Vivek Shende

Last updated
Vivek Shende
Alma mater
Scientific career
Fields Mathematics, Quantum Computing
Institutions University of California Berkeley, University of Southern Denmark, MIT
Thesis Hilbert schemes of points on integral plane curves  (2011)
Doctoral advisor Rahul Pandharipande

Vivek Vijay Shende is an American mathematician known for his work on algebraic geometry, symplectic geometry and quantum computing. He is a professor of Quantum Mathematics at Syddansk Universitet [1] while on leave from University of California Berkeley. [2]

Contents

Doctoral studies and early career

Shende defended his Ph.D. dissertation "Hilbert schemes of points on integral plane curves" at Princeton University in 2011 under the supervision of Rahul Pandharipande. [3] From 2011 to 2013, he was a Simons Postdoctoral Fellow at MIT mentored by Paul Seidel. Shende joined Berkeley as an assistant professor in 2013 and became an associate professor in 2019. He supervised at least four doctoral degrees at Berkeley. [3]

Awards and accomplishments

In 2021, after moving to Denmark, Shende received sizable grants intended to support the creation of a new research group. The Danish National Research Foundation awarded Shende its DNRF Chair. [4] The Villum Foundation funded Shende's research in mathematical aspects of String theory through the Villum Investigator program. [5] This is one of the largest and most prestigious grants for individual researchers in Denmark.

As a Berkeley professor, Shende received the National Science Foundation CAREER Award in 2017 [6] and a Sloan Research Fellowship in Mathematics in 2015. [7]

In 2010, Shende proved, together with Martijn Kool and Richard Thomas, the Göttsche conjecture on the universality of formulas counting nodal curves on surfaces, [8] a problem in algebraic geometry whose history stretches back more than a century. [9]

During his undergraduate studies at the University of Michigan, he performed computer science research with Igor L. Markov and John P. Hayes. Shende shared in 2004 the IEEE Donald O. Pederson Award in Solid-State Circuits [10] as the lead author of the work on synthesis of reversible logic circuits. [11] This paper proved the existence of reversible circuits that implement certain permutations and developed algorithms for finding such circuits. Shende was also the lead author of the work on synthesis of quantum circuits [12] that developed the quantum Shannon decomposition and algorithms for finding asymptotically optimal quantum circuits that implement a given -qubit unitary matrix, as well as quantum circuits that construct a given -qubit quantum state. Shende obtained formulas and algorithms for implementing smallest possible quantum circuits for 2-qubit unitary matrices. [13] [14] For the 3-qubit Toffoli gate, he proved that six CNOT gates are necessary in a circuit that implements it, [15] showing that the widely used six-CNOT decomposition is optimal. These publications are highly cited (per Google Scholar) and their results laid the foundation of compilers for quantum computers.

Mathematics education

Shende taught college-level Calculus, Discrete Mathematics as well as Linear Algebra and Differential Equations courses at Berkeley. In 2021 he cosigned, along with many professional mathematicians, an open letter to Governor Gavin Newsom and other California officials asking to replace the proposed new California Math curriculum framework. [16] The framework was adopted in 2023 despite these objections. [17]

Related Research Articles

<span class="mw-page-title-main">Quantum computing</span> Technology that uses quantum mechanics

A quantum computer is a computer that exploits quantum mechanical phenomena. On small scales, physical matter exhibits properties of both particles and waves, and quantum computing leverages this behavior using specialized hardware. Classical physics cannot explain the operation of these quantum devices, and a scalable quantum computer could perform some calculations exponentially faster than any modern "classical" computer. In particular, a large-scale quantum computer could break widely used encryption schemes and aid physicists in performing physical simulations; however, the current state of the art is largely experimental and impractical, with several obstacles to useful applications.

<span class="mw-page-title-main">Qubit</span> Basic unit of quantum information

In quantum computing, a qubit or quantum bit is a basic unit of quantum information—the quantum version of the classic binary bit physically realized with a two-state device. A qubit is a two-state quantum-mechanical system, one of the simplest quantum systems displaying the peculiarity of quantum mechanics. Examples include the spin of the electron in which the two levels can be taken as spin up and spin down; or the polarization of a single photon in which the two spin states can also be measured as horizontal and vertical linear polarization. In a classical system, a bit would have to be in one state or the other. However, quantum mechanics allows the qubit to be in a coherent superposition of multiple states simultaneously, a property that is fundamental to quantum mechanics and quantum computing.

Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. It is one of the few known quantum algorithms with compelling potential applications and strong evidence of superpolynomial speedup compared to best known classical (non-quantum) algorithms. On the other hand, factoring numbers of practical significance requires far more qubits than available in the near future. Another concern is that noise in quantum circuits may undermine results, requiring additional qubits for quantum error correction.

