Tufts Quantum Computing Seminar

Jan 10, 2025

Title:  From Hadrons to Nuclei with first principles: Where will we gain quantum advantage?

Speaker: James Vary, Iowa State University

Jan 16, 2025

Title:  Experimental estimation of ground state energies on quantum computers, Part II

Speaker: Will Kirby, IBM

Abstract: I will discuss results of two recent large-scale experiments performed on superconducting quantum processors, implementing quantum algorithms for estimating ground state energies. The first algorithm, called sampled-based quantum diagonalization, is adapted to Hamiltonians where the number of terms makes expectation value estimation impractical, but where sparse proxies for ground states can be prepared using a quantum circuit. The second algorithm, called Krylov quantum diagonalization, is adapted to Hamiltonians where approximate time-evolutions can be implemented using low-depth circuits. These form complementary approaches to the problem of ground state energy estimation on noisy quantum processors.

Jan 23, 2025

Title: Slow Mixing of Quantum Gibbs Samplers

Speaker: Bobak Kiani, Harvard Univeristy

Abstract: Preparing thermal (Gibbs) states is a common task in physics and computer science. The mixing time denotes the time needed for a Gibbs sampler to approximate a target Gibbs state. Lower bounding the mixing time in quantum systems is more challenging than in classical systems due to the lack of established tools. We present a method based on a quantum bottleneck lemma that generalizes classical techniques, focusing on quantum analogs of distance, such as Bohr spectrum jumps and operator locality. Using this lemma, we establish exponential lower bounds on mixing times for Gibbs samplers across several Hamiltonian families. Examples include random K-SAT, spin glasses, stabilizer codes, and models with transverse fields, such as the ferromagnetic 2D transverse field Ising model.

Jan 30, 2025

Title: Advancing Practical Quantum Computing Through Hardware and Algorithm Synergies

Speaker: Daiwei Zhu, IonQ

Abstract: Quantum computing is poised to revolutionize both academia and industry in the near future. With recent breakthroughs accelerating progress, a pressing question emerges: what quantum algorithms can be practically implemented on next-generation quantum hardware to outperform classical solutions? Addressing this challenge requires advancements in both hardware and algorithms. This talk explores these dual fronts, providing an accessible introduction to ion-trap quantum computing—one of the most promising hardware platforms—and highlighting recent algorithms that show potential on near-term quantum devices.

Feb 6, 2025

Title: Two principle-based formulations of quantum theory

Speaker: Howard Barnum, UNM

Abstract: I'll give characterizations of finite-dimensional quantum theory's framework of density matrices (states) and POVM elements (measurement outcomes) for describing systems, from simple postulates whose physical and informational meaning and appeal is clear.  Each first characterizes a class of Euclidean Jordan-algebraic (EJA) systems.  This is already only a slightly larger class than the usual quantum theory: real, complex, and quaternionic quantum theory, systems whose state spaces are balls, and 3-dimensional octonionic quantum theory. Complex quantum theory then follows from "local tomography", or    "energy observability": the generators of continuous symmetries of the state space (potential reversible dynamics) are observables. The first characterization (with Cozmin Ududec and John van de Wetering) uses: (1) Homogeneity: any strictly positive element of the cone of unnormalized states may be taken to any other by a symmetry of this cone, (2) Pure Transitivity: any pure state may be taken to any other pure state by a symmetry of the normalized state space. Time permitting, I'll discuss a second characterization (with Joachim Hilgert), using: (1) Spectrality: every state is a convex combination of perfectly distinguishable pure states, (2) Strong Symmetry: every set of perfectly distinguishable pure states may be taken to any other such set (of the same size) by a symmetry of the state space. The physical, informational, and operational significance of the postulates will be discussed.

Feb 20, 2025

Title: Can effective descriptions of bosonic systems be considered complete?

Speaker: Ulysse Chabaud, École Normale Supérieure de Paris

Abstract: Bosonic statistics give rise to remarkable phenomena, from the Hong–Ou–Mandel effect to Bose–Einstein condensation, with applications spanning fundamental science to quantum technologies. Modeling bosonic systems relies heavily on effective descriptions: typical examples include truncating their infinite-dimensional state space and restricting their dynamics to a simple class of Hamiltonians, such as polynomials of canonical operators, which are used to define quantum computing over bosonic modes. However, many natural bosonic Hamiltonians do not belong to this simple class, and some quantum effects harnessed by bosonic computers inherently require infinite-dimensional spaces, questioning the validity of such effective descriptions of bosonic systems. How can we trust results obtained with such simplifying assumptions to capture real effects?Driven by the increasing importance of bosonic systems for quantum technologies, we solve this outstanding problem by showing that these effective descriptions do in fact capture the relevant physics of bosonic systems. Our technical contribution is twofold: firstly, we prove that any physical, bosonic unitary evolution can be strongly approximated by a finite-dimensional unitary evolution; secondly, we show that any finite-dimensional unitary evolution can be generated exactly by a bosonic Hamiltonian that is a polynomial of canonical operators. Beyond their fundamental significance, our results have implications for classical and quantum simulations of bosonic systems, they provide universal methods for engineering bosonic quantum states and Hamiltonians, they show that polynomial Hamiltonians do generate universal gate sets for quantum computing over bosonic modes, and they lead to an infinite-dimensional Solovay–Kitaev theorem.

