High-fidelity gates in a single josephson qubit

We demonstrate new experimental procedures for measuring small errors in a superconducting quantum bit (qubit). By carefully separating out gate and measurement errors, we construct a complete error budget and demonstrate single qubit gate fidelities of 0.98, limited by energy relaxation. We also introduce a new metrology tool-- Ramsey interference error filter-that can measure the occupation probability of the state |2> which is outside the computational basis, down to 10{-4}, thereby confirming that our quantum system stays within the qubit manifold during single qubit logic operations.     

Quantum state reconstruction by entangled measurements

We address quantum state reconstruction for d-dimensional systems based on measuring, on the system of interest and a probe, of a single entangled observable defined on the bipartite system/probe Hilbert space. We show that the statistics of the measurement and the knowledge of the probe preparation suffice to reliably reconstruct the density matrix of the system, as well as the expectation value of any desired operator, including those not corresponding to observable quantities. The statistical robustness of the reconstruction is examined and a method is developed to minimize statistical errors by tuning the probe preparation. Numerical simulations of the whole reconstruction procedure are also presented for qubit systems.     

A small error-correction code for protecting three-qubit quantum information

We present a quantum error correction code which protects three quantum bits (qubits) of quantum information against one erasure, i.e., a single-qubit arbitrary error at a known position. The present code has a high encoding efficiency, since only one auxiliary qubit is needed for one message qubit on average. In addition, we note that the code can also work even in a worse case that the interaction with the environment causes a leakage out of the qubit space. The code may have some applications in the storage of quantum information for small-scale quantum computing, quantum information processing, and quantum communication.     

Benchmarking quantum control methods on a 12-qubit system

In this Letter, we present an experimental benchmark of operational control methods in quantum information processors extended up to 12 qubits. We implement universal control of this large Hilbert space using two complementary approaches and discuss their accuracy and scalability. Despite decoherence, we were able to reach a 12-coherence state (or a 12-qubit pseudopure cat state) and decode it into an 11 qubit plus one qutrit pseudopure state using liquid state nuclear magnetic resonance quantum information processors.     

The remote implementation of all possible generalized quantum measurement on single atomic qubit in a quantum network

To implement generalized quantum measurement (GQM) one has to extend the original Hilbert space. Generally speaking, the additional dimensions of the ancilla space increase as the number of the operators of the GQM n increases. This paper presents a scheme for deterministically implementing all possible n-operator GQMs on a single atomic qubit by using only one 2-dimensional ancillary atomic qubit repeatedly, which remarkably reduces the complexity of the realistic physical system. Here the qubit is encoded in the internal states of an atom trapped in an optical cavity and single-photon pulses are employed to provide the interaction between qubits. It shows that the scheme can be performed remotely, and thus it is suitable for implementing GQM in a quantum network. What is more, the number of the total ancilla dimensions in our scheme achieves the theoretic low bound.     

Compressing the hidden variable space of a qubit

In previously exhibited hidden variable models of quantum state preparation and measurement, the number of continuous hidden variables describing the actual state of single realizations is never smaller than the quantum state manifold dimension. We introduce a simple model for a qubit whose hidden variable space is one-dimensional, i.e., smaller than the two-dimensional Bloch sphere. The hidden variable probability distributions associated with quantum states satisfy reasonable criteria of regularity. Possible generalizations of this shrinking to an N-dimensional Hilbert space are discussed.     

Fermionic Quantum Computation

We define a model of quantum computation with local fermionic modes (LFMs)—sites which can be either empty or occupied by a fermion. With the standard correspondence between the Foch space of m LFMs and the Hilbert space of m qubits, simulation of one fermionic gate takes O(m) qubit gates and vice versa. We show that using different encodings, the simulation cost can be reduced to O(log m) and a constant, respectively. Nearest neighbors fermionic gates on a graph of bounded degree can be simulated at a constant cost. A universal set of fermionic gates is found. We also study computation with Majorana fermions which are basically halves of LFMs. Some connection to qubit quantum codes is made.     

Nilpotent quantum mechanics and SUSY

Formalism where fundamental variables are nilpotent, but in contrast to the super-mathematics, not anticommutative but commutative gives another version of realization of the Pauli exclusion principle. We discuss some aspects of nilpotent quantum mechanics realized in generalized Hilbert space of functions of nilpotent commuting variables. The qubits are natural objects described by such a formalism. Supersymmetric system of qubit and fermion is presented.     

Distributed quantum computation with superconducting qubit via LC circuit using dressed states

A scheme is proposed where two superconducting qubits driven by a classical field interacting separately with two distant LC circuits connected by another LC circuit through mutual inductance,are used for implementing quantum gates.By using dressed states,quantum state transfer and quantum entangling gate can be implemented.With the help of the time-dependent electromagnetic field,any two dressed qubits can be selectively coupled to the data bus (the last LC circuit),then quantum state can be transferred from one dressed qubit to another and multi-mode entangled state can also be formed.As a result,the promising perspectives for quantum information processing of mesoscopic superconducting qubits are obtained and the distributed and scalable quantum computation can be implemented in this scheme.     

Quantum computing by an optimal control algorithm for unitary transformations

Quantum computation is based on implementing selected unitary transformations representing algorithms. A generalized optimal control theory is used to find the driving field that generates a prespecified unitary transformation. The approach is independent of the physical implementation of the quantum computer and it is illustrated for one and two qubit gates in model molecular systems, where only part of the Hilbert space is used for computation.     

