Research on Quantum Algorithms
at the Institute for Quantum Information and Matter
J. Preskill, L. Schulman, Caltech
preskill@caltech.edu / www.iqim.caltech.edu/
Objective
• Improved rigorous estimates of thresholds for
fault-tolerant quantum computation.
• Quantum algorithms beyond the hidden
subgroup paradigm.
• Quantum and classical simulation methods for
quantum many-body systems.
• New approaches to physically robust quantum
computation.
Objective Approach
• Quantum algorithms for simulating local quantum
systems.
• Novel applications of the quantum Fourier
transform and other transforms.
• Customizing quantum fault tolerance for physically
motivated noise models.
• Schemes for physically robust quantum storage and
processing.
• Characterizing Hamiltonian complexity.
• Quantum-resistant classical cryptography.
Magic state distillation with low overhead.
Status
• Quantum circuit obfuscation schemes based on the
connections between quantum circuits and braids.
• Proposed quantum-resistant cryptosystem based on
hardness of solving systems of quadratic equations.
• Efficient magic-state distillation protocol using a
new class of triorthogonal quantum codes.
• Scheme for performing protected quantum gates
based on a continuous-variable quantum codes.
• Sufficient condition on noise correlations for
scalable quantum computing.
Research on Quantum Algorithms
at the Institute for Quantum Information and Matter
J. Preskill, L. Schulman, Caltech
preskill@caltech.edu / www.iqim.caltech.edu/
• Progress on last year’s objectives – FY12-13
- Quantum algorithms for simulating particle collisions in fermionic quantum field theories.
- Proposed quantum-resistant cryptosystem based on hardness of solving systems of quadratic equations.
- Quantum circuit obfuscation schemes based on the connections between quantum circuits and braids.
- Efficient magic-state distillation protocol using a new class of triorthogonal quantum codes.
- Efficient algorithm for testing stability of two-dimensional tensor-network states vs. local perturbations.
- Scheme for performing protected quantum gates based on a continuous-variable quantum codes.
- Sufficient condition on noise correlations for scalable quantum computing.
- Near-optimal dynamical decoupling schemes for multi-level quantum systems.
- New class of highly entangled many-body states which can be efficiently simulated.
• Research plan for the next 12 months – FY13-14
-
Quantum algorithms for simulating quantum field theories with gauge fields and massless particles.
Quantum algorithms for simulating thermalization of quantum systems.
Quantum algorithms for interpolating band-limited functions on continuous groups.
Renormalization group analysis of three-dimensional topological quantum codes.
Probability distributions that can be sampled efficiently quantumly but not classically.
Structurally inhomogeneous tensor network states for strongly disordered systems.
• Long term objectives
- Bring large-scale quantum computers closer to realization by proposing and analyzing new schemes for
protecting quantum systems from noise.
- Conceive, develop, and analyze new applications of quantum computing to physics and mathematics.
Research on Quantum Algorithms at the IQIM
Faculty:
John Preskill
Alexei Kitaev
Leonard Schulman
Gil Refael
Faculty Associates:
Todd Brun
Daniel Lidar
Steven van Enk
Kirill Shtengel
Sandy Irani
Postdocs:
Gorjan Alagic
Glen Evenbly
Alexey Gorshkov
→ NIST
Zhengcheng Gu
→ Perimeter
Students:
Michael Beverland
Peter Brooks → HRL
Bill Fefferman
Jeongwan Haah → MIT
Isaac Kim → Perimeter
Alex Kubica
Shaun Maguire
Evgeny Mozgunov
Sujeet Shukla
Undergrads (4 in 2012, 3 in 2013)
Nate Lindner
→ Technion
Spiros Michalakis
Fernando Pastawski
Ling Wang
Beni Yoshida
Visitors:
Many
Postdocs arriving 2013-14:
Mario Berta (ETH)
Andrew Essin (Colorado)
O. Landon-Cardinal (Sherbrooke)
Kristan Temme (MIT)
Some research themes at the IQIM
• Power of quantum computing. Simulating quantum field theories, preparing
thermal states, obfuscating quantum circuits with braids, quantum-resistant
public key based on multivariate quadratic equations, quantum algorithms for
interpolating band-limited functions on continuous groups, probability
distributions that can be sampled efficiently quantumly but not classically.
•Fault-tolerant quantum computing. Magic-state distillation protocol using
triorthogonal quantum codes, RG analysis of self-correcting quantum memory
in 3D, universal topological quantum computing with realistic materials,
protected gates for superconducting qubits, universal dynamical decoupling,
asymmetric Bacon-Shor codes for protection against biased noise.
• Experiment and implementation. Attractive photons in a quantum nonlinear
mediua, Kitaev honeycomb and other exotic spin models with polar molecules,
realizing fractional Chern insulators with dipolar spins.
