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staq– A full-stack quantum processing toolkit

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arXiv 2019年

作者： Gheorghiu, Vlad Amy, Matthew softwareQ Inc. KitchenerON Canada Department of Mathematics & Statistics Dalhousie University HalifaxNS Canada Institute for Quantum Computing University of Waterloo WaterlooON Canada Department of Combinatorics and Optimization University of Waterloo WaterlooON Canada

We describe staq, a full-stack quantum processing toolkit written in standard C++. staq is a quantum compiler toolkit, comprising of tools that range from quantum optimizers and translators to physical mappers for quantum devices with restricted connectives. The design of staq is inspired from the UNIX philosophy of "less is more", i.e. staq achieves complex functionality via combining (piping) small tools, each of which performs a single task using the most advanced current state-of-the-art methods. We also provide a set of illustrative benchmarks. Copyright © 2019, The Authors. All rights reserved.

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Beyond quadratic speedups in quantum attacks on symmetric schemes

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arXiv 2021年

作者： Bonnetain, Xavier Schrottenloher, André Sibleyras, Ferdinand Institute for Quantum Computing Department of Combinatorics and Optimization University of Waterloo WaterlooON Canada Université de Lorraine CNRS Inria Nancy France Cryptology Group CWI Amsterdam Netherlands NTT Social Informatics Laboratories

In this paper, we report the first quantum key-recovery attack on a symmetric block cipher design, using classical queries only, with a more than quadratic time speedup compared to the best classical attack. We study the 2XOR-Cascade construction of Gaži and Tessaro (EUROCRYPT 2012). It is a key length extension technique which provides an n-bit block cipher with 5n/2 bits of security out of an n-bit block cipher with 2n bits of key, with a security proof in the ideal model. We show that the offline-Simon algorithm of Bonnetain et al. (ASIACRYPT 2019) can be extended to, in particular, attack this construction in quantum time Õ(2n), providing a 2.5 quantum speedup over the best classical attack. Regarding post-quantum security of symmetric ciphers, it is commonly assumed that doubling the key sizes is a sufficient precaution. This is because Grover's quantum search algorithm, and its derivatives, can only reach a quadratic speedup at most. Our attack shows that the structure of some symmetric constructions can be exploited to overcome this limit. In particular, the 2XOR-Cascade cannot be used to generically strengthen block ciphers against quantum adversaries, as it would offer only the same security as the block cipher itself. Copyright © 2021, The Authors. All rights reserved.

关键词： quantum cryptography

Synthesizing efficient circuits for Hamiltonian simulation

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arXiv 2022年

作者： Mukhopadhyay, Priyanka Wiebe, Nathan Zhang, Hong Tao Institute for Quantum Computing University of Waterloo Canada Department of Combinatorics and Optimization University of Waterloo Canada Department of Computer Science University of Toronto Canada Pacific Northwest National Laboratory United States Department of Mathematics University of Toronto Canada

We provide a new approach for compiling quantum simulation circuits that appear in Trotter, qDRIFT and multi-product formulas to Clifford and non-Clifford operations that can reduce the number of non-Clifford operations by a factor of up to 4. In fact, the total number of gates reduce in many cases. We show that it is possible to implement an exponentiated sum of commuting Paulis with at most m (controlled)-rotation gates, where m is the number of distinct non-zero eigenvalues (ignoring sign). Thus we can collect mutually commuting Hamiltonian terms into groups that satisfy one of several symmetries identified in this work which allow an inexpensive simulation of the entire group of terms. We further show that the cost can in some cases be reduced by partially allocating Hamiltonian terms to several groups and provide a polynomial time classical algorithm that can greedily allocate the terms to appropriate groupings. We further specifically discuss these optimizations for the case of fermionic dynamics and provide extensive numerical simulations for qDRIFT of our grouping strategy to 6 and 4-qubit Heisenberg models, LiH, H2 and observe a factor of 1.8-3.2 reduction in the number of non-Clifford gates. This suggests Trotter-based simulation of chemistry in second quantization may be even more practical than previously believed. © 2022, CC BY.

