I am a theoretical physicist working on Quantum information and computation theory.
All my papers can be found here .
Current Group Members
- Undergraduate Students: Joey Li, Yikai Wu
The theory of quantum information and quantum computation is an interdisciplinary field at the boundary of physics, engineering, and computer science. On the one hand, it looks at the fundamental limits of nature on computation and communication, and on the other hand, it studies more practical questions, such as how to overcome decoherence and build a fault-tolerant quantum computer, or how to efficiently simulate the ground state and the dynamics of a many-body system. I have broad interests in Quantum Information Science (Read a short overview of this field).
I believe the revolution that happened in quantum information science in the last two decades, is going to have a profound influence on the rest of physics, and I am interested to work in this direction. In addition to this aspect of my research program, I am interested in all sorts of topics in quantum information science, from quantum algorithms and quantum cryptography, to open quantum systems, quantum error correction and quantum metrology.
Here are some of the topics I have worked on in the past:
Quantum Thermodynamics and Quantum Resource Theories
(Quantum Clocks, Quantum Reference frames, Coherence, Asymmetry,….)
What is a Quantum Resource Theory?
If one looks at the scientific history of the theory of entanglement, the turning point is easily seen to occur in the mid-nineties, at the point when researchers in quantum information theory began to consider entanglement as “a resource as real as energy”. It gradually became clear that the entanglement theory should be understood asa framework to study questions about manipulating resource states for performing certain tasks, similar to the theory of thermodynamics. From this point on, entangled states and entangling operations were defined as those states and operations that cannot be implemented when one only has access to Local Operations and Classical Communication. Researchers then began to systematically answer questions such as: under this kind of restriction when is it possible to convert one resource state into another? How do we quantify the resource? What is the resource cost of simulating an operation? Subsequently, motivated by the success of the resource theory approach to entanglement, many researchers started applying this approach to understand other properties of quantum systems, such as coherence, asymmetry and athermality in quantum thermodynamics.
- I. Marvian, Coherence distillation machines are impossible in quantum thermodynamics, arXiv:1805.01989.
- G. Gour, D. Jennings, F. Buscemi, R. Duan, I. Marvian, Quantum majorization and a complete set of entropic conditions for quantum thermodynamics, arXiv:1708.04302 (To appear in Nature Communications).
- I. Marvian and R. W. Spekkens, How to quantify coherence: Distinguishing speakable and unspeakable notions, Phys. Rev. A 94 , 052324 (2016 ), Editors’ Suggestion, arXiv:1602.08049 .
- I. Marvian and R. W. Spekkens, Extending Noether’s theorem by quantifying the asymmetry of quantum states, Nature Communications 5 , 3821 (2014 ), arXiv:1404.3236.
- A. Kolchinsky, I. Marvian, C. Gokler, , Z. Liu, , P. Shor, O. Shtanko, K. Thompson, D.Wolpert, S. Lloyd, Maximizing free energy gain, arXiv:1705.00041.
- I. Marvian and R. W. Spekkens, The theory of manipulations of pure state asymmetry I: basic tools and equivalence classes of states under symmetric operations, New J. Phys. 15 , 033001 (2013), arXiv:1602.08049.
- I. Marvian and R. W. Spekkens, Modes of asymmetry: the application of harmonic analysis to symmetric quantum dynamics and quantum reference frames, Phys. Rev. A 90 , 062110 (2014 ), arXiv:1312.0680.
Local Symmetric Quantum Circuits and their applications
According to an elementary result in quantum computing, any unitary transformation on a composite system can be generated using 2-local unitaries, i.e., those which act only on two subsystems. Beside its fundamental importance in quantum computing, this result can also be regarded as a statement about the dynamics of systems with local Hamiltonians: although locality puts various constraints on the short-term dynamics, it does not restrict the possible unitary evolutions that a composite system with a general local Hamiltonian can experience after a sufficiently long time.
In a recent work I ask if such universality remains valid in the presence of conservation laws and global symmetries. In particular, can k-local symmetric unitaries on a composite system generate all symmetric unitaries on that system? Interestingly, it turns out that the answer is negative in the case of continuous symmetries, such as U(1) and SU(2): generic symmetric unitaries cannot be implemented, even approximately, using local symmetric unitaries. In fact, the difference between the dimensions of the manifolds of all symmetric unitaries and its subgroup generated by k-local symmetric unitaries, constantly increases with the system size.
Energy-conserving unitaries with local interactions:
Interestingly, it turns out that this no-go theorem can be circumvented using ancillary qubits, i.e., auxiliary systems initially prepared in a fixed state which return to their initial states at the end of the process. For instance, I show that using 2-local Hamiltonian X X+Y Y and local Pauli Z, which are both invariant under rotations around z, it is possible to implement all uniatiries that are invariant under this symmetry, provided that one can employ an ancillary qubit. Moreover, any energy-conserving unitary on a composite system can be implemented in a similar fashion, using a single ancillary qubit
Iman Marvian, Locality and Conservation Laws: How, in the presence of symmetry, locality restricts realizable unitaries, arXiv:2003.05524
Quantum Algorithms and Learning theory
- A. Steffens, P. Rebentrost, I. Marvian, J. Eisert, S. Lloyd, An efficient quantum algorithm for spectral estimation, New J. Phys. 19 (3 ), 033005 (2017 ), arXiv:1609.08170 .
- P. Rebentrost, A Steffens, I. Marvian, S. Lloyd, Quantum singular-value decomposition of nonsparse low-rank matrices, Physical review A 97 (1), 012327 (2018).
I. Marvian and S. Lloyd, Universal Quantum Emulator, arXiv:1606.02734.
Quantum Error Suppression for Adiabatic Quantum Computation, Open Quantum systems
- I. Marvian and D. A. Lidar, Quantum speed limits for leakage and decoherence, Phys. Rev. Lett. 115 , 210402 (2015 ), arXiv:1505.07850 .
- I. Marvian and D. A. Lidar, Quantum error suppression with commuting Hamiltonians: Two-local is too local , Phys. Rev. Lett. 113 , 260504 (2014 ), arXiv:1410.5487.
I. Marvian, Exponential suppression of decoherence and relaxation of quantum systems using energy penalty, arXiv:1602.03251.
Symmetry-Protected topological order
and computational phases of matter
- I. Marvian, Symmetry-Protected Topological Entanglement, Phys. Rev. B 95 , 045111 (2017 ), arXiv:1307.6617.
Quantum Speed Limits and Uncertainty relations
I. Marvian, R.W. Spekkens, and Paolo Zanardi, Quantum speed limits, coherence and asymmetry, Phys. Rev. A 93 , 052331 (2016 ), Editors’ Suggestion, arXiv:1510.06474.
I. Marvian and D. A. Lidar, Quantum speed limits for leakage and decoherence, Phys. Rev. Lett. 115 , 210402 (2015 ), arXiv:1505.07850 .
P. Coles, V. Katariya, S. Lloyd, I. Marvian, M. Wilde, Entropic Energy-Time Uncertainty Relation, arXiv:1805.07772.
I completed my PhD in Physics in October 2012 at the University of Waterloo and Perimeter Institute for Theoretical Physics in Waterloo, Ontario. My PhD thesis is titled Symmetry, Asymmetry and Quantum Information, and is available here. After PhD, I worked at the University of Southern California (Nov 2012-Aug 2015) and MIT (Sept 2015-Dec 2017) as postdoctoral researcher. I joined Duke university as an assistant professor in January 2018.