• Quantum many-body physics. Classifying locally definable quantum
phases, area law and sub-exponential algorithm for 1D systems, fractional
Majorana fermions at the edges of abelian quantum Hall states, class of highly
entangled many-body states which can be efficiently simulated, structurally
inhomogeneous tensor network states for strongly disordered systems.
Jordan, Lee, Preskill
Quantum algorithms for quantum field theories
-- Feynman diagrams have limited precision,
particularly at strong coupling.
-- Classical lattice methods can compute
static properties, but cannot simulate
dynamics
A quantum computer can simulate particle collisions, even at high energy
and strong coupling, using resources (number of qubits and gates) scaling
polynomially with precision, energy, and number of particles.
-- Estimate errors due to regulating (spatial lattice and approximating
continuous variable fields by qubits).
-- Efficient procedure for preparing (strongly-coupled) vacuum and initial
wave packet states, simulating time evolution, measuring final state.
Does the quantum circuit model capture the
computational power of Nature?
What about quantum gravity?
Simulating quantum field theory
Jordan, Lee, Preskill
Input: a list of incoming particle momenta (particles are actually wave
packets with some momentum spread).
Output: a list of outgoing particle momenta.
Goal is to sample accurately from the distribution of final state particles that
would be produced in a high energy collision in a (strongly coupled) field
theory.
Previous work: Consider a self-coupled scalar field in d = 1, 2, 3, spatial
dimensions. Digitize field at each lattice point using nb qubits, where nb
scales logarithmically with energy and accuracy.
Procedure:
(1) Prepare free field vacuum.
(2) Prepare free field wavepackets.
(3) Adiabatically turn on the coupling constant (t).
(4) Evolve for time T using interacting Hamiltonian H.
(5) Adiabatically turn off coupling
(6) Measure field modes of free theory.
Need to discretize the problem, and keep track of resulting errors.
Simulating fermionic quantum field theory
Jordan, Lee, Preskill
Input: a list of incoming particle momenta (particles are actually wave packets
with some momentum spread).
Output: a list of outgoing particle momenta.
Goal is to sample accurately from the distribution of final state particles that
would be produced in a high energy collision in a (strongly coupled) field
theory.
This year’s work: Consider a self-coupled fermionic field in d = 1 spatial
dimensions (e.g., Gross-Neveu model).
Procedure:
(1) Prepare uncoupled fermion modes.
(2) Adiabatically turn on nearest neighbor coupling between modes.
(3) Adiabatically turn on the coupling constant (t).
(4) Excite spatially localized wave packets with time-dependent sources.
(5) Measure charge and postselect on detecting one particle.
(6) Evolve for time T using interacting Hamiltonian H.
(7) Nondestructively measure energy and momentum of outgoing particles.
Need to discretize the problem, and keep track of resulting errors.
Simulating fermionic quantum field theory
Jordan, Lee, Preskill
Free fermion vacuum is not Gaussian – prepare it by adiabatically turning on
nearest neighbor coupling between modes.
Fermi minus sign: Use Bravyi-Kitaev encoding at cost O(log L). When a
fermionic gate is applied, relative sign of |0> and |1> depends on occupation
numbers of other modes (e.g. the number of occupied modes to the left of the
given site). We could represent fermion operators as (Jordan-Wigner) nonlocal
string operators at cost O(L), or we could store the partial sums of mode
occupation numbers, but then updates have cost O(L). Better: cleverly choose
partial sums which allow computation of (-1)’s in O(log L) and can be updated
in time O(log L).
Exciting wave packets: Modulate source spatially and temporally to match one
particle states. Make the source weak to avoid creating more than one
particle, but it usually produces nothing. Measure and abort if not particle
created (okay for a collision of a constant number of particles).
Advantage over previous method (in which coupling ramps on after
wavepacket created): works for bound states.
Simulating fermionic quantum field theory
Jordan, Lee, Preskill
Procedure:
(1) Prepare uncoupled fermion modes.
(2) Adiabatically turn on nearest neighbor coupling between modes.
(3) Adiabatically turn on the coupling constant (t).
(4) Excite spatially localized wave packets with time-dependent sources.
(5) Measure charge and postselect on detecting one particle.
(6) Evolve for time T using interacting Hamiltonian H.
(7) Nondestructively measure energy and momentum of outgoing particles.
Need to discretize the problem, and keep track of resulting errors.
Cost is dominated by the adiabatic preparation of the vacuum. Adiabaticity
enforces turn-on time
T  O 1/ a 4ò



