Examples of geometric phases abound in many areas of physics. They offer both fundamental insights into many physical phenomena and lead to interesting practical implementations. One of them, as indicated recently, might be an inherently fault-tolerant quantum computation. This, however, requires to deal with geometric phases in the presence of noise and interactions between different physical subsystems. Despite the wealth of literature on the subject of geometric phases very little is known about this very important case. Here we report the first experimental study of geometric phases for mixed quantum states. We show how different they are from the well understood, noiseless, pure-state case.PACS numbers: 03.65. Bz, 42.50.Dv, A quantum system can retain a memory of its motion when it undergoes a cyclic evolution, e.g its quantum state may acquire a geometric phase factor in addition to the dynamical one [1,2]. For pure quantum states this effect is well understood and it has been demonstrated in a wide variety of physical systems [3]. Its potential application to perform the fault-tolerant quantum computation has been the subject of more recent investigations [4,5,6]. In contrast, relatively little is known about geometric phases, and more generally, about quantum holonomies of mixed or entangled quantum states. Here we report an NMR experiment which constitutes the first experimental study of quantum holonomies for mixed quantum states. We observed and measured the geometric phase of a mixed state of a spin half nuclei. Our experimental data are in a good agreement with the recent theoretical predictions by Sjöqvist et al [7].The geometric phase of pure states is an intriguing property of quantum systems undergoing parallel cyclic evolutions. The parallel transport of a particular vector |Ψ implies no change in phase when |Ψ(t) evolves into |Ψ(t + dt) , for some infinitesimal change of the parameter t. Although locally there is no phase change, the system may acquire a non-trivial phase after completing a closed loop parameterized by t. The origin of this phase can be traced to an underlying curvature of the parameter space, depending only on the geometry of the path and is resilient to certain dynamical perturbations of the evolution, e.g. it is independent of the speed of the evolution. Therefore, it is a potential method for performing intrinsically fault-tolerant quantum logic gates, a very desirable feature for practical implementations of quantum computation. However, quantum systems that interact with other systems, be it components in a quantum computer or otherwise, become entangled and cannot be described by a state vector |Ψ . In this context the notion of parallel transport and geometric phases must be extended to mixed quantum states.Mathematically, Uhlmann was the first to address the issue of a mixed state holonomy [8]. In his approach a system in a mixed state is embedded, as a subsystem, in a larger system that is in a pure state. Given a mixed state of the subsystem there are infinitely man...

When prior partial information about a state to be cloned is available, it can be cloned with a fidelity higher than that of universal quantum cloning. We experimentally verify this intriguing relationship between the cloning fidelity and the prior information by reporting the first experimental optimal quantum state-dependent cloning, using nuclear magnetic resonance techniques. Our experiments may further have important implications into many quantum information processing protocols.

There has been much recent effort to realize quantum devices in many different physical systems. Among them, nuclear magnetic resonance (NMR) has been the first to demonstrate nontrivial quantum algorithms with small numbers of qubits and hence is a prototype for the key ingredients needed to build quantum computers. An important building block in many quantum applications is the scattering circuit, which can be used as a quantum multimeter to perform various quantum information processing tasks directly without recourse to quantum tomography. We implement in NMR a three-qubit version of the multimeter and also demonstrate a single-qubit fingerprinting

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Following a key idea of unconventional geometric quantum computation developed earlier [Phys. Rev. Lett. 91, 197902 (2003)], here we propose a more general scheme in such an intriguing way: γ d = αg + ηγg, where γ d and γg are respectively the dynamic and geometric phases accumulated in the quantum gate operation, with η as a constant and αg being dependent only on the geometric feature of the operation. More arrestingly, we demonstrate the first experiment to implement a universal set of such kind of generalized unconventional geometric quantum gates with high fidelity in an NMR system. PACS numbers: 03.67. Lx, 03.65.Vf, Quantum computation has been paid intensive interest for the past decade because quantum computers are believed to be much more powerful and efficient than their classical counterparts due to their quantum nature [1]. Significant progresses have recently been achieved in the field of quantum computing. Nevertheless, there are still great challenges in physical implementation of quantum computation. One of them is to suppress the noises in quantum gates to an acceptable level, which is essential to build a scalable quantum computer. Recently, a promising approach based on geometric phases [2,3,4] was proposed to achieve built-in fault-tolerant quantum gates with higher fidelities [5,6,7,8,9,10,11] since the geometric phase depends only on the global feature of the evolution path and is believed to be robust against local fluctuations. On the other hand, in the same spirit, an interesting unconventional geometric quantum computation(GQC) scheme was proposed [12]; such kind of two-qubit gate was indeed reported experimentally in trapped ions [13] and was designed with superconducting qubits [14]. In this scheme, the dynamic phase γ d is ensured to be proportional to the geometric phase γ g , namely, γ d = ηγ g , (η = 0, −1) with η as a proportional constant.In this paper, we propose that the above unconventional GQC scheme [12] can be further generalized in such an intriguing manner: γ d = α g + ηγ g , where α g is a coefficient dependent only on the geometric feature of the quantum evolution path in the gate operation. It is elaborated that this generalized unconventional GQC can be realized in physical systems like NMR. In particular, we report the first experimental implementation of a universal set of such kind of unconventional geometric gates with high fidelity in an NMR system. Before we present our new results, let us first elucidate how to realize a single-qubit gate with the generalized unconventional geometric phase shift in the cyclic evolution [11]. For an one-qubit system, consider two orthogonal cyclic states |ψ + and |ψ − , which satisfy the relation U (τ ) |ψ ± = exp(±iγ) |ψ ± , where γ is the total phase accumulated and U (τ ) is the evolution operator of a cyclic evolution with τ as the periodicity. We can write |ψ + = e (Fig.1), |↑ and |↓ are the two eigenstates of the z-component of the spin-1/2 operator (σ z /2) and they constitute the computational basis for the qubit. For...

An important quantum search algorithm based on the quantum random walk performs an oracle search on a database of N items with O( √ phN) calls, yielding a speedup similar to the Grover quantum search algorithm. The algorithm was implemented on a quantum information processor of three-qubit liquid-crystal nuclear magnetic resonance (NMR) in the case of finding 1 out of 4, and the diagonal elements' tomography of all the final density matrices was completed with comprehensible one-dimensional NMR spectra. The experimental results agree well with the theoretical predictions.

This is a publisher's note for 'Experimental quantum multimeter and one-qubit fingerprinting' [Phys. Rev. A74, 042319 (2006)

We propose a scheme to implement high-fidelity conditional phase gates on pair of trapped ions immersed in a two-dimensional Coulomb crystal, using interaction mediated by all axial modes without side-band addressing. We show through numerical calculations that only local modes can be excited to achieve entangling gates through shaping the laser beams, so that the complexity of the quantum gate does not increase with the size of the system. These results suggest a promising approach for realization of large scale fault-tolerant quantum computation in two dimensional traps architecture.