Ancilla-driven quantum computation for qudits and continuous variables (original) (raw)
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Extending ancilla driven universal quantum computation beyond stepwise determinism
2016
A major research goal in the field of quantum computation is the construction of the universal quantum computer (UQC): a device that can implement any quantum algorithm. Several theoretical schemes for implementing UQC have been developed which require different sets of resources and capabilities with varying implications for the optimum experimental implementations. The ancilla driven quantum computation scheme (ADQC) comprises two subsystems: a memory register of qubits on which information is retained and processed and an ancilla system of qubits which couple to the register. This coupling is represented in the ADQC scheme by a fixed quantum gate. By preparing the ancilla in selected states before applying this gate and then measuring it in selected measurement basis afterwards, quantum gates are enacted on the register qubits. ADQC is deterministic in that the probability of the outcome after performing the entire procedure is 1 but we have to apply corrections to the procedure at each step that depend on the probabilistic outcome of the ancilla measurement. An important resource in this model is the availability of a maximally entangling two-qubit gate between the ancilla and register qubits because if the gate is not maximally entangling, the resulting gates on the register can not be selected with stepwise determinism. It is proven in this thesis that in fact ADQC with non-maximally entangling interaction gates is universal. This requires showing that single-and two-qubit unitary gates can be efficiently implemented probabilistically. We also show a relationship between the expected time of the probabilistic implementation of a gate and the ability to control the ancilla. In the ADQC model, the ancilla is controlled with single qubit unitary gates just before interacting with the register and just before measurement. We show that the increase in time caused by a loss of maximally entangling two-qubit gates can be counteracted by control over the ancilla. This needs not be the ability to perform any single qubit unitary to the ancilla but just the ability to perform a specific small finite set of operations. This is important because the resource requirements described by a scheme affect the properties of possible experimental implementations. The ADQC scheme was originally designed to be used with physical implementations of quantum computing that involves qubits coming from different physical systems that have different properties. This may restrict the availability of couplings between the register and ancilla systems equivalent to maximally entangling quantum gates. By further focusing on the model under specific restrictions, such as minimal control of the ancilla system or long distance separation between register qubits, we find certain properties of the physical implementation that may best suit it for ADQC beyond stepwise determinism. Minimal control appears best suited for symmetric ancilla-register interactions; use over long distances suits a transmitter going to an unknown receiver with possible small errors in the receiver's interaction with the ancilla.
Ancilla-driven universal quantum computation
Physical Review A, 2010
We propose a method of manipulating a quantum register remotely with the help of a single ancilla that "steers" the evolution of the register. The fully controlled ancilla qubit is coupled to the computational register solely via a fixed unitary two-qubit interaction, E, and then measured in suitable bases. We characterize all interactions E that induce a unitary, step-wise deterministic measurement back-action on the register sufficient to implement any arbitrary quantum channel. Our scheme offers significant experimental advantages for implementing computations, preparing states and performing generalized measurements as no direct control of the register is required.
Generalized measurements via a programmable quantum processor
Physical Review A, 2003
We show that it is possible to control the trade-off between information gain and disturbance in generalized measurements of qudits by utilizing the programmable quantum processor. This universal quantum machine allows us to perform a generalized measurement on the initial state of the input qudit to construct a Husimi function of this state. The trade-off between the gain and the disturbance of the qudit is controlled by the initial state of ancillary system that acts as a program register for the quantum-information distributor. The trade-off fidelity does not depend on the initial state of the qudit.
Some two qubit interactions are singly sufficient for universal quantum computation but not without the use of an ancilla. Recent schemes for universal quantum computation have focused on hybrid physical systems using ancillae. In them, the application of resources is shifted to the ancilla system. We consider which 2-qubit interactions are universal in ancilla schemes where direct connections between main register qubits are forbidden. By the use of ancilla driven operations and repeat-until-success style random gates, a single fixed symmetric gate can be universal be control of the number of repetitions alone.