where a is the lattice spacing and is the error. Using a high
G  O (TL / a )1 o (1)
-order Trotter approximation, the number of gates needed is:
The error due to nonzero lattice spacing scales as ~ a, hence cost scales with
error as
G  O (1/ ò)6 o (1)
(seems pessimistic)



Simulating quantum field theory
Future plans:
Massless particles (infrared safe observables).
Gauge fields (start with strong coupling limit).
Ground state preparation by cooling.
Nonzero temperature and chemical potential.
Simulate standard model of particle physics in BQP.
Quantum gravity?
Obfuscation
G. Alagic,
T. Jeffery,
S. Jordan
Take a circuit C and produce another circuit O(C), so that:
1. functionality is preserved;
2. size is not much bigger (say polynomial);
3. it’s hard to “reverse-engineer” O(C) (at a minimum, O(C) -> C is hard).
Can we have an algorithm that does this for all circuits?
State of affairs in research
– lots of motivation (software/hardware copy protection, homomorphic
encryption, turning private key schemes into public key schemes, etc.)
– known formalizations of (3) are all too hard:
• O(C) no more useful than a black box that performs C?
(impossible, Barak et al ’01)
• O(C1) indistinguishable from O(C2) for equivalent C1, C2?
(collapses PH, Goldwasser Rothblum ’07)
– little is known about quantum obfuscation
• are there classical algorithms for obfuscating quantum circuits?
• are there quantum states that allow us to do obfuscated computation?
Quantum Obfuscation
1.
2.
G. Alagic,
T. Jeffery,
S. Jordan
What if we ask for a slightly weaker condition (3)?
Can we obfuscate quantum circuits?
Results [Alagic Jeffery Jordan ’13]
– efficient classical algorithms for obfuscating both quantum and
classical circuits
– “weaker” condition 3: indistinguishability under a subset of the set of
all circuit relations
Core idea
– if we had an efficient canonical form for circuits (a coNP-hard
problem), we would satisfy Goldwasser-Rothblum trivially
– but topological quantum computation gives us a pretty good mapping
quantum circuits
braids
and braids do have efficient canonical forms!
– in fact, this mapping exists for classical reversible circuits too, if we
use a different representation of the braid group
– If Bob claims to have a quantum computer, Alice can propose that Bob
execute a quantum circuit that obfuscates a classical circuit, where
Alice can easily check the answer.
Approximation theory on groups
G. Alagic,
A. Russell,
L. Schulman
The Discrete Fourier Transform (DFT)
– basis of countless proofs, algorithms, signal processing tasks, etc.
– the fast classical (FFT) algorithms for computing the DFT are very useful in
practice
– their quantum analogues (QFT) are exponentially faster (in a certain
sense) and are a basis for amazing things like Shor’s algorithm
What if the group is continuous instead of finite (say the circle or SU(2))?
