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In this work, we explore a new approach to designing both algorithms and error detection codes for preparing approximate ground states of molecules. We propose a classical algorithm to find the optimal stabilizer state by using excitations…
In this paper, we develop a quantitative inverse theory for the Gowers uniformity norm $\|\cdot\|_{\mathsf{U}^4}$ in general finite abelian groups. We identify a new type of obstructions to uniformity, which we call almost-cubic…
Consider the task of verifying that a given quantum device, designed to produce a particular entangled state, does indeed produce that state. One natural approach would be to characterise the output state by quantum state tomography; or…
The stability of several clock protocols based on 2 to 20 entangled atoms is evaluated numerically by a simulation that includes the effect of decoherence due to classical oscillator noise. In this context the squeezed states discussed by…
First, a canonical form for stabilizer parity check matrices of arbitrary size and rank is derived. Next, it is shown that the closely related canonical form of the Clifford group can be computed in time $O(n^3)$ for $n$ qubits, which…
Entanglement plays an indispensable role in numerous quantum information and quantum computation tasks, underscoring the need for efficiently verifying entangled states. In recent years, quantum state verification has received increasing…
In this paper we estimate the fidelity of stabilizer and CSS codes. First, we derive a lower bound on the fidelity of a stabilizer code via its quantum enumerator. Next, we find the average quantum enumerators of the ensembles of finite…
We investigate the problem of bounding the quantum process fidelity given bounds on the fidelities between target states and the action of a process on a set of pure input states. We formulate the problem as a semidefinite program and prove…
Bell sampling is a simple yet powerful measurement primitive that has recently attracted a lot of attention, and has proven to be a valuable tool in studying stabiliser states. Unfortunately, however, it is known that Bell sampling fails…
Stabiliser states play a central role in the theory of quantum computation. For example, they are used to encode computational basis states in the most common quantum error correction schemes. Arbitrary quantum states admit many stabiliser…
Conventional fault-tolerant quantum error-correction schemes require a number of extra qubits that grows linearly with the code's maximum stabilizer generator weight. For some common distance-three codes, the recent "flag paradigm" uses…
Stabilizer states constitute a set of pure states which plays a dominant role in quantum error correction, measurement--based quantum computation, and quantum communication. Central in these applications are the local symmetries of these…
We propose a quantum tomography scheme for pure qudit systems which adopts random base measurements and generative learning methods, along with a built-in fidelity estimation approach to assess the reliability of the tomographic states. We…
We study feedback stabilization of continuous-time linear systems under finite data-rate constraints in the presence of unknown disturbances. A communication and control strategy based on sampled and quantized state measurements is…
Typical studies of quantum error correction assume probabilistic Pauli noise, largely because it is relatively easy to analyze and simulate. Consequently, the effective logical noise due to physically realistic coherent errors is relatively…
We establish the \emph{inverse conjecture for the Gowers norm over finite fields}, which asserts (roughly speaking) that if a bounded function $f: V \to \C$ on a finite-dimensional vector space $V$ over a finite field $\F$ has large Gowers…
In this paper, we show that coherence witness for a single qubit itself yields conditions for nonlocality and entanglement inequalities for multiqubit systems. It also yields a condition for quantum discord in two--qubit systems. It is…
The task of state discrimination for a set of mutually orthogonal pure states is trivial if one has access to the corresponding sharp (projection-valued) measurement, but what if we are restricted to an unsharp measurement? Given that any…
In the context of measurement-based quantum computation a way of maintaining the coherence of a graph state is to measure its stabilizer operators. Aside from performing quantum error correction, it is possible to exploit the information…
We derive sampling functions for estimation of quantum state fidelity with Schr\"odinger cat-like states, which are defined as superpositions of two coherent states with opposite amplitudes. We also provide sampling functions for fidelity…