Feb 27,2025

Title: Quantum Simulation of QCD Jets

Speaker: Wenyang Qian, Instituto Galego de Física de Altas Enerxías

Abstract: Quark and gluon jets provide one of the best ways to probe the matter produced in ultrarelativistic high-energy collisions, from cold nuclear matter to the hot quark-gluon plasma. We propose a unified quantum simulation framework to simulate the dynamics of multiple particles using the (3+1)-dimensional QCD Hamiltonian on the light front, particularly suited for studies involving quark and gluon jets scattered on nuclear matter in heavy-ion collisions. We describe scalable methods for mapping physical degrees of freedom onto qubits and for simulating in-medium jet evolution. We test our framework on quantum simulators by implementing an algorithm that directly maps second-quantized Fock states onto qubits and uses Trotterized simulation for time evolution. This allows us to study the evolution of quark and gluon jets up to three gluons in a Fock state, and investigate key observables such as jet momentum broadening, particle production, and parton distribution functions.

Mar 6, 2025

Title: On the average-case hardness of BosonSampling

Speaker: Shaun Datta, Stanford Univerisity

Abstract: BosonSampling is a popular candidate for near-term quantum advantage, which has now been experimentally implemented several times.  The original proposal of Aaronson and Arkhipov from 2011 showed that classical hardness of BosonSampling is implied by a proof of the ``Gaussian Permanent Estimation'' conjecture.  This conjecture states that $e^{-n\log{n}-n-O(\log n)}$ additive error estimates to the output probability of most random BosonSampling experiments are \textsf{\#P}-hard.  Proving this conjecture has since become the central question in the theory of quantum advantage. In this work we make progress by proving that $e^{-n\log n -n - O(n^\delta)}$ additive error estimates to output probabilities of most random BosonSampling experiments are \textsf{\#P}-hard, for any $\delta>0$.  In the process, we circumvent all known barrier results for proving the hardness of BosonSampling experiments.  This is nearly the robustness needed to prove hardness of BosonSampling---the remaining hurdle is now ``merely'' to show  that the $n^\delta$ in the exponent can be improved to $O(\log n).$ We also obtain an analogous result for Random Circuit Sampling. Our result allows us to show, for the first time, a hardness of classical \emph{sampling} result for random BosonSampling experiments, under an anticoncentration conjecture.  Specifically, we prove the impossibility of multiplicative-error sampling from random BosonSampling experiments with probability $1-e^{-O(n)}$, unless the Polynomial Hierarchy collapses.

Mar 13, 2025

Title: Studying fermions to understand simulability of quantum circuits

Speaker: Andrew Projansky, Dartmouth college

Abstract: A central issue in quantum information theory is to better understand the border between quantum and classical. In an age in which our quantum computers are both noisy and costly, it is important to know when classical simulation methods may suffice for problems of interest. By studying circuits motivated by fermionic systems, we can understand the quantum/classical border better than ever before. In this talk I will discuss the theory behind matchgates, fermionic encodings, and recent results in the simulability of Clifford/matchgate hybrid circuits (arxiv:2312.08447, arxiv:2410.10068). This discussion will take us to the edge of simulable quantum circuits, providing a framework for understanding Clifford and matchgate circuits in tandem while highlighting the relation of fermionic encodings to quantum complexity.

Mar 27, 2025

Title: Quantum fault tolerance with constant-space and logarithmic-time overheads

Speaker: Quynh Nguyen, Harvard University

Abstract: In a model of fault-tolerant quantum computation with quick and noiseless polyloglog-time auxiliary classical computation, we construct a fault tolerance protocol with constant-space and O˜(logN)-time overhead, where O˜(⋅) hides sub-polylog factors. Our construction utilizes constant-rate quantum locally testable codes (qLTC), new fault-tolerant gadgets on qLTCs and qLDPC codes, and a new analysis framework. In particular, 1) we develop a new magic state distillation scheme with (log 1/ε)^γ spacetime overhead, where γ→0. 2) We prove that the recent family of almost-good qLTCs of Dinur-Lin-Vidick admit parallel single-shot decoders. 3) We develop logical state preparation and logical gate procedures with O˜(1)-spacetime overhead on qLTCs. Our work gives the lowest spacetime overhead to date, which, for the first time, matches that of classical fault tolerance up to sub-polylog factors. We conjecture this is optimal up to sub-polylog factors. Based on join work (https://arxiv.org/abs/2411.03632) with Chris Pattison.