关键词： Hamiltonians

Noise and microresonance of critical current in Josephson junction induced by Kondo trap states

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Physical Review B 2011年第23期84卷 235102-235102页

作者： M. H. Ansari F. K. Wilhelm Department of Combinatorics and Optimization and Institute for Quantum Computing University of Waterloo 200 University Ave. W Waterloo ON Canada N2L 3G1 Department of Physics and Astronomy and Institute for Quantum Computing University of Waterloo 200 University Ave. W Waterloo ON Canada N2L 3G1

We analyze the impact of trap states in the oxide layer of a superconducting tunnel junction on the fluctuation of the Josephson critical current, thus on coherence in superconducting qubits. Two mechanisms are usually considered: the current blockage due to repulsion at the occupied trap states and the noise from electrons hopping across a trap. We extend previous studies of noninteracting traps to the case where the traps have onsite electron repulsion inside one ballistic channel. The repulsion not only allows the appropriate temperature dependence of 1/f noise, but also the control of the coupling between the computational qubit and the spurious two-level systems inside the oxide dielectric. We use second-order perturbation theory, which allows to obtain analytical formulas for the interacting bound states and spectral weights, limited to small and intermediate repulsions. Remarkably, it still reproduces the main features of the model as identified from the numerical renormalization group. We present analytical formulations for the subgap bound state energies, the singlet-doublet phase boundary, and the spectral weights. We show that interactions can reverse the supercurrent across the trap. We finally work out the spectrum of junction resonators for qubits in the presence of onsite repulsive electrons and analyze its dependence on microscopic parameters that may be controlled by fabrication.

关键词： OXIDES ELECTRONS NOISE JOSEPHSON junctions JOSEPHSON effect SUPERCONDUCTORS

Achieving Fault Tolerance on Capped Color Codes with Few Ancillas

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PRX quantum 2022年第3期3卷 030322-030322页

作者： Theerapat Tansuwannont Debbie Leung Institute for Quantum Computing and Department of Physics and Astronomy University of Waterloo Waterloo Ontario N2L 3G1 Canada Duke Quantum Center and Department of Electrical and Computer Engineering Duke University Durham North Carolina 27708 USA Institute for Quantum Computing and Department of Combinatorics and Optimization University of Waterloo Waterloo Ontario N2L 3G1 Canada Perimeter Institute for Theoretical Physics Waterloo Ontario N2L 2Y5 Canada

Attaining fault tolerance while maintaining low overhead is one of the main challenges in a practical implementation of quantum circuits. One major technique that can overcome this problem is the flag technique, in which high-weight errors arising from a few faults can be detected by a few ancillas and distinguished using subsequent syndrome measurements. The technique can be further improved using the fact that, for some families of codes, errors of any weight are logically equivalent if they have the same syndrome and weight parity, as shown in our previous work [Tansuwannont and Leung, Phys. Rev. A 104, 042410 (2021)]. In this work, we develop a notion of distinguishable fault set that captures both concepts of flags and weight parities, and extend the use of weight parities in error correction to families of capped and recursive capped color codes. We also develop fault-tolerant protocols for error correction, measurement, state preparation, and logical T-gate implementation via code switching, which are sufficient for performing fault-tolerant Clifford computation on a capped color code, and performing fault-tolerant universal quantum computation on a recursive capped color code. Our protocols for a capped or a recursive capped color code of any distance require only two ancillas, assuming that the ancillas can be reused. The concept of distinguishable fault set also leads to a generalization of the definitions of fault-tolerant gadgets proposed by Aliferis, Gottesman, and Preskill.

关键词： quantum computation quantum error correction

Unconditionally-secure and reusable public-key authentication 1

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6th Conference on the Theory of quantum Computation, Communication, and Cryptography, TQC 2011

作者： Ioannou, Lawrence M. Mosca, Michele Institute for Quantum Computing University of Waterloo 200 University Avenue Waterloo ON N2L 3G1 Canada Department of Combinatorics and Optimization University of Waterloo 200 University Avenue Waterloo ON N2L 3G1 Canada Perimeter Institute for Theoretical Physics 31 Caroline Street North Waterloo ON N2L 2Y5 Canada

We present a quantum-public-key identification protocol and show that it is secure against a computationally-unbounded adversary. This demonstrates for the first time that unconditionally-secure and reusable public-ke... 详细信息

ISBN: (数字)9783642544293

ISBN: (纸本)9783642544286

关键词： Authentication

Limitations of the Macaulay matrix approach for using the HHL algorithm to solve multivariate polynomial systems

