of input states we find an average output state fidelity of 86%.     

Compressed quantum simulation of the Ising model

Jozsa et al. [Proc. R. Soc. A 466, 809 2009)] have shown that a match gate circuit running on n qubits can be compressed to a universal quantum computation on log(n)+3 qubits. Here, we show how this compression can be employed to simulate the Ising interaction of a 1D chain consisting of n qubits using a universal quantum computer running on log(n) qubits. We demonstrate how the adiabatic evolution can be realized on this exponentially smaller system and how the magnetization, which displays a quantum phase transition, can be measured. This shows that the quantum phase transition of very large systems can be observed experimentally with current technology.     

Cat-qubits for quantum computation

The development of quantum Josephson circuits has created a strong expectation for reliable processing of quantum information. While this progress has already led to various proof-of-principle experiments on small-scale quantum systems, a major scaling step is required towards many-qubit protocols. Fault-tolerant computation with protected logical qubits usually comes at the expense of a significant overhead in the hardware. Each of the involved physical qubits still needs to satisfy the best achieved properties (coherence times, coupling strengths and tunability). Here, and in the aim of addressing alternative approaches to deal with these obstacles, I overview a series of recent theoretical proposals, and the experimental developments following these proposals, to enable a hardware-efficient paradigm for quantum memory protection and universal quantum computation.     

Quantum computation with surface-state electrons by rapid population passages

Quantum computation requires coherently controlling the evolutions of qubits.Usually,these manipulations are implemented by precisely designing the durations(such as theπ-pulses)of the Rabi oscillations and tunable interbit coupling.Relaxing this requirement,herein we show that the desired population transfers between the logic states can be deterministically realized(and thus quantum computation could be implemented)both adiabatically and non-adiabatically,by performing the duration-insensitive quantum manipulations.Our proposal is specifically demonstrated with the surface-state of electrons floating on the liquid helium,but could also be applied to the other artificially controllable systems for quantum computing.     

Coherence and Entanglement Dynamics in Training Variational Quantum Perceptron

In quantum computation, what contributes supremacy of quantum computation? One of the candidates is known to be a quantum coherence because it is a resource used in the various quantum algorithms. We reveal that quantum coherence contributes to the training of variational quantum perceptron proposed by Y. Du et al., arXiv:1809.06056 (2018). In detail, we show that in the first part of the training of the variational quantum perceptron, the quantum coherence of the total system is concentrated in the index register and in the second part, the Grover algorithm consumes the quantum coherence in the index register. This implies that the quantum coherence distribution and the quantum coherence depletion are required in the training of variational quantum perceptron. In addition, we investigate the behavior of entanglement during the training of variational quantum perceptron. We show that the bipartite concurrence between feature and index register decreases since Grover operation is only performed on the index register. Also, we reveal that the concurrence between the two qubits of index register increases as the variational quantum perceptron is trained.