# Michał OszmaniecCenter for Theoretical Physics, Polish Academy of Sciences

Michał Oszmaniec

PhD

## About

62

Publications

6,904

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

1,504

Citations

Introduction

Associate professor leading quantum computing group in Center for Theoretical Physics PAS in Warsaw

Additional affiliations

February 2012 - February 2015

## Publications

Publications (62)

We propose a scheme to implement general quantum measurements, also known as Positive Operator Valued Measures (POVMs) in dimension $d$ using only classical resources and a single ancillary qubit. Our method is based on the probabilistic implementation of $d$-outcome measurements which is followed by postselection of some of the received outcomes....

Quantum complexity is a measure of the minimal number of elementary operations required to approximately prepare a given state or unitary channel. Recently, this concept has found applications beyond quantum computing -- in studying the dynamics of quantum many-body systems and the long-time properties of AdS black holes. In this context Brown and...

Estimation of expectation values of incompatible observables is an essential practical task in quantum computing, especially for approximating energies of chemical and other many-body quantum systems. In this work we introduce a method for this purpose based on performing a single joint measurement that can be implemented locally and whose marginal...

We investigate circuit complexity of unitaries generated by time evolution of randomly chosen strongly interacting Hamiltonians in finite dimensional Hilbert spaces. Specifically, we focus on two ensembles of random generators -- the so called Gaussian Unitary Ensemble (GUE) and the ensemble of diagonal Gaussian matrices conjugated by Haar random u...

We present a classical algorithm for simulating universal quantum circuits composed of "free" nearest-neighbour matchgates or equivalently fermionic-linear-optical (FLO) gates, and "resourceful" non-Gaussian gates. We achieve the promotion of the efficiently simulable FLO subtheory to universal quantum computation by gadgetizing controlled phase ga...

Boson sampling (BS) is viewed to be an accessible quantum computing paradigm to demonstrate computational advantage compared to classical computers. In this context, the evolution of permanent calculation algorithms attracts a significant attention as the simulation of BS experiments involves the evaluation of vast number of permanents. For this re...

The geometrical arrangement of a set of quantum states can be completely characterized using relational information only. This information is encoded in the pairwise state overlaps, as well as in Bargmann invariants of higher degree written as traces of products of density matrices. We describe how to measure Bargmann invariants using suitable gene...

We introduce distance measures between quantum states, measurements, and channels based on their statistical distinguishability in generic experiments. Specifically, we analyze the average Total Variation Distance (TVD) between output statistics of protocols in which quantum objects are intertwined with random circuits and measured in standard basi...

In this work, we present an in-depth study of average-case quantum distances introduced in Maciejewski et al. (2022). The average-case distances approximate, up to the relative error, the average Total-Variation (TV) distance between measurement outputs of two quantum processes, in which quantum objects of interest (states, measurements, or channel...

Quantum error mitigation allows to reduce the impact of noise on quantum algorithms. Yet, it is not scalable as it requires resources scaling exponentially with the circuit size. In this work, we consider biased-noise qubits affected only by bit-flip errors, which is motivated by existing systems of stabilized cat qubits. This property allows us to...

Estimation of expectation values of incompatible observables is an essential practical task in quantum computing, especially for approximating energies of chemical and other many-body quantum systems. In this Letter, we introduce a method for this purpose based on performing a single joint measurement that can be implemented locally and whose margi...

We propose a scheme to implement general quantum measurements, also known as Positive Operator Valued Measures (POVMs) in dimension d using only classical resources and a single ancillary qubit. Our method is based on probabilistic implementation of d-outcome measurements which is followed by postselection of some of the received outcomes. We conje...

Fermionic linear optics (FLO) is a restricted model of quantum computation, which in its original form is known to be efficiently classically simulable. We show that, when initialized with suitable input states, FLO circuits can be used to demonstrate quantum computational advantage with strong hardness guarantees. Based on this, we propose a quant...