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arXiv 2021年

作者： Ding, Jintai Gheorghiu, Vlad Gilyén, András Hallgren, Sean Li, Jianqiang University of Cincinnati OH United States Institute for Quantum Computing Dept. of Combinatorics & Optimization University of Waterloo ON Canada Institute for Quantum Information and Matter Caltech PasadenaCA United States Department of Computer Science and Engineering Pennsylvania State University PA United States

Recently Chen and Gao [CG21] proposed a new quantum algorithm for Boolean polynomial system solving, motivated by the cryptanalysis of some post-quantum cryptosystems. The key idea of their approach is to apply a quantum Linear System (QLS) algorithm to a Macaulay linear system over C, which is derived from the Boolean polynomial system. The efficiency of their algorithm depends on the condition number of the Macaulay matrix. In this paper, we give a strong lower bound on the condition number as a function of the Hamming weight of the Boolean solution, and show that in many (if not all) cases a Grover-based exhaustive search algorithm outperforms their algorithm. Then, we improve upon Chen and Gao’s algorithm by introducing the Boolean Macaulay linear system over C by reducing the original Macaulay linear system. This improved algorithm could potentially significantly outperform the brute-force algorithm, when the Hamming weight of the solution is logarithmic in the number of Boolean variables. © 2021, CC BY.

关键词： Linear systems

A (quasi-)polynomial time heuristic algorithm for synthesizing T-depth optimal circuits

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arXiv 2021年

作者： Gheorghiu, Vlad Mosca, Michele Mukhopadhyay, Priyanka Institute for Quantum Computing University of Waterloo WaterlooON Canada softwareQ Inc. KitchenerON Canada Dept. of Combinatorics and Optimization University of Waterloo WaterlooON Canada Perimeter Institute for Theoretical Physics WaterlooON Canada

We investigate the problem of synthesizing T-depth optimal quantum circuits over the Clifford+T gate set. First we construct a special subset of T-depth 1 unitaries, such that it is possible to express the T-depth-optimal decomposition of any unitary as product of unitaries from this subset and a Clifford (up to global phase). The cardinality of this subset is at most n·25.6n. We use nested meet-in-the-middle (MITM) technique to develop algorithms for synthesizing provably depth-optimal and T-depth-optimal circuits for exactly implementable unitaries. Specifically, for synthesizing T-depth-optimal circuits, we get an algorithm with space and time complexity (Equation presented) and (Equation presented) respectively, where d is the minimum T-depth and c ≥ 2 is a constant. This is much better than the complexity of the algorithm by Amy et al.(2013), the previous best with a complexity (Equation presented), where k > 2.5 is a constant. We design an even more efficient algorithm for synthesizing T-depth-optimal circuits. The claimed efficiency and optimality depends on some conjectures, which have been inspired from the work of Mosca and Mukhopadhyay (2020). To the best of our knowledge, the conjectures are not related to the previous work. Our algorithm has space and time complexity poly(n, 25.6n, d) (or poly(nlog n, 25.6n, d) under some weaker assumptions). © 2021, CC BY-NC-ND.

关键词： Heuristic algorithms

Revivals imply quantum many-body scars

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Physical Review B 2020年第20期101卷 205107-205107页

作者： Álvaro M. Alhambra Anurag Anshu Henrik Wilming Perimeter Institute for Theoretical Physics Waterloo Ontario Canada N2L 2Y5 Institute for Quantum Computing and Department of Combinatorics and Optimization University of Waterloo Waterloo Ontario Canada N2L 3G1 Institute for Theoretical Physics ETH Zurich 8093 Zurich Switzerland

We derive general rigorous results relating revivals in the dynamics of quantum many-body systems to the entanglement properties of energy eigenstates. For a D-dimensional lattice system of N sites initialized in a low-entangled and short-range correlated state, our results show that a perfect revival of the state after a time of at most O(poly(N)) implies the existence of at least O(N/log2D(N)) “quantum many-body scars”: energy eigenstates with energies placed in an equally spaced ladder and with Rényi entanglement entropy of at most O(log(N))+O(|∂A|) for any region A of the lattice. This shows that quantum many-body scars are a necessary consequence of revivals, independent of particularities of the Hamiltonian leading to them. We also present results for approximate revivals and for revivals of expectation values of observables and prove that the duration of revivals of states has to become vanishingly short with increasing system size.

关键词： Eigenstate thermalization quantum entanglement quantum quench quantum statistical mechanics