– finitely many sums becomes infinitely many integrals.
– two simplifications: only consider band-limited f (doesn’t oscillate too
much), and sample the function at a nicely spaced finite set of points
– for the circle, this boils down to “discretize and use DFT”
Approximation theory on groups
New feature of continuous case:
We can use Fourier inversion to reconstruct the values of the function anywhere
on the group.
Why study the continuous non-abelian case?
– signals in practice might be continuous instead of discrete
– we care about nonabelian spaces (e.g., spherical harmonics, SU(2))
– we need more quantum-algorithmic primitives for exponential speedups
Results [Alagic Russell Schulman 2013]
– a theorem about reconstructing band-limited functions on compact
groups
• setting: any compact group
• input: random samples of a band-limited function f
• output: the list of Fourier coefficients of f
– a number of samples cubic in the band limit is sufficient for a good
estimate
– the reconstruction is inner-product-preserving in the limit
(Multivariate Quadratic + Code)-Based Cryptosystem
Post-Quantum: honest players are classical and polynomial-time, but
adversary might have a quantum computer.
Adversary knows public key, needs to solve a hard problem to decrypt
(invert a one-way function). Private key provides a trap door for efficient
decryption.
Preferably based on a problem which is (average case) hard. Problem
has structure which enables the trap door, but is hidden from the
adversary.
Preferably a simple scheme, so potential attacks are obvious --- no well
hidden vulnerabilities.
Schulman
Post-quantum cryptography
Number theoretic (abelian hidden subgroup problems): vulnerable to
quantum attacks. RSA, elliptic curve, Diffie-Hellman, etc.
Lattice cryptosystems: based on hardness of shortest/closest vector
problems. Worst-case to average case reduction.
Reduce to dihedral (nonabelian) hidden subgroup. Reasons for concern:
-- Single-register coset measurements info. theoretically sufficient.
-- Kuperberg algorithm: Time 2O ( n )
McEliece: based on hardness of decoding general linear EC codes.
Public key C = M G P
G generates linear code, M is random matrix, P is random permutation.
Encode v as vC + correctable errors (weight t).
Code is efficiently decodable, and has to be carefully chosen.
New proposal: a code-based scheme in which the scrambled code is not
public.
Schulman
(Multivariate Quadratic + Code)-Based Cryptosystem
Public: three-index 2N
2N
L binary tensor
Tijl   k Rijk Ckl  ail b jl
R is random 2N 2N K binary tensor , {a, b} are 2L random length-(2N)
vectors, and C is generator of a scrambled length-L efficiently decodable
linear code, which can correct most errors of weight for some > ¼ L.
Clear text: Length-N binary string x.
Encrypted text: Length-L binary string y (L > 8N). Append length-N r, s to x.


