scholarly journals Data re-uploading for a universal quantum classifier

Quantum ◽  
2020 ◽  
Vol 4 ◽  
pp. 226 ◽  
Author(s):  
Adrián Pérez-Salinas ◽  
Alba Cervera-Lierta ◽  
Elies Gil-Fuster ◽  
José I. Latorre
Keyword(s):  
Quantum Circuit ◽  
Complex Data ◽  
Bloch Sphere ◽  
Single Qubit ◽  
Multiple Dimensions ◽  
Universal Quantum

A single qubit provides sufficient computational capabilities to construct a universal quantum classifier when assisted with a classical subroutine. This fact may be surprising since a single qubit only offers a simple superposition of two states and single-qubit gates only make a rotation in the Bloch sphere. The key ingredient to circumvent these limitations is to allow for multiple data re-uploading. A quantum circuit can then be organized as a series of data re-uploading and single-qubit processing units. Furthermore, both data re-uploading and measurements can accommodate multiple dimensions in the input and several categories in the output, to conform to a universal quantum classifier. The extension of this idea to several qubits enhances the efficiency of the strategy as entanglement expands the superpositions carried along with the classification. Extensive benchmarking on different examples of the single- and multi-qubit quantum classifier validates its ability to describe and classify complex data.

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.

scholarly journals Universal Quantum Computing and Three-Manifolds

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 773 ◽  
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 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 positive operator-valued measure (POVM) that one recognizes to be a 3-manifold M 3 . More precisely, the d-dimensional POVMs defined from subgroups of finite index of the modular group P S L ( 2 , Z ) correspond to d-fold M 3 - coverings over the trefoil knot. In this paper, we also investigate 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 M 3 ’s obtained from Dehn fillings are explored.

An upper bound on the threshold quantum decoherence rate

2004 ◽  
Vol 4 (3) ◽  
pp. 222-228
Author(s):  
A.A. Razborov
Keyword(s):  
Upper Bound ◽  
Random Noise ◽  
Quantum Circuit ◽  
Quantum Decoherence ◽  
Single Qubit ◽  
Constant Rate ◽  
Decoherence Rate

Let $\eta_0$ be the supremum of those $\eta$ for which every poly-size quantum circuit can be simulated by another poly-size quantum circuit with gates of fan-in $\leq 2$ that tolerates random noise independently occurring on all wires at the constant rate $\eta$. Recent fundamental results showing the principal fact $\eta_0>0$ give estimates like $\eta_0\geq 10^{-6}\mbox{--}10^{-4}$, whereas the only upper bound known before is $\eta_0\leq 0.74$.}{In this note we improve the latter bound to $\eta_0\leq 1/2$, under the assumption ${\bf QP}\not\subseteq {\bf QNC^1}$. More generally, we show that if the decoherence rate $\eta$ is greater than 1/2, then we can not even store a single qubit for more than logarithmic time. Our bound also generalizes to the simulating circuits allowing gates of any (constant) fan-in $k$, in which case we have $\eta_0\leq 1-\frac 1k$.

The implementation of universal quantum memory and gates based on large-scale diamond surface

2016 ◽  
Vol 14 (05) ◽  
pp. 1650026
Author(s):  
Xiao-Ning Qi ◽  
Yong Zhang
Keyword(s):  
Quantum State ◽  
Large Scale ◽  
Quantum Memory ◽  
Quantum Gate ◽  
Nitrogen Vacancy ◽  
Diamond Surface ◽  
Single Qubit ◽  
Model Based ◽  
Universal Quantum ◽  
Jc Model

Nitrogen-vacancy (NV) centers implanted beneath the diamond surface have been demonstrated to be effective in the processing of controlling and reading-out. In this paper, NV center entangled with the fluorine nuclei collective ensemble is simplified to Jaynes–Cummings (JC) model. Based on this system, we discussed the implementation of quantum state storage and single-qubit quantum gate.

scholarly journals Measuring the Tangle of Three-Qubit States

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 436 ◽  
Author(s):  
Adrián Pérez-Salinas ◽  
Diego García-Martín ◽  
Carlos Bravo-Prieto ◽  
José Latorre
Keyword(s):  
Direct Measurement ◽  
Canonical Form ◽  
Quantum Circuit ◽  
Quantum Gates ◽  
Tripartite Entanglement ◽  
Single Qubit ◽  
Optimal Values ◽  
Random States ◽  
Qubit States ◽  
Computational Basis

We present a quantum circuit that transforms an unknown three-qubit state into its canonical form, up to relative phases, given many copies of the original state. The circuit is made of three single-qubit parametrized quantum gates, and the optimal values for the parameters are learned in a variational fashion. Once this transformation is achieved, direct measurement of outcome probabilities in the computational basis provides an estimate of the tangle, which quantifies genuine tripartite entanglement. We perform simulations on a set of random states under different noise conditions to asses the validity of the method.

Experimental demonstration of optimized quantum process tomography on the IBM quantum experience

2020 ◽  
pp. 2040004
Author(s):  
Akshay Gaikwad ◽  
Krishna Shende ◽  
Kavita Dorai
Keyword(s):  
Quantum Circuit ◽  
Quantum Gates ◽  
Experimental Demonstration ◽  
Superconducting Qubit ◽  
Quantum Process ◽  
Single Qubit ◽  
Quantum Process Tomography ◽  
Process Tomography ◽  
Quantum Processor ◽  
Least Squares Optimization

We experimentally performed complete and optimized quantum process tomography of quantum gates implemented on superconducting qubit-based IBM QX2 quantum processor via two constrained convex optimization (CCO) techniques: least squares optimization and compressed sensing optimization. We studied the performance of these methods by comparing the experimental complexity involved and the experimental fidelities obtained. We experimentally characterized several two-qubit quantum gates: identity gate, a controlled-NOT gate, and a SWAP gate. The general quantum circuit is efficient in the sense that the data needed to perform CCO-based process tomography can be directly acquired by measuring only a single qubit. The quantum circuit can be extended to higher dimensions and is also valid for other experimental platforms.

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.

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