April 3, 2025

Title: Decoded Quantum Interferometry: An algebraic perspective

Speaker: Alexander Schmidhuber, MIT

Abstract: I will explain Decoded Quantum Interferometry (DQI) using an algebraic perspective based on elementary symmetric polynomials. DQI uses the quantum Fourier transform to reduce optimization problems to decoding problems. For approximating optimal polynomial fits to data over finite fields, DQI efficiently achieves a better approximation ratio than any polynomial time classical algorithm known to us, thus suggesting exponential quantum speedup. Sparse unstructured optimization problems such as max-k-XORSAT are reduced to decoding of LDPC codes. We prove a theorem which allows the performance of DQI to be calculated instance-by-instance based on the empirical performance of classical LDPC decoders such as belief propagation. We demonstrate this by benchmarking on an instance with over 30,000 variables.

Joint work with Stephen Jordan, Noah Shutty, Mary Wootters, Adam Zalcman, Robbie King, Sergei Isakov and Ryan Babbush.  

April 10, 2025

Title: Decoded Quantum Interferometry: A new approach to quantum optimization

Speaker: Stephen Jordan, Google

Abstract: Whether quantum computers can achieve exponential speedups in optimization has been a major open question in quantum algorithms since the field began. I will describe a new quantum algorithm called Decoded Quantum Interferometry (DQI), which uses the quantum Fourier transform to reduce optimization problems to decoding problems. For approximating optimal polynomial fits to data over finite fields, DQI efficiently achieves a better approximation ratio than any polynomial-time classical algorithm that we are aware of, thus suggesting exponential quantum speedup. DQI can also be applied to sparse unstructured optimization problems such as max-k-XORSAT. Answering whether DQI can achieve quantum advantage on these unstructured problems is an open question but can be addressed numerically, even for large optimization problems with tens of thousands of variables. This is joint work with Noah Shutty, Mary Wootters, Adam Zalcman, Alexander Schmidhuber, Robbie King, Sergei V. Isakov, and Ryan Babbush. I will aim for this talk to be broadly accessible and will not assume prior knowledge in optimization or decoding.

April 17, 2025

Title: Learning arbitrary quantum interactions with Heisenberg-limited scaling

Speaker: Hongye Hu, Harvard

Abstract:  Learning the unknown interactions that govern a quantum system is crucial for quantum information processing, device benchmarking, and quantum sensing. The problem, known as Hamiltonian learning, is well understood under the assumption that interactions are local, but this assumption may not hold for arbitrary Hamiltonians. Previous methods all require high-order inverse polynomial dependency with precision, unable to surpass the standard quantum limit and reach the gold standard Heisenberg-limited scaling. Whether Heisenberg-limited Hamiltonian learning is possible without prior assumptions about the interaction structures, a challenge we term ansatz-free Hamiltonian learning, remains an open question. In this work, we present a quantum algorithm to learn arbitrary sparse Hamiltonians without any structure constraints using only black-box queries of the system's real-time evolution and minimal digital controls to attain Heisenberg-limited scaling in estimation error. Our method is also resilient to state-preparation-and-measurement errors, enhancing its practical feasibility. Moreover, we establish a fundamental trade-off between total evolution time and quantum control on learning arbitrary interactions, revealing the intrinsic interplay between controllability and total evolution time complexity for any learning algorithm. These results pave the way for further exploration into Heisenberg-limited Hamiltonian learning in complex quantum systems under minimal assumptions, potentially enabling new benchmarking and verification protocols.

April 24, 2025

Title: Characterizing quantum state-space with a single quantum measurement

Speaker: Matt Weiss , UMB

Abstract: Can the state-space of d-dimensional quantum theory be derived from studying the behavior of a single "reference" measuring device? The answer is yes, if the measuring device corresponds to a complex-projective 3-design. In this privileged case, not only does each quantum state correspond to a probability-distribution over the outcomes of a single measurement, but also the probability-distributions which correspond to quantum states can be elegantly characterized as those which respect a generalized uncertainty principle. The latter takes the form of a lower-bound on the variance of a natural class of observables as measured by the reference. We give simple equations which pure-state probability distributions must satisfy, and contextualize these results by showing how 3-designs allow the structure-coefficients of the Jordan algebra of observables to be extracted from the probabilities which characterize the reference measurement itself. This lends credence to the view that quantum theory ought to be primarily understood as a set of normative constraints on probability assignments which reflect nature's lack of hidden variables, and further cements the significance of 3-designs in quantum information science.

May 1, 2025

Title: Evaluating Quantum Computing Technologies at Apollo Quantum

Speaker: Peter Johnson and Max Radin, Apollo Quantum

Abstract: Imagine that an unexpected quantum hardware breakthrough produced a million high-quality qubits in the near future. Would we be ready? We started Apollo Quantum to help government and industry become ready for the future by providing unbiased evaluation of quantum technologies. In this talk, we’ll share how our team, after six years at Zapata AI and deep involvement in DARPA’s Quantum Benchmarking program, came to focus on estimating full-stack quantum resource requirements. We’ll outline our methodology for assessing the utility and cost of quantum applications and discuss how this work supports broader efforts to guide quantum development toward practical, utility-scale computing.