Simple family of nonadditive quantum codes

Most known quantum codes are additive, meaning the code can be described as the simultaneous eigenspace of an Abelian subgroup of the Pauli group. While in some scenarios such codes are strictly suboptimal, very little is understood about how to construct nonadditive codes with good performance. Here we present a family of distance 2 nonadditive quantum codes for all odd block lengths n, that has a particularly simple form. Our codes detect single qubit errors (or correct single qubit erasures) while encoding a higher dimensional space than is possible with an additive code or, for n> or =11, any previous codes. We exhibit the encoding circuits and automorphism group for our codes as well.     

Two-Step Deterministic Remote Preparation of an Arbitrary Quantum State

We present a two-step deterministic remote state preparation protocol for an arbitrary qubit with the aid of a three-particle Greenberger-Horne-Zeilinger state. Generalization of this protocol for higher-dimensional Hilbert space systems among three parties is also given. We show that only single-particle von Neumann measurements, local operations, and classical communication are necessary. Moreover, since the overall information of the quantum state can be divided into two different pieces, which may be at different locations, this protocol may be useful in the quantum information field.     

Average mutual information of the random block-message ensembles for many-letters

By making use of the theoretical framework presented by Bostroem(K.J.Bostroem,LANL quant-ph/0009052),we generalize the standard quantum information theory of block messages with fixed block length to the variable one.We show that the states belonging to a sufficiently large hilbert space are the highly distinguishable states.We also consider the collection states (product states of more than one qubit state) and seek a “pretty good measurement” (PGM) with measurement vectors to improve the mutual information.The average mutual information over random block-message ensembles with variable block length n is discussed in detail.     

Active suppression of dephasing in Josephson-junction qubits

Simple majority code correcting k dephasing errors by encoding a qubit of information into 2k+1 physical qubits is studied quantitatively. We derive an equation for quasicontinuous evolution of the density matrix of encoded quantum information under the error correction procedure in the presence of correlated dephasing noise. A specific design of a Josephson-junction nanocircuit implementing this scheme is suggested.     

Deep strong coupling regime of the Jaynes-Cummings model

We study the quantum dynamics of a two-level system interacting with a quantized harmonic oscillator in the deep strong coupling regime (DSC) of the Jaynes-Cummings model, that is, when the coupling strength g is comparable or larger than the oscillator frequency ω (g/ω?1). In this case, the rotating-wave approximation cannot be applied or treated perturbatively in general. We propose an intuitive and predictive physical frame to describe the DSC regime where photon number wave packets bounce back and forth along parity chains of the Hilbert space, while producing collapse and revivals of the initial population. We exemplify our physical frame with numerical and analytical considerations in the qubit population, photon statistics, and Wigner phase space.     

Automatic quantum error correction

Criteria are given by which dissipative evolution in the weak coupling limit can transfer populations and coherences between quantum subspaces, without a loss of coherence. The result is a form of quantum error correction implemented by the joint evolution of a system with a cold bath. It requires no external intervention and, in principle, no ancilla. An example of such a system, consisting of three dipole ordered spin 1/2 particles in a resonator, is given. The qubit, or the triple quantum coherence of the spins, is protected against all spin-flip errors.     

The transition from quantum Zeno to anti-Zeno effects for a qubit in a cavity by varying the cavity frequency

We propose a strategy to demonstrate the transition from the quantum Zeno effect (QZE) to the anti-Zeno effect (AZE) using a superconducting qubit coupled to a transmission line cavity, by varying the central frequency of the cavity mode. Our results are obtained without the rotating wave approximation (RWA), and the initial state (a dressed state) is easy to prepare. Moreover, we find that in the presence of both qubit?s intrinsic bath and the cavity bath, the emergence of the QZE and the AZE behaviors relies not only on the match between the qubit energy-level-spacing and the central frequency of the cavity mode, but also on the coupling strength between the qubit and the cavity mode.     

States in the Hilbert space formulation and in the phase space formulation of quantum mechanics

We consider the problem of testing whether a given matrix in the Hilbert space formulation of quantum mechanics or a function considered in the phase space formulation of quantum theory represents a quantum state. We propose several practical criteria for recognising states in these two versions of quantum physics. After minor modifications, they can be applied to check positivity of any operators acting in a Hilbert space or positivity of any functions from an algebra with a ∗$\ast$-product of Weyl type.     

噪声情况下的量子网络直接通信

提出和研究了噪声情况下的量子网络直接通信. 通信过程中所有量子节点共享多粒子Greenberger-Horne-Zeilinger (GHZ)量子纠缠态; 发送节点将手中共享的GHZ态的粒子作为控制比特、传输秘密信息的粒子作为目标比特, 应用控制非门(CNOT)操作; 每个接收节点将手中共享GHZ 态的粒子作为控制比特、接收到的秘密信息粒子作为目标比特, 再次应用CNOT门操作从而获得含误码的秘密信息. 每个接收节点从秘密信息中提取部分作为检测比特串, 并将剩余的秘密信息应用奇偶校验矩阵纠正其中存在的比特翻转错误, 所有接收节点获得纠正后的秘密信息. 对协议安全、吞吐效率、通信效率等进行了分析和讨论.