QuICS Special Seminar

In recent years, the use of Gottesman-Kitaev-Preskill (GKP) Codes to  implement fault-tolerant quantum computation has gained significant traction and evidence for their experimental utility has steadily grown.  But what does it even mean for quantum computation with the GKP code to be fault tolerant?  In this talk, we discuss the structure of logical Clifford gates for the GKP code and how their understanding leads to a classification of the space of all GKP Codes.

Reservoir engineering has become valuable for preparing and stabilizing quantum systems. Notably, it has enabled the demonstration of dissipatively stabilized Schrödinger’s cat qubits through engineered two-photon loss which are interesting candidates for bosonic error-corrected quantum computation. Reservoir engineering is however limited to simple operators often derived from weak low-order expansions of some native system Hamiltonians. In this talk, I will introduce a novel reservoir engineering approach for stabilizing multi-component Schrödinger’s cat states.

While the search for quantum advantage typically focuses on speedups in execution time, quantum algorithms also offer the potential for advantage in space complexity. Previous work has shown such advantages for data stream problems, in which elements arrive and must be processed sequentially without random access, but these have been restricted to specially-constructed problems [Le Gall, SPAA `06] or polynomial advantage [Kallaugher, FOCS `21]. We show an exponential quantum space advantage for the maximum directed cut problem.

The approximate stabilizer rank of a quantum state is the minimum number of terms in any approximate decomposition of that state into stabilizer states. We expect that the approximate stabilizer rank of n-th tensor power of the “magic” T state scale exponentially in n, otherwise there is a polynomial time classical algorithm to simulate arbitrary polynomial time quantum computations.  Despite this intuition, several attempts using various techniques could not lead to a better than a linear lower bound on the “exact” rank.

I’ll tell you how quantum spin chains, some of the simplest quantum mechanical systems, encode a number of solutions to problems in representation theory, combinatorics, and algebraic geometry. This is revealed by the quantum integrability of the spin chains and the theory of (quantized) symmetric functions. This suggests a program to uncover the computational complexity of these computational problems, informed by the physics of 1d quantum integrable systems. 

ATL 3100A and Virtual Via Zoom

Abstract: TBA

The standard approach to universal fault-tolerant quantum computing is to develop a general-purpose quantum error correction mechanism that can implement a universal set of logical gates fault-tolerantly. Given such a scheme, any quantum algorithm can be realized fault-tolerantly by composing the relevant logical gates from this set. However, we know that quantum computers provide a significant quantum advantage only for specific quantum algorithms.

The concept of antidistinguishability of quantum states has been studied to investigate foundational questions in quantum mechanics. It is also called quantum state elimination, because the goal of such a protocol is to guess which state, among finitely many chosen at random, the system is not prepared in (that is, it can be thought of as the first step in a process of elimination). Antidistinguishability has been used to investigate the reality of quantum states, ruling out psi-epistemic ontological models of quantum mechanics [Pusey et al., Nat.

In this talk, I will discuss a general formalism for detecting and correcting faults in a Clifford circuit. The scheme is based on the observation that the set of all possible outcome bit-strings of a Clifford circuit is a linear code, which we call the outcome code. From the outcome code we construct a corresponding stabilizer code, the spacetime code. Our construction extends the circuit-to-code construction of Bacon, Flammia, Harrow and Shi, revisited recently by Gottesman.

Demonstrations of quantum advantage for random circuit and boson sampling over the past few years have generated considerable excitement for the future of quantum computing and has further spurred the development of a wide range of gate-based digital quantum computers, which represent quantum programs as a sequence of quantum gates acting on one and two qubits.