May 8, 2025

Title: Unitary Matrix Synthesis using AI

Speaker: Gianni De Fabritiis, ICREA

Abstract: Unitary matrix synthesis is the process of decomposing a unitary operator into a sequence of quantum gates drawn from a specified gate set. This decomposition is a critical component of the quantum compilation stack, particularly in the context of achieving fault-tolerant quantum computation. Owing to the exponential growth of the search space with the number of qubits, developing synthesis methods that are accurate, efficient, and scalable remains a significant challenge. In response, recent research has begun exploring the use of artificial intelligence techniques to support this task. 

May 15, 2025

Title: Learning shallow quantum circuits and quantum states prepared by shallow circuits in polynomial time

Speaker: Yunchao Liu, Harvard University

Abstract:  In this talk we give polynomial time algorithms for the following two problems: (1) Given access to an unknown constant depth quantum circuit U on a finite-dimensional lattice, learn a constant depth circuit that approximates U to small diamond distance. (2) Given copies of an unknown quantum state |ψ>=U|0^n> that is prepared by an unknown constant depth circuit U on a finite-dimensional lattice, learn a constant depth circuit that prepares |ψ>. These algorithms extend to the case when the depth of U is polylog(n) with a quasi-polynomial run-time. The key techniques are simple and efficient procedures that reconstruct a quantum many-body system of low circuit complexity from its local observables. The goal of this talk is to present simple and accessible pictures that convey the key ideas. Based on arxiv 2401.10095 (STOC 2024) and arxiv 2410.23618 (STOC 2025)

May 22, 2025

Title: Quantum Convolution: From Theory To Application

Speaker: Kaifeng Bu, Ohio State Univerisity 

Abstract: Convolution plays a crucial role across numerous scientific disciplines, including probability theory, and information theory. In this talk, I will introduce a theoretical framework for quantum convolution within quantum computation. While quantum computation promises to surpass classical computation, the source of this advantage remains a key question. I will also present a method to test and quantify quantum advantage using this quantum convolution.  Based on references: arXiv:2302.07841 (PNAS 2023),2401.12105 (PRL 2025), and 2401.14385(IEEE TIT 2025).

Sept 5, 2024

Title: Hamiltonian simulation for low-energy states with optimal time dependence

Speaker: Alexander Zlokapa, MIT

Abstract: We consider the task of time evolving a state confined to the low-energy subspace of a Hamiltonian. We define a condition on the Hamiltonian that we term "gap-amplifiability", which encompasses all previously considered settings for low-energy simulation. We present an algorithm that achieves an asymptotic improvement over all known algorithms for the low-energy simulation of gap-amplifiable Hamiltonians. Our algorithm has logarithmic dependence on the error and is tight with respect to all other parameters. In the query model, we provide matching lower bounds under common access models; in the gate model, we provide lower bounds that are tight up to logarithmic factors. Finally, in the absence of gap-amplifiability, we show a strengthened version of the no fast-forwarding theorem for quantum simulation: the low-energy property offers no benefit to time evolution in the worst case. Our upper bounds are based on spectral gap amplification and the quantum singular value transform; our query lower bounds use the adversary method for a Grover-like Hamiltonian and the polynomial method; our gate lower bounds use the clock Hamiltonian with a low-energy initial wavepacket.

Sept 12, 2024

Title: Overcomplete Weyl-Heisenberg coherent states: Gabor frame theory

Speaker: Kasso Okoudjou, Tufts University

Abstract: J. von Neumann and D. Gabor independently claimed that any square integrable function can be decomposed into a superposition of space-phase shifts of a gaussian along the unit 2-dimensional lattice. It took a few decades before these claimed were substantiated thereby given rise to the mathematical field of time-frequency analysis. In this talk I will introduce the tenets of this field using the notion of frames. After a brief review of the finite dimensional case, I will survey the theory of Gabor frames on the Hilbert space of square integrable functions and will conclude with some application of the theory to quantum chemistry.

Sept 19, 2024

Title:  Neutral atom quantum processors and the error correction frontier

Speaker: Dolev Bluvstein, Harvard University

Abstract: We will discuss recent advances in quantum information processing using dynamically reconfigurable arrays of neutral atoms. With this platform we have realized programmable quantum processing with encoded logical qubits, combining the use of 280 physical qubits, high two-qubit gate fidelities, arbitrary connectivity, and mid-circuit readout. Using this logical processor with various types of error-correcting codes, we demonstrate that we can improve logical two-qubit gates by increasing code size, outperform physical qubit fidelities, create logical GHZ states, and perform computationally complex quantum simulation of information scrambling. We will show new results exploring trotterized digital implementations of quantum simulation, new theoretical advances enabling large speed-up in error correction using transversal gates and correlated decoding, as well as recent experimental advances enabling deep computation.