In logic circuits, the Toffoli gate, also known as the CCNOT gate (“controlled-controlled-not”), invented by Tommaso Toffoli, is a CNOT gate with two control qubits and one target qubit. That is, the target qubit will be inverted if the first and second qubits are both 1. It is a universal reversible logic gate, which means that any classical reversible circuit can be constructed from Toffoli gates. Formally, we describe the Toffoli gate with the following truth table and matrix:

<span class="mw-page-title-main">Quantum circuit</span> Model of quantum computing

In quantum information theory, a quantum circuit is a model for quantum computation, similar to classical circuits, in which a computation is a sequence of quantum gates, measurements, initializations of qubits to known values, and possibly other actions. The minimum set of actions that a circuit needs to be able to perform on the qubits to enable quantum computation is known as DiVincenzo's criteria.

Quantum error correction (QEC) is used in quantum computing to protect quantum information from errors due to decoherence and other quantum noise. Quantum error correction is theorised as essential to achieve fault tolerant quantum computing that can reduce the effects of noise on stored quantum information, faulty quantum gates, faulty quantum preparation, and faulty measurements. This would allow algorithms of greater circuit depth.

The Clifford group encompasses a set of quantum operations that map the set of n-fold Pauli group products into itself. It is most famously studied for its use in quantum error correction.

Quantum programming is the process of designing or assembling sequences of instructions, called quantum circuits, using gates, switches, and operators to manipulate a quantum system for a desired outcome or results of a given experiment. Quantum circuit algorithms can be implemented on integrated circuits, conducted with instrumentation, or written in a programming language for use with a quantum computer or a quantum processor.

<span class="mw-page-title-main">Controlled NOT gate</span> Quantum logic gate

In computer science, the controlled NOT gate, controlled-X gate, controlled-bit-flip gate, Feynman gate or controlled Pauli-X is a quantum logic gate that is an essential component in the construction of a gate-based quantum computer. It can be used to entangle and disentangle Bell states. Any quantum circuit can be simulated to an arbitrary degree of accuracy using a combination of CNOT gates and single qubit rotations. The gate is sometimes named after Richard Feynman who developed an early notation for quantum gate diagrams in 1986.

In quantum computing, the Gottesman–Knill theorem is a theoretical result by Daniel Gottesman and Emanuel Knill that states that stabilizer circuits, circuits that only consist of gates from the normalizer of the qubit Pauli group, also called Clifford group, can be perfectly simulated in polynomial time on a probabilistic classical computer. The Clifford group can be generated solely by using CNOT, Hadamard, and phase gate S; and therefore stabilizer circuits can be constructed using only these gates.

Daniel Amihud Lidar is the holder of the Viterbi Professorship of Engineering at the University of Southern California, where he is a professor of electrical engineering, chemistry, physics & astronomy. He is the director and co-founder of the USC Center for Quantum Information Science & Technology (CQIST), the director of the USC-IBM Quantum Innovation Center, as well as scientific director of the USC-Lockheed Martin Quantum Computing Center, notable for his research on control of quantum systems and quantum information processing.

John Patrick Hayes is an Irish-American computer scientist and electrical engineer, the Claude E. Shannon Chair of Engineering Science at the University of Michigan. He supervised over 35 doctoral students, coauthored seven books and over 340 peer-reviewed publications. His Erdös number is 2.

<span class="mw-page-title-main">Quantum machine learning</span> Interdisciplinary research area at the intersection of quantum physics and machine learning

Quantum machine learning is the integration of quantum algorithms within machine learning programs.

IBM Quantum Platform is an online platform allowing public and premium access to cloud-based quantum computing services provided by IBM. This includes access to a set of IBM's prototype quantum processors, a set of tutorials on quantum computation, and access to an interactive textbook. As of February 2021, there are over 20 devices on the service, six of which are freely available for the public. This service can be used to run algorithms and experiments, and explore tutorials and simulations around what might be possible with quantum computing.

Quil is a quantum instruction set architecture that first introduced a shared quantum/classical memory model. It was introduced by Robert Smith, Michael Curtis, and William Zeng in A Practical Quantum Instruction Set Architecture. Many quantum algorithms require a shared memory architecture. Quil is being developed for the superconducting quantum processors developed by Rigetti Computing through the Forest quantum programming API. A Python library called pyQuil was introduced to develop Quil programs with higher level constructs. A Quil backend is also supported by other quantum programming environments.

In quantum computing and quantum information theory, the Clifford gates are the elements of the Clifford group, a set of mathematical transformations which normalize the n-qubit Pauli group, i.e., map tensor products of Pauli matrices to tensor products of Pauli matrices through conjugation. The notion was introduced by Daniel Gottesman and is named after the mathematician William Kingdon Clifford. Quantum circuits that consist of only Clifford gates can be efficiently simulated with a classical computer due to the Gottesman–Knill theorem.

