QuICS Special Seminar

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.

Simulating Fermionic Hamiltonians requires a mapping from fermionic to qubit operators. This mapping must obey the underlying algebra of fermionic operators; in particular, their specific anticommutation relations. The traditional mapping is the Jordan-Wigner encoding, which is simple and qubit minimal, but can incur significant overheads during simulation. This is because the qubit weight of fermionic operators is high, i.e. operators typically must involve many qubits. New mappings address this trade-off and hold other intriguing features.

Decoding algorithms based on approximate tensor network contraction have proven tremendously successful in decoding 2D local quantum codes such as surface/toric codes and color codes, effectively achieving optimal decoding accuracy. We introduce several techniques to generalize tensor network decoding to higher dimensions so that it can be applied to 3D codes as well as 2D codes with noisy syndrome measurements (phenomenological noise or circuit-level noise).

Calibrating and re-calibrating quantum processors to achieve and maintain error rates below fault tolerance thresholds in the presence of drift will be a key engineering challenge in emerging large scale quantum information processing systems. To address this problem, we are adapting a canonical technique in classical electrical and control engineering: combining Kalman filters with linear-quadratic regulators for streaming adaptive control. We start by identifying a gate set error mode for a device.

Learning properties of quantum processes is a fundamental task in physics. It is well known that full process tomography scales exponentially in the number of qubits. In this work, we consider online learning quantum processes in a mistake bounded model and prove exponentially improved bounds compared to the stronger notion of diamond norm learning. The problem can be modelled as an interactive game over any given number of rounds, T, between a learner and an adversary.

In this session, new and current QuICS members will introduce themselves and their research. Organized by Yi-Kai Liu.

Concatenating bosonic error-correcting codes with qubit codes can substantially boost the error-correcting power of the original qubit codes. It is not clear how to concatenate optimally, given that there are several bosonic codes and concatenation schemes to choose from, including the recently discovered Gottesman-Kitaev-Preskill (GKP) – stabilizer codes [Phys. Rev. Lett. 125, 080503 (2020)] that allow protection of a logical bosonic mode from fluctuations of the conjugate variables of the mode.

The noncommutative sum-of-squares (ncSoS) hierarchy was introduced by Navascues--Pironio--Acin as a sequence of semidefinite programming relaxations for approximating values of "noncommutative polynomial optimization problems," which were originally intended to generalize quantum values of nonlocal games. Recent work has started to analyze the hierarchy for approximating ground energies of local Hamiltonians, initially through rounding algorithms which output product states for degree-2 ncSoS.