Sept 26, 2024

Title: Logical processors and decoders for early fault-tolerant quantum computation

Speaker: Madelyn Cain, Harvard University

Abstract: Quantum error correction is essential to perform reliable quantum computation at scale. Here we report experimental and theoretical progress towards scalable error-corrected computation. First, we realize a programmable quantum processor based on encoded logical qubits, utilizing logical-level hardware-efficient control in reconfigurable neutral atom arrays. Using this logical processor, we demonstrate improvement of a two-qubit logic gate by scaling surface code distance from d=3 to d=7, and realize classically complex sampling circuits on up to 48 logical qubits by co-designing the algorithm with the error correcting code. In performing such algorithms, we observe that the experimental performance can be substantially improved by accounting for error propagation during transversal entangling gates and decoding the logical qubits jointly. We study this correlated decoding technique and find that by tracking the deterministic propagation of stabilizer measurement errors through the circuit, it enables the number of noisy syndrome extraction rounds in transversal Clifford circuits to be reduced from O(d) to O(1), where d is the code distance. We then show that by correctly handling feedforward operations and assuming fast classical decoding, this technique can be used to reduce the spacetime cost of universal computation by a factor of O(d). These results demonstrate that correlated decoding is emerging as a core building block both in new theories of fault-tolerance and in practical reductions to the cost of large-scale computation.

Oct 10, 2024

Title: Algorithmic Fault Tolerance for Fast Quantum Computing

Speaker: Chen Zhao, QuEra

Abstract: Fast, reliable logical operations are essential for the realization of useful quantum computers, as they are required to implement practical quantum algorithms at large scale. By redundantly encoding logical qubits into many physical qubits and using syndrome measurements to detect and subsequently correct errors, one can achieve very low logical error rates. However, for most practical quantum error correcting (QEC) codes such as the surface code, it is generally believed that due to syndrome extraction errors, multiple extraction rounds — on the order of the code distance d — are required for fault-tolerant computation. We show that contrary to this common belief, fault-tolerant logical operations can be performed with constant time overhead for a broad class of QEC codes, including the surface code with magic state inputs and feed-forward operations, to achieve “algorithmic fault tolerance”. Through the combination of transversal operations and novel strategies for correlated decoding, despite only having access to partial syndrome information, we prove that the deviation from the ideal measurement result distribution can be made exponentially small in the code distance. We supplement this proof with circuit-level simulations in a range of relevant settings, demonstrating the fault tolerance and competitive performance of our approach. Our work sheds new light on the theory of quantum fault tolerance, potentially reducing the space-time cost of practical fault-tolerant quantum computation by orders of magnitude.

Oct 17, 2024

Title:  Experimental estimation of ground state energies on quantum computers

Speaker: Will Kirby, IBM

Abstract: I will discuss results of two recent large-scale experiments performed on superconducting quantum processors, implementing quantum algorithms for estimating ground state energies. The first algorithm, called sampled-based quantum diagonalization, is adapted to Hamiltonians where the number of terms makes expectation value estimation impractical, but where sparse proxies for ground states can be prepared using a quantum circuit. The second algorithm, called Krylov quantum diagonalization, is adapted to Hamiltonians where approximate time-evolutions can be implemented using low-depth circuits. These form complementary approaches to the problem of ground state energy estimation on noisy quantum processors.

Oct 24, 2024

Title: pyLIQTR: A Tool for Quantum Computing Applications in Physical Science

Speaker: Kevin Obenland, MIT Lincoln Laboratory

Abstract: Quantum computing provides a fundamentally new capability that has the promise of accelerating the development of applications in physical science. These applications include quantum chemistry, condensed matter systems, and high-energy-density physics, among others. In order to assess the capabilities of quantum computing for these applications, we must identify specific problems and parameter regimes, develop workflows that leverage quantum computing algorithms, and assess the resources required by quantum computing implementations used in the workflows. As part of the DARPA Quantum Benchmarking program, MIT Lincoln Laboratory is actively developing a tool called pyLIQTR, which provides implementations of important quantum kernels used in the workflows of applications in physical science. With the implementations provided by our tool, one can measure the quantum resources for applications at utility scale. In this talk, I will describe the pyLIQTR tool and show resource analysis results for problems that include local and periodic quantum chemistry, the Fermi-Hubbard model, and plasma physics.