yl  ij ( xr )i ( xs ) j   Rijk Ckl  ail b jl   yl(code)  yl(error)
 k

where yl(error))=1 with probability ¼ (product of two random bits).
Decryption: Decode to find yl(error)). Each l for which yl(error))=1 provides linear
equations for xr and xs. 2N such equations suffice (hence L > 8N).
Security: Here the scrambled code is hidden by the noise. (Known attacks on
McEliece use the publicly known scrambled code.) Adversary needs to solve a
random system of quadratic equations to find x, if unable to infer structure of
the public tensor T. To ensure hardness of tensor decomposition, dual of C
should have positive fractional distance.
Schulman
(Multivariate Quadratic + Code)-Based Cryptosystem
-- Codes with the desired properties are not known.
-- One way around this is to use higher-order tensors; e.g. with
an 4-index tensor we can reduce the correctable error rate of C
to 1/8 (still requiring the dual to have positive fractional
distance), and then minimum distance decoding is feasible
(but still no known codes). With an 7-index tensor the
correctable error rate becomes 1/64, and suitable efficiently
decodable codes have been constructed by Guruswami 2009.
-- That means a larger public key, but the key size can be
reduced somewhat by linearly hashing down the extra
dimensions until their size is proportional to the security
parameter.
-- Basing security on the hardness of tensor decomposition is
a new feature in public key cryptography.
Schulman
Protected superconducting qubit
Feigel’man & Ioffe
Doucot & Vidal
Kitaev
Physically robust encodings have been proposed using superconducting
circuits containing Josephson junctions, for example the “0-Pi qubit”. The
circuit’s energy E( ), as a function of the superconducting phase difference
between its leads, is a periodic function with period to an excellent
approximation.
“0-Pi qubit”:
0
E  f (2 )  O  exp  c(size)  
Two states localized near =0 and = are the basis states of a protected
qubit. The barrier is high enough to suppress bit flips, and the stable
degeneracy suppresses phase errors. Protection arises because the
encoding of quantum information is highly nonlocal, and splitting of
degeneracy scales exponentially with size of the device.
Brooks, Kitaev, Preskill
Brooks,
Kitaev,
Preskill
Protected phase gate

  
exp  i Z 
 4 

C
0-Pi qubit
L
L/C
/ (2e) 2  1 k 
0
For reliable quantum computing, we need not just very stable qubits, but
also the ability to apply very accurate nontrivial quantum gates to the
qubits.
Accurate (Clifford group) phase gates can be applied to 0-Pi qubits by
turning on and off the coupling between a qubit (or pair of qubits) and a
harmonic oscillator (an LC circuit whose inductance is large in natural
units). In principle the gate error becomes exponentially small as the
inductance grows.
The reliability of the gate arises from a continuous-variable quantum errorcorrecting code underlying its operation, in which a qubit is embedded in
the infinite-dimensional Hilbert space of a harmonic oscillator. Coupling the
0-Pi qubit to the oscillator sends the oscillator on a state-dependent phase
space excursion during which it acquires a geometric phase that is
protected by the code.
Protected phase gate

  
exp  i Z 
 4 

C
0-Pi qubit
L
L/C
/ (2e) 2  1 k 
0
Switch is really a tunable Josephson junction:
Q2  2
H

 J (t ) cos    
2C 2 L
V()

Under suitable adiabaticity
conditions, closing the switch
transforms a broad oscillator
state (e.g. the ground state)
into a grid state (approximate
codeword).
D

1
Peaks are at even or odd multiples of  depending on whether  is 0 or , i.e. on
whether qubit is 0 or 1. Inner width squared is (JC)-1/2 and outer width is (L/C)1/2
J1  C / J
switching time
 1  LC
1
 L / C   80
1/2
JC
  8
1/2
 J / C  80
| C
Perror
( )
calculable contribution to
error due to diabatic effects
and Q-space spreading
Large inductance
The intrinsic error scales like
Is


exp -(1/4) L / C .
L / C  80 reasonable?
Manucharyan et al. 2009, Masluk et al. 2012, Bell et al. 2012 achieved
~ 20 with a chains of Josephson junctions. The inductance scales
linearly with the length of the chain, but there are potential obstacles to
building very long chains. Another possible approach is to exploit the
large (kinetic) inductance in amorphous superconductors.
What about universal quantum computation and measurement?
-- If we can prepare and measure in the basis |0 ± |1, a noisy /4
single-qubit phase gate (F > .93), augmented by state distillation,
suffices for fault-tolerant universality (Bravyi & Kitaev 2005).
-- It is also okay if measurements are noisier than gates, as we can
protect measurements using repetition (or coding)
-- So if we can really do a two-qubit phase gate with high fidelity, that’s
worth a lot!