In this work, we perform an in-depth study of recently introduced average-case quantum distances. The average-case distances approximate the average Total-Variation (TV) distance between measurement outputs of two quantum processes, in which quantum objects of interest (states, measurements, or channels) are intertwined with random circuits. Contra...

We introduce operational distance measures between quantum states, measurements, and channels based on their average-case distinguishability. To this end, we analyze the average Total Variation Distance (TVD) between statistics of quantum protocols in which quantum objects are intertwined with random circuits and subsequently measured in the comput...

Epsilon-nets and approximate unitary t-designs are natural notions that capture properties of unitary operations relevant for numerous applications in quantum information and quantum computing. In this work we study quantitative connections between these two notions. Specifically, we prove that, for d dimensional Hilbert space, unitaries constituti...

The geometrical arrangement of a set of quantum states can be completely characterized using relational information only. This information is encoded in the pairwise state overlaps, as well as in Bargmann invariants of higher degree written as traces of products of density matrices. We describe how to measure Bargmann invariants using suitable gene...

Measurement noise is one of the main sources of errors in currently available quantum devices based on superconducting qubits. At the same time, the complexity of its characterization and mitigation often exhibits exponential scaling with the system size. In this work, we introduce a correlated measurement noise model that can be efficiently descri...

We consider the problem of certification of arbitrary ensembles of pure states and projective measurements solely from the experimental statistics in the prepare-and-measure scenario assuming the upper bound on the dimension of the Hilbert space. To this aim, we propose a universal and intuitive scheme based on establishing perfect correlations bet...

We present an in-depth study of the problem of multiple-shot discrimination of von Neumann measurements in finite-dimensional Hilbert spaces. Specifically, we consider two scenarios: minimum error and unambiguous discrimination. In the case of minimum error discrimination, we focus on discrimination of measurements with the assistance of entangleme...

Measurement noise is one of the main sources of errors in currently available quantum devices based on superconducting qubits. At the same time, the complexity of its characterization and mitigation often exhibits exponential scaling with the system size. In this work, we introduce a correlated measurement noise model that can be efficiently descri...

Fermionic Linear Optics (FLO) is a restricted model of quantum computation which in its original form is known to be efficiently classically simulable. We show that, when initialized with suitable input states, FLO circuits can be used to demonstrate quantum computational advantage with strong hardness guarantees. Based on this, we propose a quantu...

Epsilon-nets and approximate unitary $t$-designs are natural notions that capture properties of unitary operations relevant for numerous applications in quantum information and quantum computing. The former constitute subsets of unitary channels that are epsilon-close to any unitary channel. The latter are ensembles of unitaries that (approximately...

We present a comprehensive study of the impact of non-uniform, i.e. path-dependent, photonic losses on the computational complexity of linear-optical processes. Our main result states that, if each beam splitter in a network induces some loss probability, non-uniform network designs cannot circumvent the efficient classical simulations based on los...

The so-called preparation uncertainty that occurs in the quantum world can be understood well in purely operational terms, and its existence in any given theory, perhaps differently than in quantum mechanics, can be verified by examining only measurement statistics. Namely, one says that uncertainty occurs in some theory when for some pair of obser...

We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies on performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction of a Positive-Operator Valued Measure (POVM) describing the given quantum measurement d...

We consider the problem of certification of arbitrary ensembles of pure states and projective measurements solely form the experimental statistics in the prepare-and-measure scenario assuming the upper bound on the dimension of the Hilbert space. To this aim we propose a universal and intuitive scheme based on establishing perfect correlations betw...

We present new results concerning simulation of general quantum measurements (POVMs) by projective measurements (PMs) for the task of Unambiguous State Discrimination (USD). We formulate a problem of finding optimal strategy of simulation for given quantum measurement. The problem can be solved for qubit and qutrits measurements by Semi-Definite Pr...