Oct 31, 2024

Title: Halving the Cost of Quantum Algorithms with Randomization

Speaker: John Martyn, MIT

Abstract: Quantum signal processing (QSP) provides a systematic framework for implementing a polynomial transformation of a linear operator, and unifies nearly all known quantum algorithms. In parallel, recent works have developed \emph{randomized compiling}, a technique that promotes a unitary gate to a quantum channel and enables a quadratic suppression of error (i.e., $\epsilon \rightarrow O(\epsilon^2)$) at little to no overhead. Here we integrate randomized compiling into QSP through \emph{Stochastic Quantum Signal Processing}. Our algorithm implements a probabilistic mixture of polynomials, strategically chosen so that the average evolution converges to that of a target function, with an error quadratically smaller than that of an equivalent individual polynomial. Because nearly all QSP-based algorithms exhibit query complexities scaling as $O(\log(1/\epsilon))$---stemming from a result in functional analysis---this error suppression reduces their query complexity by a factor that asymptotically approaches $1/2$. By the unifying capabilities of QSP, this reduction extends broadly to quantum algorithms, which we demonstrate on algorithms for real and imaginary time evolution, phase estimation, ground state preparation, and matrix inversion.

Nov 7, 2024

Title: Carleman embedding for the quantum simulation of fluids

Speaker: Sauro Succi, Fondazione Istituto Italiano di Tecnologia Center for Life Nano-Neuroscience at la Sapienza

Abstract:  In the last few years, significant work has been devoted to the explo- ration of the potential of quantum computing for classical physics prob- lems, most notably fluid turbulence and nonlinear transport phenomena. This is a challenge on top of a challenge because unlike quantum me- chanics, the physics of fluids is typically neither linear nor conservative. After a brief introduction to the quantum simulation of fluids in general, we shall focus on a specific technique known as Carleman linearization, as applied to three distinct formulations of the physics of fluids, namely the Navier-Stokes equations, the Lattice Boltzmann method and Grad’s generalised hydrodynamics. The merits and pitfalls of the corresponding quantum algorithms and their concrete quantum circuit implementation will be discussed and commented on. As time allows, we will argue that even in case quantum computing for classical physics would turn out into a ”mission impossible”, there are still useful lessons to be learned along the way.

Nov 14, 2024

Title: Revisiting quantum phase estimation

Speaker: Sukin(Dylan) Sim, Psi Quantum

Abstract: Quantum phase estimation (QPE) is an important subroutine in many quantum algorithms and applications. QPE has been investigated and improved from various disciplines including quantum algorithms, metrology, and signal processing. In this talk, we show how QPE can be viewed as a signal processing problem for resolving peaks in the frequency domain after preparing a windowed signal in the phase register and transforming the signal via the inverse Quantum Fourier transform. Using this perspective, one can more easily understand and visualize effects of having insufficient bits of precision, imperfectly preparing the base unitary or eigenstate, as well as methods to remedy these sources of error. We use a simple yet rich toy model to numerically verify several improvements to QPE, including the use of bidirectional phase kickback and qubitization.

Nov 21, 2024

Title: Hybrid Oscillator-Qubit Quantum Processors: Simulating Fermions, Bosons, and Gauge Fields

Speaker: Eleanor Crane, MIT

Abstract: We develop a hybrid oscillator-qubit processor framework for quantum simulation of strongly correlated fermions and bosons that avoids the boson-to-qubit mapping overhead encountered in qubit hardware. This framework gives exact decompositions of particle interactions such as density-density terms and gauge-invariant hopping, as well as approximate methods based on the Baker-Campbell Hausdorff formulas including the magnetic field term for the U(1) quantum link model in (2+1) D. We use this framework to show how to simulate dynamics using Trotterisation, perform ancilla-free partial error detection using Gauss's law, measure non-local observables, estimate ground state energies using a oscillator-qubit variational quantum eigensolver as well as quantum signal processing, and we numerically study the influence of hardware errors in circuit QED experiments. To show the advantages over all-qubit hardware, we perform an end-to-end comparison of the gate complexity for the gauge-invariant hopping term and find an improvement of the asymptotic scaling with the boson number cutoff S from O(log(S)^2) to O(1) in our framework as well as, for bosonic matter, a constant factor improvement of better than 10^4 We also find an improvement from O(log(S)) to O(1) for the U(1) magnetic field term. While our work focusses on an implementation in superconducting hardware, our framework can also be used in trapped ion, and neutral atom hardware. This work establishes digital quantum simulation with hybrid oscillator-qubit hardware as a viable and advantageous method for the study of qubit-boson models in materials science, chemistry, and high-energy physics.  (arXiv:2409.03747)

Dec 5, 2024

Title: Building the Tools to Program a Quantum Computer

Speaker: Charles Yuan, MIT

Abstract: Bringing the promise of quantum computation into reality requires not only building a quantum computer but also correctly programming it to run a quantum algorithm. To obtain asymptotic advantage over classical algorithms, quantum algorithms rely on the ability of data in quantum superposition to exhibit phenomena such as interference and entanglement. In turn, an implementation of the algorithm as a program must correctly orchestrate these phenomena in the states of qubits. Otherwise, the algorithm would yield incorrect outputs or lose its computational advantage.

Given a quantum algorithm, what are the challenges and costs to realizing it as an executable program? In this talk, I answer this question by showing how basic programming abstractions – such as data structures and control flow – upon which many quantum algorithms rely can fail to work correctly or efficiently on a quantum computer. I then show how we can leverage insights from programming languages to re-invent these abstractions to meet the demands of quantum algorithms. This approach holds out a promise of expressive and efficient tools to program a quantum computer and practically realize its computational advantage.