Bravyi, Haah
Magic State Distillation with Improved Overhead
-- In typical protocols for fault-tolerant quantum computing based on
stabilizer codes, Clifford operations (e.g. CNOT gates and 90 degree
single-qubit rotations) have relatively low overhead cost.
-- Overhead tends to be dominated by non-Clifford operations, such as 45
degree single-qubit rotations, Toffoli (controlled-controlled-NOT) gates, or
controlled-controlled phase gates.
-- For “magic-state distillation” protocols, we use codes such that the 45
degree rotation T is transversal. Triorthogonal codes admit such transversal
logical gates.
-- For logical non-Clifford gates with error rate , the cost scales like
log (1/ ), and we would like to reduce the exponent .
-- Exponent is = log(r) / log(a) if protocol yields one output copy for each r
input copies, and reduces error from p to O(pa).
-- New family of protocols asymptotically achieves = log(3) / log(2) ~ 1.6.
Best previous protocol had been = log(5) / log(2) ~ 2.3.
Triorthogonal matrix
• A binary matrix where any pair of rows has even
overlap and so does any triple.
• E.g.
• Even-weight rows shown in bold.
• Number of odd-weight rows determines number k
of encoded qubits in corresponding CSS code.
• Family of codes with length n = 3k + 8.
• Codes have distance d = 2.
Magic state distillation
Decoder
Postselect 0-synd.
X-syndrome Meas.
Designed Clifford
Encoder
By a stabilizer code based on “triorthogonal matrices”
Noisy magic states are represented by a stochastic application of Z-rotation
Distills Pi/8-rotation magic state
Distillation cost improved
• Using a new explicit family of triorthogonal matrices G(k),
• Error rate improves as
• Avg. # of input states to reach a target error rate is
• Numerical optimization, combining various protocols.
At Target error rate 10-12:
-- 2-fold improvement
from Meier-Eastin-Knill (1204.4221)
-- 10-fold improvement
from (original) Bravyi-Kitaev (2004)
In plot, upper curve is Meier et al.
Lower curve is new protocol.
Haah
Entanglement Renormalization
• Local unitary transformation,
– On nearest neighbors
• factoring out trivial degrees of freedom.
• Understand “long-range entanglement”
Laurent polynomial representation
of stabilizer code Hamiltonians
•
•
•
•
Local unitary = row operation
Trivial qubit = presence of sole 1 in a column
Coarse-graining = matrix expansion
Toric code maps to self in a coarse-graining step
Cubic code
• Cubic code factorizes to itself plus another.
23
23
Coarse-graining step:
A
B
A+B
B+B
The other factorizes
into two copies of
itself.
(X-type stabilizers are
shown.)
Branching MERA
Evenbly, Vidal (1210.1895)
•
•
•
•
Several branches in MERA
Proposed to described highly entangled critical systems.
Cubic code, a gapped spin model, turns out to fit.
Area law holds still, for being in 3D.
Highly entangled quantum circuits (arXiv:1210.1895)
t
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
0
0
0
1
Block entanglement
entropy scaling
2
2
3
3
T  
T
L
𝑆𝐿 ≈ 𝐿
scales as the bulk
of the block!
Minimal Updates in Holography (arXiv:1307.0831)
local change in
Hamiltonian
(D+1) – dimensional holographic
description of its ground state
H
IR
H

z
D – dimensional
Hamiltonian
UV
H
Minimal Updates
new ground
state

modified
Hamiltonian
R
H  H  HR
localized change in
holographic description
of ground state


