52 research outputs found
Quantum Circuits for General Multiqubit Gates
We consider a generic elementary gate sequence which is needed to implement a
general quantum gate acting on n qubits -- a unitary transformation with 4^n
degrees of freedom. For synthesizing the gate sequence, a method based on the
so-called cosine-sine matrix decomposition is presented. The result is optimal
in the number of elementary one-qubit gates, 4^n, and scales more favorably
than the previously reported decompositions requiring 4^n-2^n+1 controlled NOT
gates.Comment: 4 pages, 3 figure
Experimental determination of the Berry phase in a superconducting charge pump
We present the first measurements of the Berry phase in a superconducting
Cooper pair pump. A fixed amount of Berry phase is accumulated to the
quantum-mechanical ground state in each adiabatic pumping cycle, which is
determined by measuring the charge passing through the device. The dynamic and
geometric phases are identified and measured quantitatively from their
different response when pumping in opposite directions. Our observations, in
particular, the dependencies of the dynamic and geometric effects on the
superconducting phase bias across the pump, agree with the basic theoretical
model of coherent Cooper pair pumping.Comment: 4 pages, 3 figure
Unitary transformations for quantum computing
The last two decades have seen an enormous increase in the computational power of digital computers. This was due to the rapid technical development in manufacturing processes and controlling semiconducting structures on submicron scale. Concurrently, the electric circuits have encountered the first signs of the realm of quantum mechanics. Those effects may induce noise and thus they are typically considered harmful. However, the manipulation of the coherent quantum states might turn out be the basis of powerful computers – quantum computers. There, the computation is encoded into the unitary time evolution of a quantum mechanical state vector. Eventually, quantum mechanics could enable one, for example, to read secret electronic messages which are encrypted by the widely employed RSA cryptosystem – a task which is extremely laborious for the current digital computers.
This thesis presents a theoretical study of the coherent manipulations of pure quantum states in a quantum register, that is, quantum algorithms. An implementation of a quantum algorithm involves the initialization of the input state and its manipulation with quantum gates followed by the measurements. The physical implementation of each gate requires that it is decomposed into low-level gates whose physical realizations are explicitly known. Here, the problem is examined from two directions. Firstly, the numerical optimization scheme for controlling time-evolution of a closed quantum system is discussed. This yields a method for implementing quantum gates acting on up to three quantum bits, qubits. The approach is independent of the physical realization of the quantum computer, but it is considered explicitly for a proposed inductively coupled Josephson charge qubit register. Secondly, the techniques of numerical matrix computation are utilized to find a general method for decomposing an arbitrary n-qubit gate into a sequence of elementary gates, which act on one or two qubits.
The results of this thesis help to improve the implementation of quantum algorithms. The quantum circuit construction developed in the thesis is the first one to achieve the asymptotically minimal complexity in the number of elementary gates. In context of acceleration of quantum algorithms we present a gate-level study of Shor's algorithm and show how to accelerate the algorithm by merging several elementary gates into multiqubit gates. Finally, the requirements set by the resulting gate array are compared to the properties of superconducting qubits. This allows us to discuss the feasibility of the Josephson charge qubit register, for instance, as hardware for breaking the RSA cryptosystem.reviewe
Nanoampere pumping of Cooper pairs
The authors have employed a tunable Cooper-pair transistor, the sluice, with radio frequency control to pump current over a resistive circuit. They find that the charge transferred per pumping cycle can be controlled with the resolution of a single Cooper pair up to hundreds of pairs. The achieved nanoampere current features more than an order of magnitude improvement over the previously reported results and it is close to the theoretical maximum value for the measured sample.Peer reviewe
Measurement scheme of the Berry phase in superconducting circuits
We present a measurement scheme for observing the Berry phase in a flux
assisted Cooper pair pump - the Cooper pair sluice. In contrast to the recent
experiments, in which the sluice was employed to generate accurate current
through a resistance, we consider a device in a superconducting loop. This
arrangement introduces a connection between the pumped current and the Berry
phase accumulated during the adiabatic pumping cycles. From the adiabaticity
criterion, we derive equations for the maximum pumped current and optimize the
sluice accordingly. These results apply also to the high accuracy pumping which
results in a potential candidate for a metrological current standard. For
measuring the pumped current, an additional Josephson junction is installed
into the superconducting loop. We show in detail that the switching of this
system from superconducting state into normal state as a consequence of an
external current pulse through it may be employed to probe the pumped current.
The experimental realization of our scheme would be the first observation of
the Berry phase in superconducting circuits.Comment: 19 pages, 5 figure
Suppression of the critical current of a balanced SQUID
We present an experimental study of the magnetic flux dependence of the
critical current of a balanced SQUID with three Josephson junctions in
parallel. Unlike for ordinary dc SQUIDs, the suppression of the critical
current does not depend on the exact parameters of the Josephson junctions. The
suppression is essentially limited only by the inductances of the SQUID loops.
We demonstrate a critical current suppression ratio of higher than 300 in a
balanced SQUID with a maximum critical current 30 nA.Comment: 4 pages, 3 figure
Quantum circuits with uniformly controlled one-qubit gates
Uniformly controlled one-qubit gates are quantum gates which can be
represented as direct sums of two-dimensional unitary operators acting on a
single qubit. We present a quantum gate array which implements any n-qubit gate
of this type using at most 2^{n-1} - 1 controlled-NOT gates, 2^{n-1} one-qubit
gates and a single diagonal n-qubit gate. The circuit is based on the so-called
quantum multiplexor, for which we provide a modified construction. We
illustrate the versatility of these gates by applying them to the decomposition
of a general n-qubit gate and a local state preparation procedure. Moreover, we
study their implementation using only nearest-neighbor gates. We give upper
bounds for the one-qubit and controlled-NOT gate counts for all the
aforementioned applications. In all four cases, the proposed circuit topologies
either improve on or achieve the previously reported upper bounds for the gate
counts. Thus, they provide the most efficient method for general gate
decompositions currently known.Comment: 8 pages, 10 figures. v2 has simpler notation and sharpens some
result
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