Talks:

June 20, 2024

Title: Classifying One-Dimensional Quantum States Prepared by a Single Round of Measurements

Speaker: Rahul Sahay, Harvard University

Abstract: Measurements and feedback have emerged as powerful resources for creating many-body quantum states. However, a detailed understanding of what is possible is restricted to fixed-point representatives of phases of matter. In this talk, we go beyond this, characterizing more general patterns of many-body entanglement that can be deterministically created from measurement. Focusing on 1D, a framework is developed for the case where a single round of measurements is the only entangling operation. We show this creates matrix product states and identify necessary and sufficient tensor conditions for preparability, which uniquely determine the preparation protocol. We use these conditions to both classify preparable quantum states and characterize their physical constraints. Intriguingly, we find a trade-off between the richness of the preparable entanglement spectrum and correlation functions, naturally implying a powerful no-go theorem for preparing certain quantum states. Moreover, we connect properties of the preparation protocol to the resulting phase of matter. At a high level, our work offers a resource-theoretic perspective on preparable quantum entanglement and shows how to systematically create states of matter, away from their fixed points, in quantum devices. This is based on two recent works with Ruben Verresen [arXiv:2404.17087; arXiv:2404.16753].

June 6, 2024

Title: Functional quantum algorithms: a mélange of methods for matrix functions

Speaker: Zane Rossi, MIT

Abstract: The study of quantum algorithms is stymied by a lack of human intuition-many of these algorithms appear to rely on non-intuitive attributes unique to quantum mechanics, and as such 'good' quantum algorithms are often sporadic, requiring bespoke analysis. The quantum algorithmist is up against a triple headwind: they must (1) be delusion-hardened against non-generalizing classical heuristics, (2) have understanding of disparate classical algorithms with which to compare their work, and (3) do this all largely without access the high-level programming abstractions ubiquitous in classical computer science for over seventy years.

A partial remedy for these problems has emerged with the development of a new class of quantum algorithms, quantum signal processing (QSP) and quantum singular value transformation (QSVT), which have had success in unifying, simplifying, and improving most known quantum algorithms. QSP/QSVT transform the spectrum of linear operators encoded in unitary processes by near arbitrary continuous functions, and this simple ability-computing matrix functions quantum mechanically-has been shown to subsume diverse tasks with comparatively simple complexity analysis.

This work claims and provides a series of constructions supporting that QSP and QSVT should not be viewed solely as subroutines for transforming linear systems, but as limited examples among an extensive class of quantum algorithms converting algorithmic problems to simpler algebraic ones. We construct an array of algorithms in this class, which we call 'functional quantum algorithms', and show they ought to and can be manipulated and combined purely at the level of this algebraic reduction to constitute useful, composite quantum algorithms.

We emphasize three constructions (among a collection of auxiliary results), ordered by complexity: (a) a limited extension of QSP/QSVT-like circuit ansätze to the multivariable matrix function setting, (b) a construction of recursively composable univariate QSP/QSVT-like subroutines, and (c) a construction of modular quantum subroutines (gadgets) that can approximate generic multivariable continuous matrix functions. We provide necessary and sufficient conditions under which these algorithms can be analyzed and combined functionally, i.e., purely at the level of the scalar transformations applied, and show these assertions require significant doing given our constructions' violation of basic assumptions of standard QSP and QSVT, necessitating alternative proof techniques and quantum subroutines of independent interest. We also show how our results situate functional quantum algorithms among existing constructions of classical functional programming, identifying our constructions as instances of monads, suggesting concrete directions for high-level, flexible quantum algorithmic design and analysis.

May 30, 2024

Title: Bounding Trotter Error in the Context of Quantum Phase Estimation

Speaker: William Simon, Tufts University 

Abstract: Trotterization refers to a group of techniques for constructing quantum circuits that approximate the time-evolution operator of a particular Hamiltonian. One application of these Trotterized time-evolution operators is to implement the Quantum Phase Estimation (QPE) algorithm and estimate the eigenvalues of the underlying Hamiltonian. As the magnitude of the Trotter error scales, the quantum resources needed to compensate for this error in QPE must also grow. In this talk, I will give an overview of how Trotterized time-evolution operators are used in the context of QPE and discuss standard, state-independent bounds on the Trotter error. I will also introduce state-dependent error bounds and discuss what happens when the initial quantum state is close to the target eigenstate. Finally, I will introduce an efficient quantum algorithm for estimating these state-dependent error bounds on any initial state and discuss the implications of these bounds on the associated quantum resource estimates for running QPE.

