Universal quantum computing in linear nearest neighbor architectures

2011 ◽  
Vol 11 (3&4) ◽  
pp. 300-312
Author(s):  
Preethika Kumar ◽  
Steven R. Skinner
Keyword(s):  
Quantum Computing ◽  
Solid State ◽  
Control Parameter ◽  
Nearest Neighbor ◽  
Quantum Computer ◽  
Gate Operation ◽  
One Dimensional ◽  
Single Qubit ◽  
Universal Quantum ◽  
Target Qubit

We introduce a scheme for realizing universal quantum computing in a linear nearest neighbor architecture with fixed couplings. We first show how to realize a controlled-NOT gate operation between two adjacent qubits without having to isolate the two qubits from qubits adjacent to them. The gate operation is implemented by applying two consecutive pulses of equal duration, but varying amplitudes, on the target qubit. Since only a single control parameter is required in implementing our scheme, it is very efficient. We next show how our scheme can be used to realize single qubit rotations and two-qubit controlled-unitary operations. As most proposals for solid state implementations of a quantum computer use a one-dimensional line of qubits, the schemes presented here will be extremely useful.

scholarly journals Benchmarking an 11-qubit quantum computer

2019 ◽  
Vol 10 (1) ◽  
Author(s):  
K. Wright ◽  
K. M. Beck ◽  
S. Debnath ◽  
J. M. Amini ◽  
Y. Nam ◽  
...  
Keyword(s):  
Quantum Computing ◽  
Quantum Physics ◽  
Quantum Computer ◽  
Success Rates ◽  
Single Qubit ◽  
The Past ◽  
Large Numbers ◽  
Universal Quantum ◽  
Qubit Gate ◽  
Fully Connected

AbstractThe field of quantum computing has grown from concept to demonstration devices over the past 20 years. Universal quantum computing offers efficiency in approaching problems of scientific and commercial interest, such as factoring large numbers, searching databases, simulating intractable models from quantum physics, and optimizing complex cost functions. Here, we present an 11-qubit fully-connected, programmable quantum computer in a trapped ion system composed of 13 171Yb+ ions. We demonstrate average single-qubit gate fidelities of 99.5$$\%$$%, average two-qubit-gate fidelities of 97.5$$\%$$%, and SPAM errors of 0.7$$\%$$%. To illustrate the capabilities of this universal platform and provide a basis for comparison with similarly-sized devices, we compile the Bernstein-Vazirani and Hidden Shift algorithms into our native gates and execute them on the hardware with average success rates of 78$$\%$$% and 35$$\%$$%, respectively. These algorithms serve as excellent benchmarks for any type of quantum hardware, and show that our system outperforms all other currently available hardware.

scholarly journals Solid-state Stern–Gerlach spin splitter for magnetic field sensing, spintronics, and quantum computing

2018 ◽  
Vol 9 ◽  
pp. 1558-1563 ◽  
Author(s):  
Kristofer Björnson ◽  
Annica M Black-Schaffer
Keyword(s):  
Solid State ◽  
Magnetic Flux ◽  
Quantum Computer ◽  
Characteristic Size ◽  
Two Dimensional ◽  
Interference Effects ◽  
Switching Field ◽  
Single Qubit ◽  
Field Sensitivity ◽  
Universal Quantum

We show conceptually that the edge of a two-dimensional topological insulator can be used to construct a solid-state Stern–Gerlach spin splitter. By threading such a Stern–Gerlach apparatus with a magnetic flux, Aharanov–Bohm-like interference effects are introduced. Using ferromagnetic leads, the setup can be used to both measure magnetic flux and as a spintronics switch. With normal metallic leads a switchable spintronics NOT-gate can be implemented. Furthermore, we show that a sequence of such devices can be used to construct a single-qubit SU(2)-gate, one of the two gates required for a universal quantum computer. The field sensitivity, or switching field, b, is related to the characteristic size of the device, r, through b = h/(2πqr 2), with q being the unit of electric charge.