If we use a matrix-product
state description, then a local
change in the Hamiltonian
may require us to modify
tensors far away. With a
holographic description, we
need only modify the tensors
within a causal code of
bounded width.
Evenbly
Tensor network states for disordered systems
Evenbly
Kitaev
An area law and sub-exponential algorithm for 1D systems (Arad, Kitaev,
Landau, Varzirani). Entanglement entropy of gapped 1D system scales
linearly with reciprocol of spectal gap. An algorithm for approximating the
ground state which runs in subexponential time.
Finding the group of units in algebraic number rings of arbitrary degree (in
progress, Eisentraeger, Hallgren, and Kitaev). Toward a uniformly
polynomial algorithm that finds the period of a function on G = Rq for any q.
Classifying locally definable quantum phases of matter (Kitaev). A
definition of quantum phases with short-range entanglement, and a
proposed topological classification of all such phases in any dimension.
Research on Quantum Algorithms
at the Institute for Quantum Information
J. Preskill, A. Kitaev, L. Schulman, Caltech
preskill@caltech.edu / www.iqi.caltech.edu/
• Progress on last year’s objectives – FY11-12
- Quantum algorithms for simulating particle collisions in strongly-coupled quantum field theories.
- Proposed trap-door one-way functions based on tensor problems.
- Quantum algorithms for approximating invariants of triangulated manifolds by tensor contraction.
- Classical certificates for frustration-free ground states of commuting Hamiltonians on square lattices.
- Estimating fidelity using a number of Pauli operator expectation values independent of system size.
- Enhanced memory time for three-dimensional quantum memories without string operators.
- Performance analysis for fault-tolerant quantum computing based on asymmetric Bacon-Shor codes.
- Nonlocal order parameters for symmetry-protected phases in one dimension.
- Studies of resonating valence bond (RVB) states using the PEPS formalism.
• Research plan for the next 12 months – FY12-13
-
Extend algorithms for simulating quantum field theories to fermions, gauge fields, massless particles.
Quantum algorithms for preparing the Gibbs states of local quantum systems at nonzero temperature.
Develop efficient band-limited quantum Fourier transforms over Lie groups.
Quantum circuit obfuscation schemes based on the connections between quantum circuits and braids.
Near-optimal dynamical decoupling schemes for multi-level quantum systems.
Classification of phases for “locally definable” quantum systems in arbitrary dimensions.
• Long term objectives
- Bring large-scale quantum computers closer to realization by proposing and analyzing new schemes for
protecting quantum systems from noise.
- Conceive, develop, and analyze new applications of quantum computing to physics and mathematics.
Research on Quantum Algorithms
at the Institute for Quantum Information and Matter
J. Preskill, L. Schulman, Caltech
preskill@caltech.edu / www.iqim.caltech.edu/
• Progress on last year’s objectives – FY12-13
- Quantum algorithms for simulating particle collisions in fermionic quantum field theories.
- Proposed quantum-resistant cryptosystem based on hardness of solving systems of quadratic equations.
- Quantum circuit obfuscation schemes based on the connections between quantum circuits and braids.
- Efficient magic-state distillation protocol using a new class of triorthogonal quantum codes.
- Efficient algorithm for testing stability of two-dimensional tensor-network states vs. local perturbations.
- Scheme for performing protected quantum gates based on a continuous-variable quantum codes.
- Sufficient condition on noise correlations for scalable quantum computing.
- Near-optimal dynamical decoupling schemes for multi-level quantum systems.
- New class of highly entangled many-body states which can be efficiently simulated.
• Research plan for the next 12 months – FY13-14
-
Quantum algorithms for simulating quantum field theories with gauge fields and massless particles.
Quantum algorithms for simulating thermalization of quantum systems.
Quantum algorithms for interpolating band-limited functions on continuous groups.
Renormalization group analysis of three-dimensional topological quantum codes.
Probability distributions that can be sampled efficiently quantumly but not classically.
Structurally inhomogeneous tensor network states for strongly disordered systems.
• Long term objectives
- Bring large-scale quantum computers closer to realization by proposing and analyzing new schemes for
protecting quantum systems from noise.
- Conceive, develop, and analyze new applications of quantum computing to physics and mathematics.