May 23, 2024

Title: Tensile-strained self-assembly: Nanoscale stretching for novel quantum light sources

Speaker: Paul Simmonds, Tufts University

Abstract: Since the early 1990s, self-assembled quantum dots (QDs) have been the subject of intensive research for technologies ranging from high-stability lasers, to intermediate band solar cells. Driven by compressive strain, semiconductor QDs form spontaneously on the (001) surfaces of both III-V and group IV materials. However, QDs grown on non-(001) surfaces, and QDs grown under tensile rather than compressive strain, are becoming increasingly desirable for a variety of applications. The low fine-structure splitting of (111) QDs should make them ideal entangled photon sources; tensile-strained QDs would have dramatically reduced semiconductor band gaps, with implications for infrared optoelectronics and nanoscale band structure engineering. The issue is however, that until recently it has been enormously challenging to synthesize QDs on non-(001) surfaces, or under tensile strain, that are free from crystallographic defects. I will discuss a robust approach to QD self-assembly that overcomes these difficulties, and explain how using molecular beam epitaxy we can reliably and controllably grow defect-free, tensile-strained QDs on (111) surfaces. I will describe the application of tensile-strained self-assembly to several different material systems, and discuss data confirming the promising properties of these novel QDs for use as deterministic single- and entangled-photon light sources. Our results indicate that tensile-strained self-assembly represents a powerful new tool for the synthesis of highly symmetric QDs and the development of novel quantum materials.

May 16, 2024

Title: Quantum simulation of quantum field theory on the light-front

Speaker: Peter Love, Tufts University

Abstract: Quantum simulation is a leading future application of quantum computation. Quantum field theory poses novel challenges because of the need to regulate and renormalize the theories in order to extract physically meaningful results. Quantum simulation algorithms also require a Hamiltonian formulation of the theory. Dirac showed that relativistic theories admit three Hamiltonian formulations. The equal time formulation is commonly used for quantum field theory, whereas the front form offers several advantages for the computation of properties of composite particles. In this talk I will review work on quantum simulation of quantum field theory in the light front formulation, including questions of renormalization, simulation of scattering processes and quantum resources on the light front.

May 9, 2024

Title: The Space Below BQP

Speaker: Saeed Mehraban, Tufts University

Abstract: I will give an overview of models of quantum computing intermediate between classical polynomial time (BPP) and quantum polynomial time (BQP) and describe connections with near-term implementations of quantum computers.

May 2, 2024

Title: Intentionally Designing Models for Learning Tasks with Quantum Mechanics

Speaker: Kaitlin Gili, University of Oxford

Abstract: Classical generative machine learning research now extends far beyond general neural networks, we have models designed with specific features (focused attention, flexible sequencing, etc.) that are intentionally useful for correspondingly relevant learning tasks. In this seminar talk, the speaker will begin with a brief overview of how quantum computation has led to an exciting new set of features for designing generative models, emphasizing that these features should be utilized with intention to help researchers obtain a better understanding of how quantum is useful and for what specific learning tasks. She will walk through an example of an investigation that utilizes such an approach, demonstrating her latest results on how we can use the quantum feature of non-commutativity measurements of a quantum system generating different results when taken in a different order to design a model that can learn order effects in human psychology datasets. She will conclude with insights for conducting future research in quantum generative learning, specifically how we can combine theoretical knowledge from the fields of quantum foundations and quantum cognition to build generative models for learning tasks where classical methods are not currently excelling.

April 25, 2024

Title: Linear Combination of Unitary, How Widely Can We Use it?

Speaker: Sultana Hadi, Tufts University

Abstract: I will discuss the block encoding method which probabilistically implements a linear combination of unitary. The nature of the probabilistic method leads to using the oblivious amplitude amplification (OAA) method to increase the success probability. However, things are not that simple, and the question is to explore how close the linear combination of unitary should be for OAA to be workable.

April 18, 2024

No meeting.

April 11, 2024

Title: Calculating Energies in the Contextual Subspace

Speaker: Alexis Ralli, Tufts University

The contextual subspace variational quantum eigensolver (CS-VQE) is a hybrid quantum-classical algorithm that approximates the ground-state energy of a given qubit Hamiltonian. It achieves this by separating the Hamiltonian into contextual and noncontextual parts. The ground-state energy is approximated by classically solving the noncontextual problem, followed by solving the contextual problem using VQE, constrained by the noncontextual solution. In general, computation of the contextual correction needs fewer qubits and measurements compared with solving the full Hamiltonian via traditional VQE. We showcase the CS-VQE algorithm and present different improvements to the method.

April 4, 2024

Title: What is Quantum Noise?

Speaker: Oliver Maupin, Tufts University

Abstract: Quantum noise is the largest obstacle in the field of quantum computing. But what is noise? Why is it bad for quantum circuits? What physical mechanisms cause noise in today's NISQ devices? In this talk I will answer these questions as I present an overview of quantum noise as it impacts the results of quantum algorithms. We will cover some ways to quantify noise using quality metrics, how we can model noise at the circuit level using noise channels, and how we can differentiate between stochastic and coherent noise.