scholarly journals A silicon-based surface code quantum computer

2016 ◽  
Vol 2 (1) ◽  
Author(s):  
Joe O’Gorman ◽  
Naomi H Nickerson ◽  
Philipp Ross ◽  
John JL Morton ◽  
Simon C Benjamin
Keyword(s):  
Quantum Computing ◽  
Solid State ◽  
Quantum Computer ◽  
Fault Tolerant ◽  
Device Fabrication ◽  
Impurity Atoms ◽  
Dipole Interactions ◽  
Total Phase ◽  
Surface Code ◽  
Silicon Based

Abstract Individual impurity atoms in silicon can make superb individual qubits, but it remains an immense challenge to build a multi-qubit processor: there is a basic conflict between nanometre separation desired for qubit–qubit interactions and the much larger scales that would enable control and addressing in a manufacturable and fault-tolerant architecture. Here we resolve this conflict by establishing the feasibility of surface code quantum computing using solid-state spins, or ‘data qubits’, that are widely separated from one another. We use a second set of ‘probe’ spins that are mechanically separate from the data qubits and move in and out of their proximity. The spin dipole–dipole interactions give rise to phase shifts; measuring a probe’s total phase reveals the collective parity of the data qubits along the probe’s path. Using a protocol that balances the systematic errors due to imperfect device fabrication, our detailed simulations show that substantial misalignments can be handled within fault-tolerant operations. We conclude that this simple ‘orbital probe’ architecture overcomes many of the difficulties facing solid-state quantum computing, while minimising the complexity and offering qubit densities that are several orders of magnitude greater than other systems.

scholarly journals Quantum Computing, Seifert Surfaces, and Singular Fibers

2019 ◽  
Vol 1 (1) ◽  
pp. 12-22 ◽  
Author(s):  
Michel Planat ◽  
Raymond Aschheim ◽  
Marcelo M. Amaral ◽  
Klee Irwin
Keyword(s):  
Quantum Computing ◽  
Quantum Computer ◽  
Complete Information ◽  
Singular Fiber ◽  
Dynkin Diagrams ◽  
Singular Fibers ◽  
Seifert Surfaces ◽  
Trefoil Knot ◽  
Universal Quantum

The fundamental group π 1 ( L ) of a knot or link L may be used to generate magic states appropriate for performing universal quantum computation and simultaneously for retrieving complete information about the processed quantum states. In this paper, one defines braids whose closure is the L of such a quantum computer model and computes their braid-induced Seifert surfaces and the corresponding Alexander polynomial. In particular, some d-fold coverings of the trefoil knot, with d = 3 , 4, 6, or 12, define appropriate links L, and the latter two cases connect to the Dynkin diagrams of E 6 and D 4 , respectively. In this new context, one finds that this correspondence continues with Kodaira’s classification of elliptic singular fibers. The Seifert fibered toroidal manifold Σ ′ , at the boundary of the singular fiber E 8 ˜ , allows possible models of quantum computing.

scholarly journals Universal Quantum Computing and Three-Manifolds

2018 ◽  
Author(s):  
Michel Planat ◽  
Raymond Aschheim ◽  
Marcelo Amaral ◽  
Klee Irwin
Keyword(s):  
Quantum Computing ◽  
Modular Group ◽  
Bloch Sphere ◽  
Borromean Rings ◽  
Single Qubit ◽  
Whitehead Link ◽  
Trefoil Knot ◽  
Universal Quantum ◽  
Dehn Fillings ◽  
Knots And Links

