Related papers: The Quantum Supremacy Tsirelson Inequality
Gaussian Process Regression is a well-known machine learning technique for which several quantum algorithms have been proposed. We show here that in a wide range of scenarios these algorithms show no exponential speedup. We achieve this by…
Matrix scaling is a simple to state, yet widely applicable linear-algebraic problem: the goal is to scale the rows and columns of a given non-negative matrix such that the rescaled matrix has prescribed row and column sums. Motivated by…
We introduce $\varepsilon$-projectors, using which we can sample from limiting distributions of continuous-time quantum walks. The standard algorithm for sampling from a distribution that is close to the limiting distribution of a given…
Many quantum algorithms can be analyzed in a query model to compute Boolean functions where input is given by a black box. As in the classical version of decision trees, different kinds of quantum query algorithms are possible: exact,…
Characterization of experimental systems is an essential step in developing and improving quantum hardware. A collection of protocols known as Randomized Benchmarking (RB) was developed in the past decade, which provides an efficient way to…
Quantum theory is in principle compatible with processes that violate causal inequalities, an analogue of Bell inequalities that constrain the correlations observed by sets of parties operating in a definite causal order. Since the…
We consider a model of quantum computation we call "Varying-$Z$" (V$Z$), defined by applying controllable $Z$-diagonal Hamiltonians in the presence of a uniform and constant external $X$-field, and prove that it is universal, even in 1D.…
Randomized benchmarking (RB) is the gold standard for experimentally evaluating the quality of quantum operations. The current framework for RB is centered on groups and their representations, but this can be problematic. For example,…
One-parameter interpolations between any two unitary matrices (e.g., quantum gates) $U_1$ and $U_2$ along efficient paths contained in the unitary group are constructed. Motivated by applications, we propose the continuous unitary path…
The strength of quantum correlations is bounded from above by Tsirelson's bound. We establish a connection between this bound and the fact that correlations between two systems cannot increase under local operations, a property known as the…
We define a formal framework for equivalence checking of sequential quantum circuits. The model we adopt is a quantum state machine, which is a natural quantum generalisation of Mealy machines. A major difficulty in checking quantum…
Near term quantum computers with a high quantity (around 50) and quality (around 0.995 fidelity for two-qubit gates) of qubits will approximately sample from certain probability distributions beyond the capabilities of known classical…
In this paper we construct quantum algorithms for matrix products over several algebraic structures called semirings, including the (max,min)-matrix product, the distance matrix product and the Boolean matrix product. In particular, we…
To witness quantum advantages in practical settings, substantial efforts are required not only at the hardware level but also on theoretical research to reduce the computational cost of a given protocol. Quantum computation has the…
Sampling from the output distributions of quantum computations comprising only commuting gates, known as instantaneous quantum polynomial (IQP) computations, is believed to be intractable for classical computers, and hence this task has…
The first achievement of quantum supremacy has been claimed recently by Google for the random quantum circuit benchmark with 53 superconducting qubits. Here, we analyze the randomness of Google's quantum random-bit sampling. The heat maps…
In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum…
We generalize quantum-classical PCPs, first introduced by Weggemans, Folkertsma and Cade (TQC 2024), to allow for $q$ quantum queries to a polynomially-sized classical proof ($\mathsf{QCPCP}_{Q,c,s}[q]$). Exploiting a connection with the…
We give a classical analogue to Kerenidis and Prakash's quantum recommendation system, previously believed to be one of the strongest candidates for provably exponential speedups in quantum machine learning. Our main result is an algorithm…
We present a quasipolynomial-time algorithm for solving the weak membership problem for the convex set of separable, i.e. non-entangled, bipartite density matrices. The algorithm decides whether a density matrix is separable or whether it…