Quantum-computer architecture using nonlocal interactions
Physical Review A, 2003
Several authors have described the basic requirements essential to build a scalable quantum computer. Because many physical implementation schemes for quantum computing rely on nearest neighbor interactions, there is a hidden quantum communication overhead to connect distant nodes of the computer. In this paper we propose a physical solution to this problem which, together with the key building blocks, provides a pathway to a scalable quantum architecture using nonlocal interactions. Our solution involves the concept of a quantum bus that acts as a refreshable entanglement resource to connect distant memory nodes providing an architectural concept for quantum computers analogous to the von Neumann architecture for classical computers. PACS numbers: 03.67.-a, 03.67.Mn
Efficient measurement-based quantum computing with continuous-variable systems
2011
We present strictly efficient schemes for scalable measurement-based quantum computing using continuousvariable systems: These schemes are based on suitable non-Gaussian resource states, ones that can be prepared using interactions of light with matter systems or even purely optically. Merely Gaussian measurements such as optical homodyning as well as photon counting measurements are required, on individual sites. These schemes overcome limitations posed by Gaussian cluster states, which are known not to be universal for quantum computations of unbounded length, unless one is willing to scale the degree of squeezing with the total system size. We establish a framework derived from tensor networks and matrix product states with infinite physical dimension and finite auxiliary dimension general enough to provide a framework for such schemes. Since in the discussed schemes the logical encoding is finite-dimensional, tools of error correction are applicable. We also identify some further limitations for any continuous-variable computing scheme from which one can argue that no substantially easier ways of continuous-variable measurement-based computing than the presented one can exist.
Continuous-variable quantum information processing
Laser & Photonics Reviews, 2010
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.
Quantum Computation by Local Measurement
Annual Review of Condensed Matter Physics, 2012
Quantum computation is a novel way of information processing which allows, for certain classes of problems, exponential speedups over classical computation. Various models of quantum computation exist, such as the adiabatic, circuit and measurementbased models. They have been proven equivalent in their computational power, but operate very differently. As such, they may be suitable for realization in different physical systems, and also offer different perspectives on open questions such as the precise origin of the quantum speedup. Here, we give an introduction to the one-way quantum computer, a scheme of measurement-based quantum computation. In this model, the computation is driven by local measurements on a carefully chosen, highly entangled state. We discuss various aspects of this computational scheme, such as the role of entanglement and quantum correlations. We also give examples for ground states of simple Hamiltonians which enable universal quantum computation by local measurements.
Physical Realization of Measurement Based Quantum Computation
arXiv (Cornell University), 2023
Harnessing quantum mechanics properties, quantum computers have the potential to outperform classical computers in many applications and are envisioned to affect various aspects of our society. Different approaches are being explored for building such computers. One of such potential approaches is Measurement based quantum computation (MBQC), introduced by Raussendorf and Briegel in 2001. In MBQC a large number of qubits are prepared in a highly entangled clusters, called cluster states. The required quantum computation is then performed by a sequence of measurements. Cluster states are being physically realized using continuous variables (CV) and discrete variables (DV) approaches. CV-based approaches can be further categorized as Frequency domain multiplexing (FDM), Time domain multiplexing (TDM), Spatial domain multiplexing (SDM) and hybrid. We discuss and compare these approaches in detail. We also discuss cluster states generation in DV and report some recent results where photons and superconducting qubits are used.
Construction of a universal quantum computer
Physical Review A, 2009
We construct a universal quantum computer following Deutsch's original proposal of a universal quantum Turing machine ͑UQTM͒. Like Deutsch's UQTM, our machine can emulate any classical Turing machine and can execute any algorithm that can be implemented in the quantum gate array framework but under the control of a quantum program, and hence is universal. We present the architecture of the machine, which consists of a memory tape and a processor and describe the observables that comprise the registers of the processor and the instruction set, which includes a set of operations that can approximate any unitary operation to any desired accuracy and hence is quantum computationally universal. We present the unitary evolution operators that act on the machine to achieve universal computation and discuss each of them in detail and specify and discuss explicit program halting and concatenation schemes. We define and describe a set of primitive programs in order to demonstrate the universal nature of the machine. These primitive programs facilitate the implementation of more complex algorithms and we demonstrate their use by presenting a program that computes the NAND function, thereby also showing that the machine can compute any classically computable function.