We report an alternative scheme for implementing generalized quantum measurements that does not require the usage of an auxiliary system. Our method utilizes solely (a) classical randomness and postprocessing, (b) projective measurements on a relevant quantum system, and (c) postselection on nonobserving certain outcomes. The scheme implements arbi...

We propose a simple scheme to reduce readout errors in experiments on quantum systems with finite number of measurement outcomes. Our method relies on performing classical post-processing which is preceded by Quantum Detector Tomography, i.e., the reconstruction of a Positive-Operator Valued Measure (POVM) describing the given quantum measurement d...

We present a comprehensive study of the impact of non-uniform, i.e.\ path-dependent, photonic losses on the computational complexity of linear-optical processes. Our main result states that, if each beam splitter in a network induces some loss probability, non-uniform network designs cannot circumvent the efficient classical simulations based on lo...

For any resource theory it is essential to identify tasks for which resource objects offer advantage over free objects. We show that this identification can always be accomplished for resource theories of quantum measurements in which free objects form a convex subset of measurements on a given Hilbert space. To this aim we prove that every resourc...

For any resource theory it is essential to identify tasks for which resource objects offer advantage over free objects. We show that this identification can always be accomplished for resource theories of quantum measurements in which free objects form a convex subset of measurements on a given Hilbert space. To this aim we prove that every resourc...

We present an in-depth study of the problem of discrimination of von Neumann measurements in finite-dimensional Hilbert spaces. Specifically, we consider two scenarios: unambiguous and multiple-shot discrimination. In the first scenario we give the general expressions for the optimal discrimination probabilities with and without the assistance of e...

The so-called preparation uncertainty can be understood in purely operational terms. Namely, it occurs when for some pair of observables, there is no preparation, for which thier both exhibit deterministic statistics. However, the right-hand side of uncertainty relation is generally not operational as it depends on the quantum formalism. Also, whil...

We explore the possibility of efficient classical simulation of linear optics experiments under the effect of particle losses. Specifically, we investigate the canonical boson sampling scenario in which an $n$-particle Fock input state propagates through a linear-optical network and is subsequently measured by particle-number detectors in the $m$ o...

Implementation of generalized quantum measurements is often experimentally demanding, as it requires performing a projective measurement on a system of interest extended by the ancilla. We report an alternative scheme for implementing generalized measurements that uses solely: (a) classical randomness and post-processing, (b) projective measurement...

Implementation of generalized quantum measurements is often experimentally demanding, as it requires performing a projective measurement on a system of interest extended by the ancilla. We report an alternative scheme for implementing generalized measurements that uses solely: (a) classical randomness and post-processing, (b) projective measurement...

We explore the possibility of efficient classical simulation of linear optics experiments under the effect of particle losses. Specifically, we investigate the canonical boson sampling scenario in which an n-particle Fock input state propagates through a linear-optical network and is subsequently measured by particle-number detectors in the m outpu...

For numerous applications of quantum theory it is desirable to be able to apply arbitrary unitary operations on a given quantum system. However, in particular situations only a subset of unitary operations is easily accessible. This raises the question of what additional unitary gates should be added to a given gate-set in order to attain physical...

Standard projective measurements represent a subset of all possible measurements in quantum physics. In fact, non-projective measurements are relevant for many applications, e.g. for estimation problems or transformations among entangled states. In this work we study what quantum measurements can be simulated by using only projective measurements a...

We develop a general theory to estimate magnetic field gradients in quantum metrology. We consider a system of N particles distributed on a line whose internal degrees of freedom interact with a magnetic field. Classically, gradient estimation is based on precise measurements of the magnetic field at two different locations, performed with two inde...

We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite number of energy levels, classification problems are usually treated in frames of linear algebra. We proposed...

We show that, in contrast to ones of distinguishable particles, random bosonic states of any purity typically achieve the Heisenberg scaling in lossy phase sensing. A photon-counting measurement then does the job, while the desired states can be simulated with help of short random optical circuits.