<span class="mw-page-title-main">Quantum gate teleportation</span>

Quantum gate teleportation is a quantum circuit construction where a gate is applied to target qubits by first applying the gate to an entangled state and then teleporting the target qubits through that entangled state.

<span class="mw-page-title-main">Igor L. Markov</span> American computer scientist and engineer

Igor Leonidovich Markov is an American professor, computer scientist and engineer. Markov is known for mathematical and algorithmic results in quantum computation, work on limits of computation, research on algorithms for optimizing integrated circuits and on electronic design automation, as well as artificial intelligence. Additionally, Markov is a California non-profit executive responsible for aid to Ukraine worth tens of millions dollars.

<span class="mw-page-title-main">Dmitri Maslov</span> Computer scientist

Dmitri Maslov is a Canadian-American computer scientist known for his work on quantum circuit synthesis and optimization, quantum advantage, and benchmarking quantum computers. Currently, he is the Chief Software Architect at IBM Quantum. Maslov was formerly a program director for Quantum Information Science at the National Science Foundation. He was named a Fellow of the Institute of Electrical and Electronics Engineers in 2021 "for contributions to quantum circuit synthesis and optimization, and compiling for quantum computers."

References

  1. ↑ "Professor Vivek Shende". Syddanks Universitet. Retrieved August 19, 2023.
  2. ↑ "Professor Vivek Shende". Berkeley Mathematics. Retrieved August 19, 2023.
  3. 1 2 "Vivek Vijay Shende". The Mathematics Genealogy Project. Retrieved August 19, 2023.
  4. ↑ "Vivek Shende is the fourth researcher to receive the Danish National Research Foundation's latest funding instrument: The DNRF Chair". Danish National Research Foundation. 25 January 2021.
  5. ↑ Jane Jamshidi (April 13, 2021). "25 million grant awarded to Vivek Shende". Syddansk Universitet.
  6. ↑ "Award # 1654545; CAREER: Aspects of Microlocal Geometry". National Science Foundation Division of Mathematical Sciences. January 31, 2017.
  7. ↑ Sanders, Robert (February 23, 2015). "Sloan fellowships give research boost to nine young faculty members". Berkeley News.
  8. ↑ Kool, Martijn; Shende, Vivek; Thomas, Richard (15 Oct 2010). "A short proof of the Göttsche conjecture". Geometry & Topology. 15: 397–406. arXiv: 1010.3211 . doi:10.2140/gt.2011.15.397.
  9. ↑ Kleiman, Steven; Piene, Ragni (29 Nov 2001). "Node polynomials for families: results and examples". arXiv: math.AG/0111299 .
  10. ↑ "IEEE Transactions on Computer-Aided Design Donald O. Pederson Best Paper Award | IEEE Council on Electronic Design Automation". ieee-ceda.org. Retrieved 2023-08-12.
  11. ↑ Shende, Vivek V.; Prasad, Aditya K.; Markov, Igor L.; Hayes, John P. (2003). "Synthesis of reversible logic circuits". IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems . 22 (6): 710–722. arXiv: quant-ph/0207001 . doi:10.1109/TCAD.2003.811448.
  12. ↑ Shende, Vivek V.; Bullock, Stephen S.; Markov, Igor L. (2006). "Synthesis of quantum logic circuits". IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems . 25 (6): 1000–1010. arXiv: quant-ph/0406176 . doi:10.1109/TCAD.2005.855930.
  13. ↑ Shende, Vivek V.; Markov, Igor L.; Bullock, Stephen S. (June 30, 2004). "Minimal universal two-qubit controlled-not-based circuits". Physical Review A . 69 (6). American Physical Society: 062321. arXiv: quant-ph/0308033 . Bibcode:2004PhRvA..69f2321S. doi:10.1103/PhysRevA.69.062321.
  14. ↑ Shende, Vivek V.; Bullock, Stephen S.; Markov, Igor L. (July 19, 2004). "Recognizing small-circuit structure in two-qubit operators". Physical Review A . 70 (1). American Physical Society: 012310. arXiv: quant-ph/0308045 . Bibcode:2004PhRvA..70a2310S. doi:10.1103/PhysRevA.70.012310.
  15. ↑ Shende, Vivek V.; Markov, Igor L. (2009). "On the CNOT-cost of TOFFOLI gates". Quantum Information and Computation. 9 (5&6): 461–486. arXiv: 0803.2316 . doi:10.26421/QIC8.5-6-8.
  16. ↑ Evers, Williamson M.; Wurman, Ze’ev (July 13, 2021). "Replace the Proposed New California Math Curriculum Framework". The Independent Institute.
  17. ↑ Schwartz, Sarah (July 12, 2023). "California Adopts Controversial New Math Framework. Here's What's in It". Education Week. EdWeek.
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