81 research outputs found
Ancilla-Driven Universal Quantum Computation
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.Comment: 4 pages, 3 figure
Adiabatic graph-state quantum computation
Measurement-based quantum computation (MBQC) and holonomic quantum
computation (HQC) are two very different computational methods. The computation
in MBQC is driven by adaptive measurements executed in a particular order on a
large entangled state. In contrast in HQC the system starts in the ground
subspace of a Hamiltonian which is slowly changed such that a transformation
occurs within the subspace. Following the approach of Bacon and Flammia, we
show that any measurement-based quantum computation on a graph state with
\emph{gflow} can be converted into an adiabatically driven holonomic
computation, which we call \emph{adiabatic graph-state quantum computation}
(AGQC). We then investigate how properties of AGQC relate to the properties of
MBQC, such as computational depth. We identify a trade-off that can be made
between the number of adiabatic steps in AGQC and the norm of as well
as the degree of , in analogy to the trade-off between the number of
measurements and classical post-processing seen in MBQC. Finally the effects of
performing AGQC with orderings that differ from standard MBQC are investigated.Comment: 25 pages, 3 figure
Entangling unitary gates on distant qubits with ancilla feedback
By using an ancilla qubit as a mediator, two distant qubits can undergo a
non-local entangling unitary operation. This is desirable for when attempting
to scale up or distribute quantum computation by combining fixed static local
sets of qubits with ballistic mediators. Using a model driven by measurements
on the ancilla, it is possible to generate a maximally entangling CZ gate while
only having access to a less entangling gate between the pair qubits and the
ancilla. However this results in a stochastic process of generating control
phase rotation gates where the expected time for success does not correlate
with the entangling power of the connection gate. We explore how one can use
feedback into the preparation and measurement parameters of the ancilla to
speed up the expected time to generate a CZ gate between a pair of separated
qubits and to leverage stronger coupling strengths for faster times.
Surprisingly, by choosing an appropriate strategy, control of a binary discrete
parameter achieves comparable speed up to full continuous control of all
degrees of freedom of the ancilla.Comment: 8 pages, 11 figure
Hybrid quantum computing with ancillas
In the quest to build a practical quantum computer, it is important to use
efficient schemes for enacting the elementary quantum operations from which
quantum computer programs are constructed. The opposing requirements of
well-protected quantum data and fast quantum operations must be balanced to
maintain the integrity of the quantum information throughout the computation.
One important approach to quantum operations is to use an extra quantum system
- an ancilla - to interact with the quantum data register. Ancillas can mediate
interactions between separated quantum registers, and by using fresh ancillas
for each quantum operation, data integrity can be preserved for longer. This
review provides an overview of the basic concepts of the gate model quantum
computer architecture, including the different possible forms of information
encodings - from base two up to continuous variables - and a more detailed
description of how the main types of ancilla-mediated quantum operations
provide efficient quantum gates.Comment: Review paper. An introduction to quantum computation with qudits and
continuous variables, and a review of ancilla-based gate method
Experimental demonstration of a measurement-based realisation of a quantum channel
We introduce and experimentally demonstrate a method for realising a quantum
channel using the measurement-based model. Using a photonic setup and modifying
the bases of single-qubit measurements on a four-qubit entangled cluster state,
representative channels are realised for the case of a single qubit in the form
of amplitude and phase damping channels. The experimental results match the
theoretical model well, demonstrating the successful performance of the
channels. We also show how other types of quantum channels can be realised
using our approach. This work highlights the potential of the measurement-based
model for realising quantum channels which may serve as building blocks for
simulations of realistic open quantum systems.Comment: 8 pages, 4 figure
Computational depth complexity of measurement-based quantum computation
We prove that one-way quantum computations have the same computational power
as quantum circuits with unbounded fan-out. It demonstrates that the one-way
model is not only one of the most promising models of physical realisation, but
also a very powerful model of quantum computation. It confirms and completes
previous results which have pointed out, for some specific problems, a depth
separation between the one-way model and the quantum circuit model. Since
one-way model has the same computational power as unbounded quantum fan-out
circuits, the quantum Fourier transform can be approximated in constant depth
in the one-way model, and thus the factorisation can be done by a polytime
probabilistic classical algorithm which has access to a constant-depth one-way
quantum computer. The extra power of the one-way model, comparing with the
quantum circuit model, comes from its classical-quantum hybrid nature. We show
that this extra power is reduced to the capability to perform unbounded
classical parity gates in constant depth.Comment: 12 page
Extending ancilla driven universal quantum computation beyond stepwise determinism
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 effciently 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 overlong distances suits a transmitter going to an unknown receiver with possible small errors in the receiver's interaction with the ancilla.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 effciently 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 overlong distances suits a transmitter going to an unknown receiver with possible small errors in the receiver's interaction with the ancilla
A Non-Orthogonal Variational Quantum Eigensolver
Variational algorithms for strongly correlated chemical and materials systems
are one of the most promising applications of near-term quantum computers. We
present an extension to the variational quantum eigensolver that approximates
the ground state of a system by solving a generalized eigenvalue problem in a
subspace spanned by a collection of parametrized quantum states. This allows
for the systematic improvement of a logical wavefunction ansatz without a
significant increase in circuit complexity. To minimize the circuit complexity
of this approach, we propose a strategy for efficiently measuring the
Hamiltonian and overlap matrix elements between states parametrized by circuits
that commute with the total particle number operator. We also propose a
classical Monte Carlo scheme to estimate the uncertainty in the ground state
energy caused by a finite number of measurements of the matrix elements. We
explain how this Monte Carlo procedure can be extended to adaptively schedule
the required measurements, reducing the number of circuit executions necessary
for a given accuracy. We apply these ideas to two model strongly correlated
systems, a square configuration of H and the -system of Hexatriene
(CH)
The Complexity of Translationally Invariant Spin Chains with Low Local Dimension
We prove that estimating the ground state energy of a
translationally-invariant, nearest-neighbour Hamiltonian on a 1D spin chain is
QMAEXP-complete, even for systems of low local dimension (roughly 40). This is
an improvement over the best previously-known result by several orders of
magnitude, and it shows that spin-glass-like frustration can occur in
translationally-invariant quantum systems with a local dimension comparable to
the smallest-known non-translationally-invariant systems with similar
behaviour.
While previous constructions of such systems rely on standard models of
quantum computation, we construct a new model that is particularly well-suited
for encoding quantum computation into the ground state of a
translationally-invariant system. This allows us to shift the proof burden from
optimizing the Hamiltonian encoding a standard computational model to proving
universality of a simple model.
Previous techniques for encoding quantum computation into the ground state of
a local Hamiltonian allow only a linear sequence of gates, hence only a linear
(or nearly linear) path in the graph of all computational states. We extend
these techniques by allowing significantly more general paths, including
branching and cycles, thus enabling a highly efficient encoding of our
computational model. However, this requires more sophisticated techniques for
analysing the spectrum of the resulting Hamiltonian. To address this, we
introduce a framework of graphs with unitary edge labels. After relating our
Hamiltonian to the Laplacian of such a unitary labelled graph, we analyse its
spectrum by combining matrix analysis and spectral graph theory techniques
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