We study how useful random states are for quantum metrology, i.e., whether they surpass the classical limits imposed on precision in the canonical phase estimation scenario. First, we prove that random pure states drawn from the Hilbert space of distinguishable particles typically do not lead to super-classical scaling of precision even when allowi...

The superposition principle is one of the landmarks of quantum mechanics. The importance of
quantum superpositions provokes questions about the limitations that quantum mechanics itself
imposes on the possibility of their generation. In this work we systematically study the problem
of creation of superpositions of unknown quantum states. First, we...

The superposition principle is one of the landmarks of quantum mechanics. The
importance of quantum superpositions provokes questions about the limitations
that quantum mechanics itself imposes on the possibility of their generation.
In this work we systematically study the problem of creation of superpositions
of unknown quantum states. First, we...

One of the most important questions in quantum information theory is the
so-called separability problem. It involves characterizing the set of separable
(or, equivalently entangled) states among mixed states of a multipartite
quantum system. In this thesis we study the generalization of this problem to
types of quantum correlations that are defined...

Fermionic linear optics is a model of quantum computation which is
efficiently simulable on a classical probabilistic computer. We study the
problem of a classical simulation of fermionic linear optics augmented with
noisy auxiliary states. If the auxiliary state can be expressed as a convex
combination of pure Fermionic Gaussian states, the corres...

In any theory satisfying the no-signalling principle correlations generated
among spatially separated parties in a Bell-type experiment are subject to
certain constraints known as monogamy relations. Violation of such a relation
implies that correlations arising in the experiment must be signalling, and, as
such, they can be used to send classical...

For several types of correlations: mixed-state entanglement in systems of
distinguishable particles, particle entanglement in systems of
indistinguishable bosons and fermions and non-Gaussian correlations in
fermionic systems we estimate the fraction of non-correlated states among the
density matrices with the same spectra. We prove that for the pu...

We analyze form the topological perspective the space of all SLOCC
(Stochastic Local Operations with Classical Communication) classes of pure
states for composite quantum systems. We do it for both distinguishable and
indistinguishable particles. In general, the topology of this space is rather
complicated as it is a non-Hausdorff space. Using geom...

We investigate which pure states of $n$ photons in $d$ modes can be
transformed into each other via linear optics, without post-selection. In other
words, we study the local unitary (LU) equivalence classes of symmetric
many-qudit states. Writing our state as $f^\dagger|\Omega\rangle$, with
$f^\dagger$ a homogeneous polynomial in the mode creation...

We construct nonlinear multiparty entanglement measures for distinguishable
particles, bosons and fermions. In each case properties of an entanglement
measures are related to the decomposition of the suitably chosen representation
of the relevant symmetry group onto irreducible components. In the case of
distinguishable particles considered entangl...

Given L-qubit states with the fixed spectra of reduced one-qubit density
matrices, we find a formula for the minimal number of invariant polynomials
needed for solving local unitary (LU) equivalence problem, that is, problem of
deciding if two states can be connected by local unitary operations.
Interestingly, this number is not the same for every...

We show that multipartite mixed bipartite CC and CQ states are geometrically
and topologically distinguished in the space of states. They are characterized
by non-vanishing Euler-Poincar\'{e} characteristics on the topological side and
by the existence of symplectic and K\"{a}hler structures on the geometric side

We present a general algorithm for finding all classes of pure multiparticle states equivalent under stochastic local operations and classical communication (SLOCC). We parametrize all SLOCC classes by the critical sets of the total variance function. Our method works for arbitrary systems of distinguishable and indistinguishable particles. We also...

We give a criterion of classicality for mixed states in terms of expectation
values of a quantum observable. Using group representation theory we identify
all cases when the criterion can be computed exactly in terms of the spectrum
of a single operator.

A simple method for presenting a dynamic transition between Fresnel and Fraunhofer diffraction zones is considered. Experiments are conducted on different apertures and diffraction patterns are photographed at various distances between the screen and the aperture. A diverging lens is introduced into the experimental setup to provide enlarged Fresne...