QuICS Special Seminar

Error-correction is key to building a quantum computer. This includes both storage of quantum information as well as computing on it. Quantum low- density parity check (LDPC) codes offer a route to build these devices with low space overhead. The next question is - how do we fault-tolerantly com- pute on these codes?  Existing proposals (Cohen et al. [2110.10794], Cross et al. [2407.18393]) rely on ancilla systems appended to the original LDPC code.

Between NISQ (noisy intermediate scale quantum) approaches without any proof of robust quantum advantage and fully fault-tolerant quantum computation, we propose a scheme to achieve a provable superpolynomial quantum advantage (under some widely accepted complexity conjectures) that is robust to noise with minimal error correction requirements. We choose a class of sampling problems with commuting gates known as sparse IQP (Instantaneous Quantum Polynomial-time) circuits and we ensure its fault-tolerant implementation by introducing the tetrahelix code.

Permutation-invariant quantum error correction codes that are invariant under any permutation of the underlying particles. These codes could have potential applications in quantum sensors and quantum memories. Here I will review the field of permutation-invariant codes, from code constructions to applications.

*We strongly encourage attendees to use their full name (and if possible, their UMD credentials) to join the zoom session.*

We present a new method for analyzing and identifying errors in quantum circuits. In our approach, we define the problem using a triple {P}C{Q}, where the task is to determine whether a given set P of quantum states at the input of a circuit C produces a set of quantum states at the output that is equal to, or included in, a set Q. We propose a technique that utilizes tree automata to represent sets of quantum states efficiently, and we develop algorithms to apply the operations of quantum gates within this representation.

Aaronson, Atia, and Susskind established that swapping quantum states |ψ〉 and |ϕ〉 is computationally equivalent to distinguishing their superpositions |ψ〉 ± |ϕ〉. We extend this to a general duality principle: manipulating quantum states in one basis is equivalent to extracting values in a complementary basis. Formally, for any group, implementing a unitary representation is computationally equivalent to Fourier subspace extraction from its irreducible representations.

There has been interest in the dynamics of noninteracting bosons because of the boson sampling problem. These dynamics can be difficult to predict because of the complicated interference patterns that arise due to their indistinguishability. However, if there are unobserved, hidden degrees of freedom, the indistinguishability can be disrupted in the observations. The generalized bunching probability is defined to be the probability that noninteracting bosons undergo linear optical evolution and all arrive in a subset of sites.

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.