A single qubit may be represented on the Bloch sphere or similarly on the $3$-sphere $S^3$. Our goal is to dress this correspondence by converting the language of universal quantum computing (uqc) to that of $3$-manifolds. A magic state and the Pauli group acting on it define a model of uqc as a POVM that one recognizes to be a $3$-manifold $M^3$. E. g., the $d$-dimensional POVMs defined from subgroups of finite index of the modular group $PSL(2,\mathbb{Z})$ correspond to $d$-fold $M^3$- coverings over the trefoil knot. In this paper, one also investigates quantum information on a few \lq universal' knots and links such as the figure-of-eight knot, the Whitehead link and Borromean rings, making use of the catalog of platonic manifolds available on SnapPy. Further connections between POVMs based uqc and $M^3$'s obtained from Dehn fillings are explored.

scholarly journals Universal Quantum Computing and Three-Manifolds

2018 ◽  
Author(s):  
Michel Planat ◽  
Raymond Aschheim ◽  
Marcelo Amaral ◽  
Klee Irwin
Keyword(s):  
Quantum Computing ◽  
Bloch Sphere ◽  
Borromean Rings ◽  
Single Qubit ◽  
Whitehead Link ◽  
Trefoil Knot ◽  
Universal Quantum ◽  
Dehn Fillings ◽  
Knots And Links ◽  
Positive Operator Valued Measure

A single qubit may be represented on the Bloch sphere or similarly on the 3-sphere S3. Our goal is to dress this correspondence by converting the language of universal quantum computing (UQC) to that of 3-manifolds. A magic state and the Pauli group acting on it define a model of UQC as a positive operator-valued measure (POVM) that one recognizes to be a 3-manifold M3. More precisely, the d-dimensional POVMs defined from subgroups of finite index of the modular group PSL(2, Z) correspond to d-fold M3- coverings over the trefoil knot. In this paper, one also investigates quantum information on a few ‘universal’ knots and links such as the figure-of-eight knot, the Whitehead link and Borromean rings, making use of the catalog of platonic manifolds available on the software SnapPy. Further connections between POVMs based UQC and M3’s obtained from Dehn fillings are explored.

Both Toffoli and Controlled-NOT need little help to universal quantum computing

2003 ◽  
Vol 3 (1) ◽  
pp. 84-92
Author(s):  
Y-Y Shi
Keyword(s):  
Quantum Computing ◽  
Quantum Computation ◽  
Quantum Circuit ◽  
Single Qubit ◽  
Universal Quantum ◽  
Qubit Gate ◽  
Computational Basis ◽  
Universal Gates

What additional gates are needed for a set of classical universal gates to do universal quantum computation? We prove that any single-qubit real gate suffices, except those that preserve the computational basis. The Gottesman-Knill Theorem implies that any quantum circuit involving only the Controlled-NOT and Hadamard gates can be efficiently simulated by a classical circuit. In contrast, we prove that Controlled-NOT plus any single-qubit real gate that does not preserve the computational basis and is not Hadamard (or its like) are universal for quantum computing. Previously only a generic gate, namely a rotation by an angle incommensurate with \pi, is known to be sufficient in both problems, if only one single-qubit gate is added.

QUANTUM DOT COMPUTING GATES

2006 ◽  
Vol 04 (02) ◽  
pp. 233-296 ◽  
Author(s):  
GOONG CHEN ◽  
ZIJIAN DIAO ◽  
JONG U. KIM ◽  
ARUP NEOGI ◽  
KERIM URTEKIN ◽  
...  
Keyword(s):  
Quantum Dots ◽  
Quantum Computing ◽  
Quantum Dot ◽  
Quantum Computer ◽  
Semiconductor Quantum Dots ◽  
Quantum Gates ◽  
Promising Candidate ◽  
Universal Quantum ◽  
Physical Attributes

Semiconductor quantum dots are a promising candidate for future quantum computer devices. Presently, there are three major proposals for designing quantum computing gates based on quantum dot technology: (i) electrons trapped in microcavity; (ii) spintronics; (iii) biexcitons. We survey these designs and show mathematically how, in principle, they will generate 1-bit rotation gates as well as 2-bit entanglement and, thus, provide a class of universal quantum gates. Some physical attributes and issues related to their limitations, decoherence and measurement are also discussed.

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